Shuanglin shao
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.Enter the email address you signed up with and we'll email you a reset link.
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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 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 Schrödinger 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.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, 957–977.86 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 …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 ...Instructor: Shuanglin Shao Office: Snow Hall 615 Email: [email protected] Office Hour: MWF: 1:00 --- 2:00 PM, or by appointment. Grade Policy.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 …Shuanglin Shao. Associate Professor; Contact Info. [email protected]. 785-864-4762. 627 Snow. Personal Links. Webpage Webpage; Research — Harmonic 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. [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.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 …2.1.3 Multiscale receptive fields. The lack of details in depth maps has always been a difficulty for unsupervised monocular depth estimation. The reason is that in the theory of deep convolutional neural networks, the perceptual field of the network gradually increases with the number of layers of the network, Zhou [] founds that the network’s …Shuanglin Shao · Renming Song · Zhiqiang Cai · Shizan Fang · Hongjun Gao · Jianhua Huang · Peter Kloeden · Jicheng Liu · Xu Sun · Yanbin Tang · Fuke Wu.Shuanglin Shao Atanas Stefenov Date defended: May 11, 2015. The Dissertation Committee for Lucas Chaffee certifies that this is the approved version of the following dissertation : Commutators of Multilinear Singular Integral Operators with Pointwise Multiplication Rodolfo Torres, ChairpersonOn Marcinkiewicz integral with variable kernels (with Yong Ding and Shuanglin Shao), Indiana Univ. Math. J. 53 (2004), 805-822. Parseval's formula for ...1 ago 2023 ... Shuanglin Shao (KU). Department of Mathematics · 138 Cardwell Hall · 1228 N Martin Luther King Jr Drive, Manhattan, KS 66506 · 785-532-6750 | ...We study the existence of standing waves, of prescribed L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage ...1 ago 2023 ... Shuanglin Shao (KU). Department of Mathematics · 138 Cardwell Hall · 1228 N Martin Luther King Jr Drive, Manhattan, KS 66506 · 785-532-6750 | ...
Associate Professor, Acting Associate Chair and Director of Undergraduate Studies, Spring 2024Aug 26, 2013 · In this paper we study the existence of maximizers for two families of interpolation inequalities, namely a generalized Gagliardo–Nirenberg inequality and a new inequality involving the Riesz energy. Two basic tools in our argument are a generalization of Lieb’s Translation Lemma and a Riesz energy version of the Brézis–Lieb lemma. 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¨oindgerDOI: 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: 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, …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.…
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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...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.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 ...
Spring 2016, Math 766, Real Analysis Course Information. Course Coverage: This course is the second part of real analysis at the graduate level; the first part is Math 765.. It continues with the following topics from Chapters 7, 8, 10, 11: infinite series of functions, the Topology in the Euclidean spaces, Metric spaces, and Differentiability onShuanglin 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.Associate Professor, Acting Associate Chair and Director of Undergraduate Studies, Spring 2024
From: Shuanglin Shao [v1] Mon, 8 Oct 2007 05:42:33 UTC (11 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 …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 ShuaThe University of Kansas prohibits discrimination on th 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. Shuanglin Shao, Linear and bilinear endpoint Strichart Instructor: Shuanglin Shao Office: Snow Hall 615 Email: [email protected] Office Hour: MF: 10:00 -- 11:00 AM, or by appointment. Miscellaneous There will be a take-home final in …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 (Institute for Mathematics and itRecently, Christ and Shao [1], [2] have proved the existence oEnter the email address you signed up with a SHUANGLIN SHAO Abstract. In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schr¨odinger equation in all dimensions based on the recent linear profile decomposition result. We then present a new proof of the linear profile decomposition for the Schr¨oindgerShuanglin Shao (KU) Department of Mathematics. 138 Cardwell Hall. 1228 N Martin Luther King Jr Drive, Manhattan, KS 66506 . 785-532-6750 | 785-532-0546 fax | math ... SHUANGLIN SHAO (Communicated by Hart F. Smith) Abstract. In 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 Schrödinger equation. Dates at IASI would also like to thank Donghao Wang and Ruixiang Zhang for helpful discussion on Proposition 5.3. I would like to thank the anonymous referees for the thorough reading and for many writing suggestions that improved the presentation of this paper. I would like to also thank Susan Ruff and Shuanglin Shao for their writing advice. Shuanglin Shao is really nice guy. However, he relies heavily o[Shuanglin Shao. We prove that the extremizers to th12 dic 2014 ... ... Shao Bin Collection in the Nati SHUANGLIN SHAO; BENOIT PAUSADER. Mathematics Department, Brown University, Box 1917, Providence, Rhodes Island 02912, USA. Search for more papers by this authorMath 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 ...