Shuanglin shao.

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) ...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.Shuanglin Shao (U.C.L.A.) Restriction estimates for Paraboloids in the Cylindrically Symmetric Case In this talk, we will discuss the linear and bilinear restriction estimates for paraboloids when functions are assumed to be cylindrically symmetric. For dyadically supported functions, further estimates are available and sharp up to endpoints ...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, ...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, Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case. Rev. Mat. Iberoam. 25 (2009), no. 3, pp. 1127–1168. DOI 10.4171/RMI/591. Publication Date. 31 December 2009. Identifiers DOI 10.4171/RMI/591. Contact; Legal Notice;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.

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 $\mathbb{R}^2$. We show that the solutions to the associated Euler–Lagrange equation are exponentially decaying in the …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….

12 feb 2021 ... In: arXiv preprint math/9704212 (1997) (cit. on p. 4). [Sha08]. Shuanglin Shao. “Maximizers for the Strichartz inequalities and the Sobolev-.by 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 ... 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 ...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 the

From: Shuanglin Shao 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) [v5] 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 …

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.

Liked by Shuanglin Shao. Education UCLA Ph. D Math. 2004 - 2008. View Shuanglin's full profile See who you know in common Get introduced ...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.... Shuang; Lin, Shao; Hajat, Shakoor; Yang, Lianping; Huang, Cunrui; (2019) The impact of the 2016 flood event in Anhui Province, China on infectious diarrhea ...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; 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 ...We 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 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 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 ...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; 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 ...... shao lin stock pictures, royalty-free photos & images · lian shan shuang lin ...Shuanglin Shao. Associate Professor; Contact Info. [email protected]. 785-864-4762. 627 Snow. Personal Links. Webpage Webpage; Research — Harmonic Analysis ...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 ...

View public records and voter registration of Shuanglin Hao born 1964, includes court and personal records. ... Email: [email protected] . Shuanglin Hao Addresses ...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 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.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-André Martinez, Thierry Ramond and Johannes Sjöstrand: Global existence and uniqueness results for weak solutions of the focusing mass-critical nonlinear Schrödinger equationI 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. Seminars Spring 2022: 5/2-5/6/2022 May 2-May 6 Date: Time: Seminar: Location: Tuesday, 5/3/22: 9:00 am: Final Oral Examination for the PH.D. Degree Combinatorial and Homological Aspects of Monomial Algebras and Numerical SemigroupsAnalysis and Ergodic Theory Summer School, Lake Arrowhead ∗ September 17th - September 22nd 2006 Organizers: Ciprian Demeter, University of California, Los Angelesresearch and teaching related Posted by: Shuanglin Shao| November 5, 2020 Measure and Integration theory, Lecture 15 Theorem 6.17. (Chebyshev’s inequality.) If for , then for …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 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 ...

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.

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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 ... 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 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¨oindger32 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) 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;Home About Select to follow link Department of Mathematics History (1866-1970) EmploymentAug 1, 2013 · 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 Shao (Department of Mathematics, Kansas University, Lawrence, Ks., U.S.A.) Abstract In this paper, we study the extremal problem for the …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.

We establish the linear profile decomposition for the Airy equation with complex or real initial data in L2. As an application, we obtain a dichotomy result on the existence of maximizers for the symmetric Airy Strichartz inequality.Aug 26, 2013 · 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 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 $\norm {\widehat {f\sigma}}_ {L^4}/\norm {f}_ {\lt}$ are smooth; that any ...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;Instagram:https://instagram. osu softball schedule 2022antique pocket knives salekansas basketball schedule 2021ku closing 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 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. lori kennedy tochtropjaden robinson football Shuanglin Shao Rev. Mat. Iberoamericana 25(3): 1127-1168 (October, 2009). ABOUT FIRST PAGE CITED BY REFERENCES DOWNLOAD PAPER SAVE TO MY LIBRARY Abstract. For cylindrically symmetric functions dyadically supported on the paraboloid, we obtain a family of sharp linear and bilinear adjoint restriction estimates. ...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 ... obscurely unclearly crossword clue 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 ...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 ...