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). 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 …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. Shuanglin Shao. Associate Professor. Contact Info. [email protected] · 785-864-4762. 627 Snow. Personal Links. Webpage Webpage. Research —.12 dic 2014 ... ... Shao Bin Collection in the National Library, Singapore. Find Out More · Overview. Overview about careers at National Library Board Singapore ...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 …

kansas state volleyball tickets JINCHENG 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 provide a new proof to the characterization of the extremal functions: the only ex-tremal functions are Gaussian functions up to the natural symmetry ofShuanglin 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 ... kansas men basketball schedulekusports football Posted by: Shuanglin Shao | September 18, 2020 Measure and Integration theory, Lecture 7. Let be a real valued measurable function. Let .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 ... ku academic calendar 2024 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) Keywords14 jun 2023 ... My PhD advisor was Shuanglin Shao. I received my BFA, BA, and BS at Friends University in Wichita, KS. I also received my MS at Emporia ... tulane vs houston baseball scorenumero de home depotkobe bryant kansas jayhawks 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's Blog. research and teaching related . Posted by: Shuanglin Shao | October 31, 2020 Measure and integration theory, Lecture 14. Let be a measure space and . Definition. The norm is defined to be When , Define . Remark. (1). . Indeed, there exists such that . Then . Since the latter sets are increasing, navy advancement results spring 2022 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 ...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. xfinity tv outage in my areaiowa state kansas football ticketsliondance 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.