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作品数：1231被引量：1216H指数：13
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Jackson-type inequalities on high-dimensional spheres
《Science China Mathematics》2024年第11期2571-2586,共16页Yeli Niu Feng Dai 
supported by National Natural Science Foundation of China(Grant No.12201412);supported by the Natural Sciences and Engineering Research Council of Canada。
We study Jackson's inequality on high-dimensional spheres with respect to the modulus of smoothness defined via the rotation group.We obtain a version of Jackson's inequality with a dimensionfree constant,extending Ne...
关键词：modulus of smoothness K-FUNCTIONAL Jackson's inequality high-dimensional approximation 
Global hydrostatic approximation of the hyperbolic Navier-Stokes system with small Gevrey class 2 data In memory of Professor Geneviève Raugel被引量：2
《Science China Mathematics》2022年第6期1109-1146,共38页Marius Paicu Ping Zhang 
supported by K.C.Wong Education Foundation;supported by the Agence Nationale de la Recherche,Project IFSMACS(Interaction Fluide-Structure:Modélisation,analyse,contr?le et simulation)(Grant No.ANR-15-CE40-0010);supported by National Basic Research Program of China(Grant No.2021YFA1000800);National Natural Science Foundation of China(Grants Nos.11731007,12031006 and 11688101)。
We investigate the hydrostatic approximation of a hyperbolic version of Navier-Stokes equations,which is obtained by using the Cattaneo type law instead of the Fourier law,evolving in a thin strip R×(0,ε).The formal...
关键词：incompressible hyperbolic Navier-Stokes equations hydrostatic approximation hyperbolic Prandtl system 
A copula-based approximation to Markov chains
《Science China Mathematics》2022年第3期623-654,共32页Zhengyong Zhou Jiehua Xie Jingping Yang 
supported by the National Key R&D Program of China(Grant No.2018YFA0703900);National Natural Science Foundation of China(Grant No.11671021);supported by National Natural Science Foundation of China(Grant Nos.11761051and 11561047);the Natural Science Foundation of Jiangxi Province(Grant Nos.20181BAB211003 and 20192BAB211006)。
The Markov chain is well studied and widely applied in many areas.For some Markov chains,it is infeasible to obtain the explicit expressions of their corresponding finite-dimensional distributions and sometimes it is ...
关键词：Markov chain COPULA checkerboard copula-based Markov chain ■-convergence β-mixing property 
Characterization of image spaces of Riemann-Liouville fractional integral operators on Sobolev spaces W^(m,p)(Ω)
《Science China Mathematics》2021年第12期2611-2636,共26页Lijing Zhao Weihua Deng Jan S.Hesthaven 
supported by National Natural Science Foundation of China(Grant No.11801448);the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2018JQ1022).;supported by National Natural Science Foundation of China(Grant No.11271173).
Fractional operators are widely used in mathematical models describing abnormal and nonlocal phenomena.Although there are extensive numerical methods for solving the corresponding model problems,theoretical analysis s...
关键词：image space Riemann-Liouville integral regularity property APPROXIMATION 
Nonuniform sampling and approximation in Sobolev space from perturbation of the framelet system
《Science China Mathematics》2021年第2期351-372,共22页Youfa Li Deguang Han Shouzhi Yang Ganji Huang 
supported by National Natural Science Foundation of China(Grant Nos.61961003,61561006 and 11501132);Natural Science Foundation of Guangxi(Grant Nos.2018JJA110110 and 2016GXNSFAA380049);the talent project of Education Department of Guangxi Government for Young-Middle-Aged Backbone Teachers;supported by National Science Foundation of USA(Grant No.DMS-1712602)。
The Sobolev space H^(■)(R^(d)),where■>d/2,is an important function space that has many applications in various areas of research.Attributed to the inertia of a measurement instrument,it is desirable in sampling theo...
关键词：Sobolev space framelet series truncation error perturbation error nonuniform sampling and approximation 
Machine learning from a continuous viewpoint,I被引量：2
《Science China Mathematics》2020年第11期2233-2266,共34页Weinan E Chao Ma Lei Wu 
supported by a gift to Princeton University from iFlytek and the Office of Naval Research(ONR)Grant(Grant No.N00014-13-1-0338)。
We present a continuous formulation of machine learning,as a problem in the calculus of variations and differential-integral equations,in the spirit of classical numerical analysis.We demonstrate that conventional mac...
关键词：machine learning continuous formulation flow-based model gradient flow particle approximation 
Metrically regular mappings and its application to convergence analysis of a confined Newton-type method for nonsmooth generalized equations被引量：1
《Science China Mathematics》2020年第1期39-60,共22页Mohammed Harunor Rashid Ya-xiang Yuan 
supported by CAS-President International Fellowship Initiative (PIFI), Chinese Academy of Sciences, Beijing, China;supported by National Natural Science Foundation of China (Grants Nos. 11688101 and 11331012)
Notion of metrically regular property and certain types of point-based approximations are used for solving the nonsmooth generalized equation f(x)+F(x)?0,where X and Y are Banach spaces,and U is an open subset of X,f:...
关键词：set-valued mappings generalized equations metrically regular mapping semilocal convergence point-based approximation 
The NLS approximation for two dimensional deep gravity waves Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday
《Science China Mathematics》2019年第6期1101-1120,共20页Mihaela Ifrim Daniel Tataru 
supported by a Clare Boothe Luce Professorship;supported by the National Science Foundation of USA (Grant No. DMS-1800294);a Simons Investigator grant from the Simons Foundation
This article is concerned with in?nite depth gravity water waves in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. Our goal is to study this problem wit...
关键词：water WAVES gravity WAVES normal forms NLS APPROXIMATION 
Efficient projected gradient methods for cardinality constrained optimization被引量：2
《Science China Mathematics》2019年第2期245-268,共24页Fengmin Xu Yuhong Dai Zhihu Zhao Zongben Xu 
supported by National Natural Science Foundation of China (Grant Nos. 11571271,11631013,11331012 and 71331001);the National Science Fund for Distinguished Young Scholars (Grant No. 11125107);the National 973 Program of China (Grant Nos. 2015CB856002 and 2013CB329404)
Sparse optimization has attracted increasing attention in numerous areas such as compressed sensing, financial optimization and image processing. In this paper, we first consider a special class of cardinality constra...
关键词：SPARSE APPROXIMATION projected GRADIENT method global CONVERGENCE signal recovery index tracking 
Exponential convergence of the deep neural network approximation for analytic functions Dedicated to Professor Ta Tsien Li on the Occasion of His 80th Birthday被引量：7
《Science China Mathematics》2018年第10期1733-1740,共8页Weinan E Qingcan Wang 
supported by Office of Naval Research(ONR)(Grant No.N00014-13-1-0338);Major Program of National Natural Science Foundation of China(Grant No.91130005)
We prove that for analytic functions in low dimension, the convergence rate of the deep neural network approximation is exponential.
关键词：neural networks approximation theory analytic functions 
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