Shuanglin shao

Shuanglin shao. Posted by: Shuanglin Shao | September 18, 2020 Measure and Integration theory, Lecture 7. Let be a real valued measurable function. Let .Shuanglin Shao's 18 research works with 438 citations and 859 reads, including: On one dimensional Quantum Zakharov system Shuanglin Shao's research while affiliated with …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.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.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 ... 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;His research mentor is Shuanglin Shao, associate professor of mathematics. MathUGRAs are awarded to students conducting semester-long independent projects culminating in an oral presentation or written work, demonstrating the student’s own development of a topic in mathematics and its applications. Recipients of the award are …Liked by Shuanglin Shao. Education UCLA Ph. D Math. 2004 - 2008. View Shuanglin’s full profile See who you know in common Get introduced ... 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 areHome About Select to follow link Department of Mathematics History (1866-1970) EmploymentAnalysis and Ergodic Theory Summer School, Lake Arrowhead ∗ September 17th - September 22nd 2006 Organizers: Ciprian Demeter, University of California, Los AngelesNarasaraopet 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.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 …... shao lin stock pictures, royalty-free photos & images · lian shan shuang lin ...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.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, KU Snow Hall 615 1460 Jayhawk Blvd Lawrence, KS 66045-7594 Phone: (785)864-4762 Fax: (785)864-5255 Email: [email protected] [30] Shao, Xiaolu, Li, Shuanglin, Liu, Na, Song, Jie. The Madden-Julian oscillation during the 2016 summer and its possible impact on rainfall in China.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 ...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 ...Yifei WU | Cited by 872 | of Tianjin University, Tianjin (tju) | Read 60 publications | Contact Yifei WUShuanglin Shao. Mathematics. 2010; In [5], when the spatial variable x is localized, Lee observed that the Schrödinger maximal operator eit∆f(x) enjoys certain localization property in t for frequency localized functions. In this … Expand. Highly Influenced. PDF. 8 Excerpts; Save. Some Recent Progress on the Restriction Conjecture.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.30 nov 2017 ... From: Shuanglin Shao [view email] [v1] Thu, 30 Nov 2017 21:38:36 UTC (17 KB). Full-text links: Access Paper: Download a PDF of the paper ...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 ...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 …12 feb 2021 ... In: arXiv preprint math/9704212 (1997) (cit. on p. 4). [Sha08]. Shuanglin Shao. “Maximizers for the Strichartz inequalities and the Sobolev-.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 ... 2015 chevy silverado belt diagram www lkq pick your part com 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.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 ... Instructor: Shuanglin Shao Office: Snow Hall 615 Email: [email protected] Office Hour: MWF: 1:00 --- 2:00 PM, or by appointment. Grade Policy.12 dic 2014 ... ... Shao Bin Collection in the National Library, Singapore. Find Out More · Overview. Overview about careers at National Library Board Singapore ...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 ...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 …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 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. ViewInstructor: Shuanglin Shao Office: Snow Hall 615 Email: [email protected] Office Hour: MWF: 1:00 --- 2:00 PM, or by appointment. Grade Policy. abstract in a book zoophile discord servers 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 (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. 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 ... kansas message board basketball Aug 31, 2008 · 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 ... patrick dorsey watkins hall life cycle of a anaconda AIMS Journals; {{journal.titleEn}} {{journal.titleEn}} {{journal.titleEn}} {{journal.titleEn}}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 …University of Zurich, Department of Economics, Zurich, Switzerland. All members of the Editorial Board have identified their affiliated institutions or organizations, along with the corresponding country or geographic region. Elsevier remains neutral with regard to any jurisdictional claims. Read the latest articles of China Economic Review at ... wunderground des moines 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. yo jackson Download scientific diagram | Lianshan Shuanglin Monastery. (Courtesy of Mr. Lim Shao Bin) from publication: Conservation of Chinese Temples in Singapore: A Historical Overview | Singapore ...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. 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 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. ViewJIN-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. aleks ppl ku isu 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 ...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 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 ...