Search Results - "Science China. Mathematics"

The Brezis-Nirenberg type critical problem for the nonlinear Choquard equation by Gao, Fashun, Yang, Minbo

“…We establish some existence results for the Brezis-Nirenberg type problem of the nonlinear Choquard equation − Δ u = ( ∫ Ω | u ( y ) | 2 μ * | x − y | μ d y )…”
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MgNet: A unified framework of multigrid and convolutional neural network by He, Juncai, Xu, Jinchao

“…We develop a unified model, known as MgNet, that simultaneously recovers some convolutional neural networks (CNN) for image classification and multigrid (MG)…”
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Diffusion and mixing in fluid flow via the resolvent estimate by Wei, Dongyi

“…In this paper, we first present a Gearhart-Prüss type theorem with a sharp bound for m -accretive operators. Then we give two applications: (1) we give a…”
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A comparative analysis of optimization and generalization properties of two-layer neural network and random feature models under gradient descent dynamics by E, Weinan, Ma, Chao, Wu, Lei

“…A fairly comprehensive analysis is presented for the gradient descent dynamics for training two-layer neural network models in the situation when the…”
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One discrete dynamical model on the Wolbachia infection frequency in mosquito populations by Zheng, Bo, Li, Jia, Yu, Jianshe

“…How to prevent and control the outbreak of mosquito-borne diseases, such as malaria, dengue fever and Zika, is an urgent worldwide public health problem. The…”
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Weak Hardy-type spaces associated with ball quasi-Banach function spaces I: Decompositions with applications to boundedness of Calderón-Zygmund operators by Zhang, Yangyang, Yang, Dachun, Yuan, Wen, Wang, Songbai

“…Let X be a ball quasi-Banach function space on ℝ n . In this article, we introduce the weak Hardy-type space W H X (ℝ n ), associated with X , via the radial…”
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Global well-posedness of coupled parabolic systems by Xu, Runzhang, Lian, Wei, Niu, Yi

“…The initial boundary value problem of a class of reaction-diffusion systems (coupled parabolic systems) with nonlinear coupled source terms is considered in…”
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Searching the solution landscape by generalized high-index saddle dynamics by Yin, Jianyuan, Yu, Bing, Zhang, Lei

“…We introduce a generalized numerical algorithm to construct the solution landscape, which is a pathway map consisting of all stationary points and their…”
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Machine learning from a continuous viewpoint, I by E, Weinan, Ma, Chao, Wu, Lei

“…We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of…”
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Exponential convergence of the deep neural network approximation for analytic functions by E, Weinan, Wang, Qingcan

“…We prove that for analytic functions in low dimension, the convergence rate of the deep neural network approximation is exponential…”
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Rosenthal’s inequalities for independent and negatively dependent random variables under sub-linear expectations with applications by Zhang, LiXin

“…Classical Kolmogorov’s and Rosenthal’s inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large…”
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Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection by Liao, Hong-Lin, Song, Xuehua, Tang, Tao, Zhou, Tao

“…In this work, we are concerned with the stability and convergence analysis of the second-order backward difference formula (BDF2) with variable steps for the…”
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A monotone finite volume method for time fractional Fokker-Planck equations by Jiang, Yingjun, Xu, Xuejun

“…We develop a monotone finite volume method for the time fractional Fokker-Planck equations and theoretically prove its unconditional stability. We show that…”
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Non-Nehari manifold method for asymptotically periodic Schrödinger equations by Tang, XianHua

“…We consider the semilinear Schrödinger equation where f is a superlinear, subcritical nonlinearity. We mainly study the case where V ( x ) = V 0 ( x ) + V 1 (…”
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Convergence of ground state solutions for nonlinear Schrödinger equations on graphs by Zhang, Ning, Zhao, Liang

“…We consider the nonlinear Schrödinger equation -Δ u + (λ a ( x ) + 1) u = | u | p -1 u on a locally finite graph G = ( V , E ). We prove via the Nehari method…”
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Discretization and index-robust error analysis for constrained high-index saddle dynamics on the high-dimensional sphere by Zhang, Lei, Zhang, Pingwen, Zheng, Xiangcheng

“…We develop and analyze numerical discretization to the constrained high-index saddle dynamics, the dynamics searching for the high-index saddle points confined…”
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On local strong and classical solutions to the three-dimensional barotropic compressible Navier-Stokes equations with vacuum by Huang, Xiangdi

“…We consider the local well-posedness of strong and classical solutions to the three-dimensional barotropic compressible Navier-Stokes equations with density…”
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Distribution dependent reflecting stochastic differential equations by Wang, Feng-Yu

“…To characterize the Neumann problem for nonlinear Fokker-Planck equations, we investigate distribution dependent reflecting stochastic differential equations…”
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Uniqueness of twisted linear periods and twisted Shalika periods by Chen, Fulin, Sun, Binyong

“…Let k be a local field of characteristic zero. Let π be an irreducible admissible smooth representation of GL 2 n (k). We prove that for all but countably many…”
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Tensor absolute value equations by Du, Shouqiang, Zhang, Liping, Chen, Chiyu, Qi, Liqun

“…This paper is concerned with solving some structured multi-linear systems, which are called tensor absolute value equations. This kind of absolute value…”
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