Shuanglin shao
Shuanglin shao. 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 ...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.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.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 ...Oct 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 ... 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)864-4762SHUANGLIN 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 (IMA - University of Minnesota) On extremals to the Tomas-Stein inequality for the sphere Abstract. Tuesday, September 14, 4:00 p.m., VV B139. Alexander Nagel (UW Madison) Convolution with flag distributions on homogeneous nilpotent Lie groups Abstract. Tuesday, September 21, 4:00 p.m., VV B139. Andrej Zlatoš (UW Madison)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 ... 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 ...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 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 ...Jun 8, 2009 · DOI: 10.1142/S0219891610002256 Corpus ID: 14454549; THE MASS-CRITICAL FOURTH-ORDER SCHRÖDINGER EQUATION IN HIGH DIMENSIONS @article{Pausader2009THEMF, title={THE MASS-CRITICAL FOURTH-ORDER SCHR{\"O}DINGER EQUATION IN HIGH DIMENSIONS}, author={Benoit Pausader and Shuanglin Shao}, journal={Journal of Hyperbolic Differential Equations}, year={2009}, volume={07}, pages={651-705}, url={https://api ... Shuanglin Shao In this paper, we discuss the properties of one dimensional quantum Zakharov system which describes the nonlinear interaction between the quantum Langmuir and quantum ion-acoustic...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 …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). Dec 9, 2022 · 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, Baker University: 306 Snow 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 ...Smith Colloquium Fall 2022; Date: Speaker, Title: Local Host: October 27: Joseph Auslander Professor Emeritus, University of Maryland The Galois Theory of Minimal FlowsJIN-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.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 (Department of Mathematics, Kansas University, Lawrence, Ks., U.S.A.) Abstract In this paper, we study the extremal problem for the …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.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. The constant in defining the inverse Fourier transform is corrected;the expression of convolution of …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. Shuanglin Shao. Associate Professor. Contact Info.
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· 785-864-4762. 627 Snow. Personal Links. Webpage Webpage. Research —.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's Blog. research and teaching related . Posted by: Shuanglin Shao | December 6, 2009 Kato-smoothing effect “Kato smoothing” “is ” important in dispersive PDE.“Smoothing”, as it stands, sounds like a very good word. But why is it good? How will it be used remains as vague questions to me.Posted by: Shuanglin Shao | August 15, 2020 Lecture 1 This semester we will study the measure theory and integration theory, namely Chapters 1,2,3, and 6 in …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 3.6.1. Introduction. Breast cancer in women has become the most common cancer worldwide. There are an estimated 2.3 million new cases each year, accounting for about 11.7% of all new cancer cases. [] At present, the primary approach to treating breast cancer involves surgical resection of the lesion in conjunction with radiotherapy and …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 ...
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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 ...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). On Marcinkiewicz integral with variable kernels (with Yong Ding and Shuanglin Shao), Indiana Univ. Math. J. 53 (2004), 805-822. Parseval's formula for ...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 (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 ... 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 Semigroups12 dic 2014 ... ... Shao Bin Collection in the National Library, Singapore. Find Out More · Overview. Overview about careers at National Library Board Singapore ...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.6 mar 2023 ... ... Shuanglin Que,. Corresponding Author. Shuanglin Que.
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... Shao, B. (2017). Circular RNA hsa_circ_0021001 in peripheral blood: A ...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”.
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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 ...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. 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.
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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 …
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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 ...Michael Christ and Shuanglin Shao, Existence of extremals for a Fourier restriction inequality, Anal. PDE 5 (2012), no. 2, 261–312. MR 2970708, DOI 10.2140/apde.2012.5.261; Michael Christ and Shuanglin Shao, On the extremizers of an adjoint Fourier restriction inequality, Adv. Math. 230 (2012), no. 3, 957–977. MR 2921167, DOI 10.1016/j.aim ...
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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¨oindgerDec 13, 2018 · 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
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www.math.ku.edu/ ̃slshao Ph.D. Mathematics, University of California, Los Angeles (UCLA), 2008. M.S. Mathematics, Beijing Normal University, 2004.