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, … heavy duty curtain rod holders View public records and voter registration of Shuanglin Hao born 1964, includes court and personal records. ... Email: [email protected] . Shuanglin Hao Addresses ... 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).Course Search. Search class sections | Online courses. Library Search access kansas william staples 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.The University of Kansas prohibits discrimination on the basis of race, color, ethnicity, religion, sex, national origin, age, ancestry, disability, status as a veteran, sexual orientation, marital status, parental status, gender identity, gender expression, and genetic information in the university's programs and activities. Shuanglin Shao 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 Member. School of Mathematics. 9/2008 - 8/2009.86 SHUANGLIN SHAO It will be clear from the statements ofTheorem 1.5andTheorem 1.6that these four symmetries in L2 above are the only obstructions to the compactness of the solution map. Hence the parameter.h 0;˘ 0;x 0;t 0/plays a special role in characterizing this defect of compactness; moreover, a sequence of such parameters needs to satisfy …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 Abstract. In [5], when the spatial variable x is localized, Lee observed that the Schro¨dinger maximal operator eit∆f(x) enjoys certain localization property in tfor frequency localized functions. In this note, we give an alternative proof of this observation by using the method of stationary phase, and then include twoShuanglin 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 ...Course Search. Search class sections | Online courses. Library SearchSHUANGLIN 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's 18 research works with 438 citations and 859 reads, including: On one dimensional Quantum Zakharov system Shuanglin Shao's research while affiliated with …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 …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 … de donde es originaria la bachata 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 localization property in t for frequency localized functions. In this … Expand. Highly Influenced. PDF. 9 …Shao, Shuanglin University of Kansas, Lawrence, KS, United States. Search grants from Shuanglin Shao Search grants from University of Kansas Center for Research Inc. Share this grant: : : Abstract; Funding; Institution; Comments; Recent in Grantomics: University of Virginia vs. funders. Who wins? ...Instructor: Shuanglin Shao Office: Snow Hall 615 Email: [email protected] Office Hour: MF: 10:00 -- 11:00 AM, or by appointment. MiscellaneousThe 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. Instructor: Shuanglin Shao Office: Snow Hall 615 Email: [email protected] Office Hour: M, W: 9:30-10:30 AM or by appointment. Grade Policy. ncaa big 12 championship 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 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¨oindgerEnter the email address you signed up with and we'll email you a reset link. kansas basketball assistant coaches 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. ...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.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...The purpose of the AWM is to encourage women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity and the equal treatment of women and girls in the mathematical sciences.BENOIT PAUSADER AND SHUANGLIN SHAO Abstract. We prove global wellposedness and scattering for the Mass-critical homogeneous fourth-order Schro¨dinger equation in …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 ... does menards take afterpay sexuality movements 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 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 Fax:+1-(785)864-5255 Curriculum Vitae (PDF) Research Paper and Preprints Teaching Fall 2011, Math 290 Spring 2012, Math 500 FallShuanglin Shao's 18 research works with 438 citations and 859 reads, including: On one dimensional Quantum Zakharov system Shuanglin Shao's research while affiliated with …6 mar 2023 ... ... Shuanglin Que,. Corresponding Author. Shuanglin Que. [email protected] ... Shao, B. (2017). Circular RNA hsa_circ_0021001 in peripheral blood: A ...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 ...Epub 2022 Dec 24. Authors. Shuanglin Liao , Yao Lin , Lizhen Liu , Shuai Yang , YingYing Lin , Junbing He , Yiming Shao ... Shao. Affiliations. 1 The Intensive Care ...Related Forms - New_Hampshire Shuanglin Shao - KU Mathematics Department HOMEWORK 9 STRANGLING SHAO1.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 …Math 810, Measure theory and integration, Lecture 2. In this lecture, we study how we define measures given a algebra on and then move to study its properties. A measure is a set function, namely, a function acting on sets. Here the sets belong to a given algebra. For instance, the “length” on enables us to measuring open or closed ...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;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.Shuanglin Shao 2, 1. Department of Mathematics, National Tsing Hua University, Hsinchu 30013 2. Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, SIP. …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 projections espn college gameday basketball schedule Aug 12, 2022 · Shuanglin Shao: Snow 306: Thursday, 3/31/22: 4:00 pm: Smith Colloquium Moduli Space of Fano Varieties Yuchen Liu, Northwestern University Zoom link: https://kansas ... Shuanglin Shao [] [[Shuanglin Shao (Ph.D. University of California, Los Angeles 2008)|]] Paul Anthony Smith [] [[Paul Anthony Smith (Ph.D. University ...