DIVERGENCE

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RIGHT MEAN FOR THEα-z BURES-WASSERSTEIN QUANTUM DIVERGENCE
《Acta Mathematica Scientia》2023年第5期2320-2332,共13页Miran JEONG Jinmi HWANG Sejong KIM 
supported by the National Re-search Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(NRF-2022R1A2C4001306);supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(NRF-2022R1I1A1A01068411)。
The optimization problem to minimize the weighted sum ofα-z Bures-Wasserstein quantum divergences to given positive definite Hermitian matrices has been solved.We call the unique minimizer theα-z weighted right mean...
关键词：Rényi relative entropy Bures-Wasserstein quantum divergence right mean power mean Cartan mean Wasserstein mean 
ON THE DIMENSION OF THE DIVERGENCE SET OF THE OSTROVSKY EQUATION
《Acta Mathematica Scientia》2022年第4期1607-1620,共14页Yajuan ZHAO Yongsheng LI Wei YAN Xiangqian YAN 
supported by the National Natural Science Foundation of China(11571118,11401180 and 11971356)。
We investigate the refined Carleson’s problem of the free Ostrovsky equation{ut+■_(z)^(3)u+■_(x)^(-1)u=0,u(x,0)=f(x)where(x,t)∈R×R and f∈H^(s)(R).We illustrate the Hausdorff dimension of the divergence set for t...
关键词：Free Ostrovsky equation Hausdorff dimension divergence set 
GEOMETRY ON THE WASSERSTEIN SPACE OVER A COMPACT RIEMANNIAN MANIFOLD
《Acta Mathematica Scientia》2021年第6期1959-1984,共26页Hao DING Shizan FANG 
The first author is supported by China Scholarship Council.
We revisit the intrinsic differential geometry of the Wasserstein space over a Riemannian manifold,due to a series of papers by Otto,Otto-Villani,Lott,Ambrosio-Gigli-Savaré,etc.
关键词：constant vector fields measures having divergence Levi-Civita connection parallel translations Mckean-Vlasov equations 
AN UPBOUND OF HAUSDORFF’S DIMENSION OF THE DIVERGENCE SET OF THE FRACTIONAL SCHRODINGER OPERATOR ON H^(s)(R^(n))被引量：1
《Acta Mathematica Scientia》2021年第4期1223-1249,共27页Dan LI Junfeng LI Jie XIAO 
Li Dan and Li Junfeng were supported by NSFC-DFG(11761131002);NSFC(12071052);Xiao Jie was supported by NSERC of Canada(202979463102000).
Given n≥2 and α≥1/2,we obtained an improved upbound of Hausdorff's dimension of the fractional Schrodinger operator;that is,supf∈H^(s)(R^(n)) dim_(H){x∈R^(n):limt→0 e^(it)(-△)^(α) f(x)≠f(x)}≤n+1-2(n+1)s/n fo...
关键词：The Carleson problem divergence set the fractional Schrodinger operator Hausdorff dimension Sobolev space 
RATE OF CONVERGENCE AND EXPANSION OF RNYI ENTROPIC CENTRAL LIMIT THEOREM被引量：1
《Acta Mathematica Scientia》2015年第1期79-88,共10页孙建强 丁义明 
supported by National Basic Research Program of China(973 Program)(2011CB707802,2013CB910200);Natural Science Foundation of China Grant(11126180)
We obtain the expansion of Renyi divergence of order α （0 〈 α 〈 1） between the normalized sum of IID continuous random variables and the Caussian limit under minimal moment conditions via Edgeworth-type expansio...
关键词：Renyi divergence central limit theorem Edgeworth-type expansion rate ofconvergence 
REGULARITY FOR CERTAIN QUASILINEAR ELLIPTIC SYSTEMS OF DIVERGENCE STRUCTURE
《Acta Mathematica Scientia》2001年第2期196-202,共7页周树清 冉启康 
Supported by NNSF of China (19531060) ;by the National Educational Committee's Doctor Program Funds of China (97024811).
The regularity of the gradient of Holder continuous solutions of quasi-linear elliptic systems of the form -Dj(aij(x,u,Du)Diuk)=-Difki=gk is investigated. Partial regularity and ε-regularity are shown to hold under t...
关键词：Partial regulrity ε-regularity and elliptic systems 
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