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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 …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. Authors: Jincheng 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. The only extremal functions are Gaussian …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 Banach function space. In this context the use of a two parameter ...Michael Christ and Shuanglin Shao, Existence of extremals for a Fourier restriction inequality, Anal. PDE 5 (2012), no. 2, 261–312. MR 2970708, DOI 10.2140/apde.2012.5.261; Michael Christ and Shuanglin Shao, On the extremizers of an adjoint Fourier restriction inequality, Adv. Math. 230 (2012), no. 3, 957–977.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 …
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Shuanglin Shao: 306 Snow: Friday, 9/3/21: 10:00am: Graduate Student Probability Seminar Fundamentals of Continuous Stochastic Processes: Zoom ...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 ...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, …
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Christ, 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. 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 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
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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 ...A necessary and sufficient condition on the precompactness of extremal sequences for one-dimensional $$\alpha $$ α -Strichartz inequalities, equivalently $$\alpha $$ α -Fourier extension estimates, is established based on the profile decomposition arguments. One of our main tools is an operator-convergence dislocation property consequence which …Abstract: Unconventional superconductors have Cooper pairs with lower symmetries than in conventional superconductors. In most unconventional superconductors, ...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 (Department of Mathematics, Kansas University, Lawrence, Ks., U.S.A.) Abstract In this paper, we study the extremal problem for the …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 ... Shuanglin Shao Events from this organizer Today Upcoming November 2023 Fri 3 November 3 - November 4 19th Prairie Analysis Seminar Kansas State University, …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 ...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. Associate Professor; Contact Info.
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. 785-864-4762. 627 Snow. Personal Links. Webpage Webpage; Research — Harmonic Analysis ... 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 ...
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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.Michael Christ and Shuanglin Shao, Existence of extremals for a Fourier restriction inequality, Anal. PDE 5 (2012), no. 2, 261–312. MR 2970708, DOI 10.2140/apde.2012.5.261; Michael Christ and Shuanglin Shao, On the extremizers of an adjoint Fourier restriction inequality, Adv. Math. 230 (2012), no. 3, 957–977. MR 2921167, DOI 10.1016/j.aim ...Authors: Jincheng 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. The only extremal functions are Gaussian …From: Shuanglin Shao Mon, 8 Oct 2007 05:42:33 UTC (11 KB) [v2] Fri, 20 Jun 2008 05:30:27 UTC (9 KB) Full-text links: Download: Download a PDF of the paper titled A note on the cone restriction conjecture in the cylindrically symmetric case, by Shuanglin Shao. PDF; PostScript; Other formats Current browse context: ...``Existence of extremals for a Fourier restriction inequality'' (joint work with Shuanglin Shao) Abstract: The Fourier transform maps $ L^2(S^2)$ to $ L^4(R^3)$. We show that there exist functions which extremize the associated inequality, and that any extremizing sequence of nonnegative functions has a convergent subsequence. This was ...
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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:
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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.
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Home About Select to follow link Department of Mathematics History (1866-1970) EmploymentJoint 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. Instructor: Shuanglin Shao Office: Snow Hall 615 Email:
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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. ...BENOIT PAUSADER AND SHUANGLIN SHAO Abstract. We prove global wellposedness and scattering for the Mass-critical homogeneous fourth-order Schro¨dinger equation in …research 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 …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
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Analysis and Ergodic Theory Summer School, Lake Arrowhead ∗ September 17th - September 22nd 2006 Organizers: Ciprian Demeter, University of California, Los AngelesInstructor: Shuanglin Shao Office: Snow Hall 615 Email:
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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. ...JIN-CHENG JIANG AND SHUANGLIN SHAO Abstract. In this paper, we study the extremal problem for the Strichartz inequality for the Schr ̈ odinger equation on the R×R2. We …22 sept 2015 ... Christ, Shuanglin Shao. Mathematics. 2010. The adjoint Fourier restriction inequality of Tomas and Stein states that the mapping $f\mapsto ...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 ... 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-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 Shao. Associate Professor; Contact Info.