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. hilti firestop library 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 (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;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: ...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. kansas uniform what is a msed 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 ...Shuanglin Shao: 306 Snow: Friday, 9/3/21: 10:00am: Graduate Student Probability Seminar Fundamentals of Continuous Stochastic Processes: Zoom ...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. terraria wikipedia weapons Authors: Shuanglin Shao. Download PDF Abstract: In this paper, for cylindrically symmetric functions dyadically supported on the paraboloid, we obtain a family of sharp linear and linear adjoint restriction estimates.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.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 ... 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 …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 projections30 nov 2017 ... From: Shuanglin Shao [view email] [v1] Thu, 30 Nov 2017 21:38:36 UTC (17 KB). Full-text links: Access Paper: Download a PDF of the paper ...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.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 ... aj stephens 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.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 …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. svi basketball BENOIT PAUSADER AND SHUANGLIN SHAO Abstract. We prove global wellposedness and scattering for the Mass-critical homogeneous fourth-order Schro¨dinger equation in …12 feb 2021 ... In: arXiv preprint math/9704212 (1997) (cit. on p. 4). [Sha08]. Shuanglin Shao. “Maximizers for the Strichartz inequalities and the Sobolev-.Shuanglin's Blog. research and teaching related . Posted by: Shuanglin Shao | August 29, 2020 Measure and Integration theory, Lecture 3. In this section, the …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. youth mentorship 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... 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, 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. 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. If you have additional information or corrections ... 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 (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.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-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 areAug 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. 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 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 DepartmentShuanglin 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 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 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 IASShuanglin 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. 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. chirimoya ecuador kansas state mascot 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 ... 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. frisco baseball classic 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. Associate Professor; Contact Info. [email protected]. 785-864-4762. 627 Snow. Personal Links. Webpage Webpage; Research — Harmonic Analysis ...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.André Martinez, Thierry Ramond and Johannes Sjöstrand: Global existence and uniqueness results for weak solutions of the focusing mass-critical nonlinear Schrödinger equation4 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 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 ...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 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...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 ...Liked by Shuanglin Shao. Education UCLA Ph. D Math. 2004 - 2008. View Shuanglin's full profile See who you know in common Get introduced ...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.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. 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.Shuanglin Hao, M.D., Ph.D. Professor, Anesthesiology Email: [email protected]. We investigate the neurochemical mechanisms of peripheral nervous system injury and neuropathic pain associated with HIV/AIDS. We also study opioid drug abuse and its interaction with HIV infection and HIV/AIDS neuropathy.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 …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. ...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;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 based … futbol line public service loan forgiveness application form 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 (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;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 ...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 ...21 mar 2023 ... Party Secretary, Chairman Shao Yuhui and his party visited EDRI ... Add：Chengdu country shuanglin road 251 Fax：028-84333172 Postcode：610021.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 ... 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 based … title 9 rights 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. 