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Multidimensional Multiplicative Large Sets in Totally Minimal Systems: 《Acta Mathematica Sinica,English Series》2023年第8期1635-1649,共15页Jian Jie ZHAO; supported by the Scientific Research Fund of Zhejiang Provincial Education Department(Grant No.Y202147669);the Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ23A010006)。; In this paper,it is shown that for a residual set of points in a totally minimal system with finitely many commuting homeomorphisms,the set of return times to any non-empty open set contains a subset with positive mul...; 关键词：Multidimensional multiplicative upper Banach density totally minimal systems

Global Fujita-Kato's Type Solutions and Long-time Behavior for the Multidimensional Chemotaxis Model: 《Acta Mathematica Sinica,English Series》2022年第2期311-330,共20页Qiong Lei CHEN Xiao Nan HAO Jing Yue LI; Supported by the National Natural Science Foundation of China(Grant No.12071043);the National Key Research and Development Program of China(Grant No.2020YFA0712900)。; We establish the global well-posedness for the multidimensional chemotaxis model with some classes of large initial data,especially the case when the rate of variation of ln v0(v0 is the chemical concentration)contain...; 关键词：Critical Besov spaces chemotaxis model global well-posedness optimal time-decay rates

Almost Everywhere Convergence of Sequences of Cesàro and Riesz Means of Integrable Functions with Respect to the Multidimensional Walsh System: 《Acta Mathematica Sinica,English Series》2014年第2期311-322,共12页Gyrgy GT; Supported by project TMOP-4.2.2.A-11/1/KONV-2012-0051; The aim of this paper is to prove the a.e.convergence of sequences of the Cesaro and Riesz means of the Walsh–Fourier series of d variable integrable functions.That is,let a=（a1,...,ad）：N→Nd（d∈P）such that aj（...; 关键词：Walsh system d-dimensional Fejer and Riesz means SUBSEQUENCE almost everywhereconvergence

A Characterization of Multidimensional Multi-knot Piecewise Linear Spectral Sequence and Its Applications被引量：1: 《Acta Mathematica Sinica,English Series》2013年第9期1679-1690,共12页Xiao Na CUI Xu LIU Rui WANG Dun Yan YAN; supported by Science and Technology Research Project of Jilin Provincial Department of Education of China (Grant No. 2011175);supported by National Natural Science Foundation of China (Grant Nos. 11071250 and 11126149),supported by National Natural Science Foundation of China (Grant Nos. 11071250 and 11271162);Guangdong Provincial Government of China through the "Computational Science Innovative Research Team" program; We characterize a class of piecewise linear spectral sequences. Associated with the spectral sequence, we construct an orthonormal exponential bases for L2（[0,1）d）, which are called generalized Fourier bases. Moreo...; 关键词：Spectral sequences orthonormal exponential bases convergence analysis Bochner-Riesz means

Relaxation and Nonoccurrence of the Lavrentiev Phenomenon for Nonconvex Problems: 《Acta Mathematica Sinica,English Series》2013年第6期1185-1198,共14页Farhad HSSEINOV; The paper studies a relaxation of the basic multidimensional variational problem, when the class of admissible functions is endowed with the Lipschitz convergence introduced by Morrey. It is shown that in this setup, ...; 关键词：Multidimensional variational problem RELAXATION Lavrentiev phenomenon

Multidimensional Local Central Limit Theorem of Some Non-uniformly Hyperbolic Systems: 《Acta Mathematica Sinica,English Series》2009年第4期565-580,共16页Hong Qiang XIA; We consider Young＇s nonuniformly hyperbolic system （X, T, u） where u is the SRB measure corresponding to the system （X, T）, and show that if the components of a Holder observable f ： X → R^d are cohomologously ...; 关键词：central limit theorem transfer operator nonuniform hyperbolic diIQ[eomorphism

A Useful Extension of It 's Formula with Applications to Optimal Stopping: 《Acta Mathematica Sinica,English Series》2005年第4期779-786,共8页GeroldALSMEYER MarkusJAEGER; Partially supported by the Deutsche Forschungsgemeinschaft(DFG) under Grant SCHM 677/7-1; Given a continuous semimartingale M = （Mt）t≥〉0 and a d-dimensional continuous process of locally bounded variation V = （V^1,……, V^d）, the multidimensional Ito Formula states that f（Mt, Vt） - f（M0, V0） = ...; 关键词：Multidimensional Ito Formula Continuous semimartingale Brownian motion Geometric Brownian motion Optimal stopping Smooth fit principle American put option

Long-Time Behaviour of the Solutions for the Multidimensional Kolmogorov-Spieqel-Sivashinsky Equation被引量：3: 《Acta Mathematica Sinica,English Series》2002年第3期579-596,共18页Bo Ling GUO Bi Xiang WANG Institute of Applied Physics and Computational Mathematics, P. O. Box 8009. Beijing 100088. P. R. China; In this paper, we study the existence and long-time behaviour of the solutions for the multidimensional Kolmogorov-Spiegel-Sivashinsky equation. We first show the existence of the global solution for this equation, an...; 关键词：Global solution Approximate inertial manifold Gevrey class regularity Kolmogorov-Spiegel-Sivashinsky equation

A Hierarchy of Multidimensional Hénon-Heiles Systems: 《Acta Mathematica Sinica,English Series》2000年第3期527-534,共8页Yunbo Zeng Department of Mathematical Sciences,Tsinghua University,Beijing 100084 P.R.China; Supported by National Research Project "Nonlinear Sciences"; A hierarchy of multidimensional Hénon-Heiles(M-H-H)systems are constructed via the x-and t_n-higher-order-constrained flows of KdV hierarchy.The Lax representation for the M-H-H hierarchy is determined from the adjoi...; 关键词：Higher-order constrained flow Multidimensional Hénon-Heiles systems Lax representation Jacobi inversion problem

Dynamic Programming for Multidimensional Stochastic Control Problems被引量：2: 《Acta Mathematica Sinica,English Series》1999年第4期485-506,共22页Jin Ma Department of Mathematics,Purdue University,West Lafayette,IN 47907-1395,U S A E-mail:majin@math.purdue,eduJiongmin Yong Laboratory of Mathematics for Nonlinear Science,Department of Mathematics,and Institute of Mathematical Finance,Fudan University,Shanghai 200433,P.R.China E-mail:jyong@fudan,edu.cn; In this paper we study a general multidimensional diffusion-type stochastic control problem. Our model contains the usual regular control problem,singular control problem and impulse control problem as special cases.U...; 关键词：Stochastic control Dynamic programming Viscosity solutions Singular control Impulse control

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