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. 785-864-4762. 627 Snow. Personal Links. Webpage Webpage; Research — Harmonic Analysis ...Shuanglin Shao [*] [[Shuanglin Shao (Ph.D. University of California, Los Angeles 2008)|]] Paul Anthony Smith [*] [[Paul Anthony Smith (Ph.D. University ...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.BENOIT PAUSADER AND SHUANGLIN SHAO Abstract. We prove global wellposedness and scattering for the Mass-critical homogeneous fourth-order Schro¨dinger equation in …Jianbo Tian 1 , Xianglin Yuan 2 , Jun Xiao 3 , Qiang Zhong 4 , Chunguang Yang 3 , Bo Liu 2 , Yimin Cai 1 , Zequn Lu 1 , Jing Wang 3 , Yanan Wang 3 , Shuanglin Liu 5 , Biao Cheng 6 , Jin Wang 7 , Ming Zhang 1 , Lu Wang 1 , Siyuan Niu 1 , Zhi Yao 8 , Xiongbo Deng 9 , Fan Zhou 10 , Wei Wei 11 , Qinglin Li 12 , Xin Chen 2 , Wenqiong Chen 3 , Qin ...
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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. Guixiang XU, Professor | Cited by 1,044 | of Beijing Normal University, Beijing (bnu) | Read 59 publications | Contact Guixiang XUShuanglin 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 …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 ...
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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.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...Yifei WU | Cited by 872 | of Tianjin University, Tianjin (tju) | Read 60 publications | Contact Yifei WU
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JIN-CHENG JIANG AND SHUANGLIN SHAO Abstract. In this paper, we study the extremal problem for the Strichartz inequality for the Schr ̈ odinger equation on the R×R2. We …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
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Instructor: Shuanglin Shao Office: Snow Hall 615 Email:
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Office Hour: M, W: 9:30-10:30 AM or by appointment. Grade Policy. 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 + 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 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 ...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.Instructor: Shuanglin Shao Office: Snow Hall 615 Email:
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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 (University of Kansas). Title: On smoothness of extremizers to an adjoint Fourier restriction inequality on S2. Abstract: The extremizers to ...Instructor: Shuanglin Shao Office: Snow Hall 615 Email:
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Office Hour: MF: 10:00 -- 11:00 AM, or by appointment. Miscellaneous There will be a take-home final in …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 Semigroups
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Smith Colloquium Fall 2022; Date: Speaker, Title: Local Host: October 27: Joseph Auslander Professor Emeritus, University of Maryland The Galois Theory of Minimal Flows6 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 ...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...
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SHUANGLIN SHAO Abstract. Please send me an email if you nd mistakes. Thanks. 1. P289. # 33.1 Proof. The proof is similar to Theorem 33.1. So we skip it. 2. P289. # 33.2 Proof. We show that supfcSg= csupSfor c>0. The proof for in mum is similar. Firstly for s2S, cs csupS: So csupSis an upper bound. For >0, there exists s 0 2Ssuch that s 0 supS ... I have just uploaded to the arXiv my paper “A quantitative formulation of the global regularity problem for the periodic Navier-Stokes equation”, submitted to Dynamics of PDE.This is a short note on one formulation of the Clay Millennium prize problem, namely that there exists a global smooth solution to the Navier-Stokes equation on the torus …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 …Jun 22, 2010 · 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 $ orm {\widehat {f\sigma}}_ {L^4}/ orm {f}_ {\lt}$ are smooth; that any ...
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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.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 ...Instructor: Shuanglin Shao Office: Snow Hall 615 Email:
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Office Hour: MWF: 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 in class. The lowest homework grade will be dropped.... shao lin stock pictures, royalty-free photos & images · lian shan shuang lin ...Aug 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. 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 ...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) KeywordsInstructor: Shuanglin Shao Office: Snow Hall 615 Email:
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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.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, 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 ...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'DellShuanglin 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 Narasaraopet is a city and district headquarters of Palnadu District of the Indian state of Andhra Pradesh.The town is a municipality and mandal headquarters of Narasaraopet mandal and Headquarters of Narasaraopet revenue division.The town also is the seat of the court of Additional District Judge. Narasaraopet acts as a melting point for the Palnadu and Delta regions of the district.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...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.