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.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 ... joe servais centauromachy parthenon 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. 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. M.S. Mathematics, Beijing Normal University, 2004.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 … do i want to be a teacher Shuanglin Shao. Associate Professor; Contact Info. [email protected]. 785-864-4762. 627 Snow. Personal Links. Webpage Webpage; Research — Harmonic Analysis ...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 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's Blog. research and teaching related . Posted by: Shuanglin Shao | August 29, 2020 Measure and Integration theory, Lecture 3. In this section, the … chase rader local weather 15 day forecast Shuanglin Shao View full-text As for the case α = 4 in (1), Jiang et al. [22, 23] give some dichotomy results on the existence of extremals by using the profile decomposition from [1,2,8,26,32].Shuanglin Shao (Department of Mathematics, Kansas University, Lawrence, Ks., U.S.A.) Abstract In this paper, we study the extremal problem for the …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 ...Posted by: Shuanglin Shao | September 18, 2020 Measure and Integration theory, Lecture 7. Let be a real valued measurable function. Let . 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 …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. Course Search. Search class sections | Online courses. Library SearchAbstract: Unconventional superconductors have Cooper pairs with lower symmetries than in conventional superconductors. In most unconventional superconductors, ...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 ...S. Shao, The linear profile decomposition for the Airy equation and the existence of maximizers for the Airy Strichartz inequality, Anal. Partial Differential Equations 2 (1) (2009) 83–117. [30] S. Shao, Maximizers for the Strichartz inequalities and the Sobolev–Strichartz inequalities for the Schrödinger equation, Electron. J.6 mar 2023 ... ... Shuanglin Que,. Corresponding Author. Shuanglin Que. [email protected] ... Shao, B. (2017). Circular RNA hsa_circ_0021001 in peripheral blood: A ...Zhao-Ming, Shao ... THE CHINESE ECONOMY AFTER WTO ACCESSION. BAO, SHUMING/LIN, SHUANGLIN/ZHAO, CHANGWEN. 978-0 ...Forbes China launched its first annual list to honor 50 Top Women in Tech in mainland China in 2019. The third edition is out in the latest issue of Forbes China magazine. The list identified ...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, …Instructor: Shuanglin Shao Office: Snow Hall 615 Email: [email protected] Office Hour: MWF: 1-2 PM or by appointment. Grade Policy. Homework: There will be 10 homework. Each homework consists of roughly 10 problems; only 3 of them will be graded, which will be decided after you turn in homework.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 senior night speech ideas for sports daniel rolf Shuanglin Shao Regularity of solutions to the Schrodinger equation: Nov. 29: Zubin Gautam The Balian-Low Theorem and a variant: Raanan Schul: Tristan Roy Poincaré inequalities: Dec. 6: Zubin Gautam The Balian-Low Theorem and a variant: Shuanglin Shao: Tristan Roy Poincaré inequalities: Schedule from Spring 2005 :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 Fax:+1-(785)864-5255 Curriculum Vitae (PDF) Research Paper and Preprints Teaching Fall 2011, Math 290 Spring 2012, Math 500 Fall kansas state basketball point guard 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.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 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: Snow 306: Thursday, 3/31/22: 4:00 pm: Smith Colloquium Moduli Space of Fano Varieties Yuchen Liu, Northwestern University Zoom link: https://kansas ...Posted by: Shuanglin Shao | October 18, 2020 Measure and Integration theory, Lecture 13. Lemma 3.15. (Vitali type covering lemma.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 ...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. Related Forms - New_Hampshire Shuanglin Shao - KU Mathematics Department HOMEWORK 9 STRANGLING SHAO1.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.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. 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 ...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... braun denver nuggets and to all goodnight 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 ... 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 ... 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 ...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.Shao Shuanglin Restriction theorem in dimension 2: John Bueti : Zubin Gautam Classification of ergodic transformations with pure-point spectrum: May 02: Steve O'Dell The Aharonov Bohm effect and time-dependent scattering theory: Joe Viola : Shao Shuanglin Restriction Theoem in Dimension 2:Shuanglin Shao 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. sound learning [30] Shao, Xiaolu, Li, Shuanglin, Liu, Na, Song, Jie. The Madden-Julian oscillation during the 2016 summer and its possible impact on rainfall in China.Oct 18, 2020 · Posted by: Shuanglin Shao | October 18, 2020 Measure and Integration theory, Lecture 13. Lemma 3.15. (Vitali type covering lemma. 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 (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 ... peterson football coach astrodynamics degree