Shuanglin shao

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.

Shao 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.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.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. Shuanglin Shao is a professor in the Mathematics department at University of Kansas - see what their students are saying about them or leave a rating yourself.Associate Professor, Acting Associate Chair and Director of Undergraduate Studies, Spring 2024BEPC-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 ...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. Associate Professor; View full profile . 405 Snow Hall 1460 Jayhawk Blvd. Lawrence, KS 66045 [email protected] 785-864-3651. facebook instagram twitter ...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 ...Cite this article. Shuanglin Shao, Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case.Rev. Mat. Iberoam. 25 (2009), no. 3, pp. 1127–1168Shao 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'DellShuanglin Shao (University of Kansas) On smoothness of extremizers to an adjoint Fourier restriction inequality on S^2. Abstract. Tuesday, October 16, 4:00 p.m., VV B139. Laurent Stolovitch (University of Nice - Sophia Antipolis) Normal forms of analytic perturbations of quasihomogeneous vector fields Abstract.2.1.3 Multiscale receptive fields. The lack of details in depth maps has always been a difficulty for unsupervised monocular depth estimation. The reason is that in the theory of deep convolutional neural networks, the perceptual field of the network gradually increases with the number of layers of the network, Zhou [] founds that the network’s …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.

Mar 1, 2012 · Shuanglin Shao. Mathematics. 2007; For cylindrically symmetric functions dyadically supported on the paraboloid, we obtain a family of sharp linear and bilinear ... 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.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 (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 ...

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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 ...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 ... 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.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;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 areFall 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.

Shuanglin Shao (University of Kansas) On smoothness of extremizers to an adjoint Fourier restriction inequality on S^2. Abstract. Tuesday, October 16, 4:00 p.m., VV B139. Laurent Stolovitch (University of Nice - Sophia Antipolis) Normal forms of analytic perturbations of quasihomogeneous vector fields Abstract.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.Jan 1, 2010 · Shuanglin Shao (Institute for Mathematics and its Applications, University of Minnesota, Minneapolis) Yifei Wu (Department of Mathematics, South China University of Technology, Guangzhou, Guangdong, China) Guixiang Xu (Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing, China) Keywords See the complete profile on LinkedIn and discover Shuanglin’s connections and jobs at similar companies. View Shuanglin Shao’s profile on LinkedIn, the world’s largest …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 …B. Pausader Shuanglin Shao. Mathematics. 2009; We prove global wellposedness and scattering for the Mass-critical homogeneous fourth-order …Shao 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. Shuanglin Shao · Renming Song · Zhiqiang Cai · Shizan Fang · Hongjun Gao · Jianhua Huang · Peter Kloeden · Jicheng Liu · Xu Sun · Yanbin Tang · Fuke Wu.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 · Renming Song · Zhiqiang Cai · Shizan Fang · Hongjun Gao · Jianhua Huang · Peter Kloeden · Jicheng Liu · Xu Sun · Yanbin Tang · Fuke Wu.Shuanglin Shao In this note, we show that a pair of Gaussian functions are extremisers to a bilinear Strichartz inequality, and unique up to the symmetry group of the inequality. View

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 · 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 ...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 ... Lemma 3.15. (Vitali type covering lemma. ) Let be a collection of open balls in , and let .If , there exist disjoint such that . Proof. The set is open, then for there exists a compact set such that . Since is compact, there exists finitely many balls such that .Let be the collection of the balls. Choose that has the largest radius. Let be the collection of …Shuanglin Shao, Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case, Rev. Mat. Iberoam. 25 (2009), no. 3, 1127–1168. MR 2590695, DOI 10.4171/RMI/591; Shuanglin Shao, A note on the cone restriction conjecture in the cylindrically symmetric case, Proc. Amer. Math. Soc. 137 (2009), no. 1, 135–143.2 ene 2009 ... A restriction theorem for the Fourier transform. Bull. Amer. Math. Soc., 81:477–. 478, 1975. Shuanglin Shao. Department of Mathematics, ...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. 14 jun 2023 ... My PhD advisor was Shuanglin Shao. I received my BFA, BA, and BS at Friends University in Wichita, KS. I also received my MS at Emporia ...

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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¨oindgerShuanglin 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.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.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 (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 ...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.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 ...Yifei WU | Cited by 872 | of Tianjin University, Tianjin (tju) | Read 60 publications | Contact Yifei WUShuanglin 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.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. ... ….

Authors: Shuanglin Shao. Download PDF Abstract: In this note, we show that a pair of Gaussian functions are extremisers to a bilinear Strichartz inequality, and unique up to the symmetry group of the inequality. Comments: 6 pages.Shuanglin Shao: Vol. 2 (2009), No. 1, 83–117 DOI: 10.2140/apde.2009.2.83. Abstract: We establish the linear profile decomposition for the Airy equation with complex or real initial data in L 2. As an application, we obtain a dichotomy result on the existence of maximizers for the symmetric Airy Strichartz inequality. Keywords. gKdV ...In this thesis we are mainly concerned with local wellposedness (LWP) problems for nonlinear evolution equations, two global results will then be a direct consequence of conservation laws. A standard scheme to prove LWP is the application of the contraction mapping principle to the corresponding integral equation in a suitable …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 | …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 extrem...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;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 ...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 PDFShuanglin 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 ...Jun 8, 2009 · 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. Shuanglin shao, [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1]