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21 mar 2023 ... Party Secretary, Chairman Shao Yuhui and his party visited EDRI ... Add：Chengdu country shuanglin road 251 Fax：028-84333172 Postcode：610021.
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DOI: 10.1142/S0219891610002256 Corpus ID: 14454549; THE MASS-CRITICAL FOURTH-ORDER SCHRÖDINGER EQUATION IN HIGH DIMENSIONS @article{Pausader2009THEMF, title={THE MASS-CRITICAL FOURTH-ORDER SCHR{\"O}DINGER EQUATION IN HIGH DIMENSIONS}, author={Benoit Pausader and Shuanglin Shao}, journal={Journal of Hyperbolic Differential Equations}, year={2009}, volume={07}, pages={651-705}, url={https://api ...Shuanglin Shao · Renming Song · Zhiqiang Cai · Shizan Fang · Hongjun Gao · Jianhua Huang · Peter Kloeden · Jicheng Liu · Xu Sun · Yanbin Tang · Fuke Wu.Shuanglin Shao——The entropy estimate for the res... 时间：12月12日，9:00-10:00 地点：Zoom会议，会议号：988 9149 1513，密... 人才招聘. Copyright (C)2017 ...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 ...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. Mathematics. 2010; In [5], when the spatial variable x is localized, Lee observed that the Schrödinger maximal operator eit∆f(x) enjoys certain ...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.Aug 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. 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 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.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 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 Department 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”.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 Kim Pong and was completed in 1907.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 …Pacific Shuanglin Bio pharmacy Co Ltd, formerly Southern Shuanglin Bio-pharmacy Co Ltd, formerly Zhenxing Biopharmaceutical & Chemical Co., Ltd., is a China-based company mainly engaged in the research, development, production and sales of blood products.Tim Austin, Bradley William Rodgers, Joshua Norbert Zahl, Thai Hoang Le, Jacques Benatar, Jordan Greenblatt, Ben Krause, Nicholas Cook, Kenneth Maples, Paul Anthony Smith, Julia Sealth Garibaldi, Monica Vișan, Zaher Hani, John Bueti, Shuanglin Shao, Soonsik Kwon, Zane Li: פרסים והוקרה: מדליית פילדס (2006) פרס ...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 ...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 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.
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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 DepartmentAuthors: 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 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.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.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.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 ...
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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. 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.Shanxi Travel Guide. Shanxi (abbreviated as “Jin”) is an inland province in North China, which borders Heibei to the east, Shaanxi to the west, Henan to the south and Inner Mogolia to the north. Also, it lies west of Taihang Mountain and faces Lvliang Mountain, Yellow River in the south and Great Wall in the north.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 ...
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Download scientific diagram | Lianshan Shuanglin Monastery. (Courtesy of Mr. Lim Shao Bin) from publication: Conservation of Chinese Temples in Singapore: A Historical Overview | Singapore ...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”.
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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 ...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 ...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...JIN-CHENG JIANG AND SHUANGLIN SHAO Abstract. In this paper, we study the extremal problem for the Strichartz inequality for the Schr ̈ odinger equation on the R×R2. We …
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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... Shuang; Lin, Shao; Hajat, Shakoor; Yang, Lianping; Huang, Cunrui; (2019) The impact of the 2016 flood event in Anhui Province, China on infectious diarrhea ...Jianbo Tian 1 , Xianglin Yuan 2 , Jun Xiao 3 , Qiang Zhong 4 , Chunguang Yang 3 , Bo Liu 2 , Yimin Cai 1 , Zequn Lu 1 , Jing Wang 3 , Yanan Wang 3 , Shuanglin Liu 5 , Biao Cheng 6 , Jin Wang 7 , Ming Zhang 1 , Lu Wang 1 , Siyuan Niu 1 , Zhi Yao 8 , Xiongbo Deng 9 , Fan Zhou 10 , Wei Wei 11 , Qinglin Li 12 , Xin Chen 2 , Wenqiong Chen 3 , Qin ...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 2, 1. Department of Mathematics, National Tsing Hua University, Hsinchu 30013 2. Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, SIP. …Jianbo Tian 1 , Xianglin Yuan 2 , Jun Xiao 3 , Qiang Zhong 4 , Chunguang Yang 3 , Bo Liu 2 , Yimin Cai 1 , Zequn Lu 1 , Jing Wang 3 , Yanan Wang 3 , Shuanglin Liu 5 , Biao Cheng 6 , Jin Wang 7 , Ming Zhang 1 , Lu Wang 1 , Siyuan Niu 1 , Zhi Yao 8 , Xiongbo Deng 9 , Fan Zhou 10 , Wei Wei 11 , Qinglin Li 12 , Xin Chen 2 , Wenqiong Chen 3 , Qin ...MathSciNet Ph.D. University of California, Los Angeles 2008 Dissertation: Restriction Estimates for Paraboloids and Cones in the Cylindrically Symmetric Case Mathematics …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 …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 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. 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.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 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 In this paper, we discuss the properties of one dimensional quantum Zakharov system which describes the nonlinear interaction between the quantum Langmuir and quantum ion-acoustic...Shuanglin's Blog. research and teaching related . Posted by: Shuanglin Shao | December 6, 2009 Kato-smoothing effect “Kato smoothing” “is ” important in dispersive PDE.“Smoothing”, as it stands, sounds like a very good word. But why is it good? How will it be used remains as vague questions to me.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 ...
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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 ... Shuanglin Shao. Associate Professor; Contact Info.
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Shuanglin Shao In this paper, we discuss the properties of one dimensional quantum Zakharov system which describes the nonlinear interaction between the quantum Langmuir and quantum ion-acoustic... SHUANGLIN SHAO; BENOIT PAUSADER. Mathematics Department, Brown University, Box 1917, Providence, Rhodes Island 02912, USA. Search for more papers by this authorPosted by: Shuanglin Shao | September 18, 2020 Measure and Integration theory, Lecture 7. Let be a real valued measurable function. Let . 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; 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 ...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 Department of Mathematics, KU Snow Hall 615 1460 Jayhawk Blvd Lawrence, KS 66045-7594 Phone: (785)864-4762 Fax: (785)864-5255 Email:
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Shuanglin's Blog. research and teaching related . Posted by: Shuanglin Shao | August 29, 2020 Measure and Integration theory, Lecture 3. In this section, the main theorem is the Carath\’eodory theorem. It enables us to construct measures from outer measures. We introduce the concept of outer measure.Shuanglin Shao University of Kansas + 2008–09. 2008–09. Xianjin Chen University of Science and Technology of China. Mark Herman University of Rochester. YunKyong Hyon National Institute for Mathematical Sciences (NIMS) Mark Iwen Michigan State University. Srividhya Jeyaraman Indiana University.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 …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.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 Kim Pong and was completed in 1907.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 …Shuanglin Shao. Shuanglin Shao. Associate Professor. Contact Info.
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· 785-864-4762. 627 Snow. Personal Links. Webpage Webpage. Research —.Shuanglin Shao - United States | Professional Profile | LinkedIn Shuanglin Shao -- United States 47 followers 47 connections Join to view profile UCLA Activity As the #Shenzhou13 space mission...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. 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 (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) KeywordsShanxi Travel Guide. Shanxi (abbreviated as “Jin”) is an inland province in North China, which borders Heibei to the east, Shaanxi to the west, Henan to the south and Inner Mogolia to the north. Also, it lies west of Taihang Mountain and faces Lvliang Mountain, Yellow River in the south and Great Wall in the north.
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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.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 (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 ... Posted by: Shuanglin Shao | August 15, 2020 Math 810: measure theory and integration. Lecture 1. 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 ...Shuanglin Shao. Mathematics. 2007; For cylindrically symmetric functions dyadically supported on the paraboloid, we obtain a family of sharp linear and bilinear ...Shuanglin Shao. Shuanglin Shao. Associate Professor. Contact Info.
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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. 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.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
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