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FRACTAL: 作品数：971被引量：1490H指数：15; 导出分析报告; 相关领域：理学更多>>; 相关作者：李后强赵华明谢和平盛京邢修三更多>>; 相关机构：中国科学院北京理工大学四川大学武汉大学更多>>; 相关期刊：更多>>; 相关基金：国家自然科学基金国家重点基础研究发展计划中国博士后科学基金国家教育部博士点基金更多>>

Geodesic metrics on fractals and applications to heat kernel estimates: 《Science China Mathematics》2023年第5期907-934,共28页Qingsong Gu Ka-Sing Lau Hua Qiu Huo-Jun Ruan; supported by National Natural Science Foundation of China(Grant Nos.12101303 and 12171354);supported by National Natural Science Foundation of China(Grant No.12071213);supported by National Natural Science Foundation of China(Grant No.11771391);supported by the Hong Kong Research Grant Council;the Natural Science Foundation of Jiangsu Province in China(Grant No.BK20211142);Zhejiang Provincial National Science Foundation of China(Grant No.LY22A010023);the Fundamental Research Funds for the Central Universities of China(Grant No.2021FZZX001-01)。; It is well known that for a Brownian motion, if we change the medium to be inhomogeneous by a measure μ, then the new motion(the time-changed process) will diffuse according to a different metric D(·, ·).In 2009, K...; 关键词：Brownian motion heat kernel metric chain condition nested fractal quasisymmetry resistance metric Sierpinski carpet weight function

Spectral decimation for a graph-directed fractal pair: 《Science China Mathematics》2022年第12期2503-2520,共18页Shiping Cao Hua Qiu Haoran Tian Lijian Yang; supported by National Natural Science Foundation of China(Grant No.12071213);the Natural Science Foundation of Jiangsu Province in China(Grant No.BK20211142);。; We introduce a graph-directed pair of planar self-similar sets that possess fully symmetric Laplacians. For these two fractals, due to Shima’s celebrated criterion, we point out that one admits the spectral decimatio...; 关键词：fractal Laplacian spectral decimation Dirichlet spectrum Neumann spectrum

Self-similar fractals: An algorithmic point of view: 《Science China Mathematics》2014年第4期755-766,共12页WANG Qin XI LiFeng ZHANG Kai; supported by National Natural Science Foundation of China(Grants Nos.11071224 and 11371329);Program for New Century Excellent Talents in University;Natural Science Foundation of Zhejiang Province(Grants Nos.LY12F02011 and LR13A1010001);Foundation of Zhejiang Educational Committee(Grant No.Y201226044); This paper studies the self-similar fractals with overlaps from an algorithmic point of view.A decidable problem is a question such that there is an algorithm to answer"yes"or"no"to the question for every possible inp...; 关键词：FRACTAL DECIDABILITY DIMENSION separation condition

New schemes with fractal error compensation for PDE eigenvalue computations被引量：6: 《Science China Mathematics》2014年第2期221-244,共24页SUN JiaChang; supported by National Natural Science Foundation of China (Grant Nos.60970089,61170075 and 91230109); With an error compensation term in the fractal Rayleigh quotient of PDE eigen-problems,we propose a new scheme by perturbing the mass matrix Mhto Mh=Mh+Ch2mKh,where Khis the corresponding stif matrix of a 2m 1 degree ...; 关键词：PDE eigenvalues computation generalized matrix eigen-problem discrete Rayleigh quotient

Martin boundary and exit space on the Sierpinski gasket被引量：2: 《Science China Mathematics》2012年第3期475-494,共20页LAU Ka-Sing NGAI Sze-Man; We define a new Markov chain on the symbolic space representing the Sierpinski gasket (SG),and show that the corresponding Martin boundary is homeomorphic to the SG while the minimal Martin boundary is the three verti...; 关键词：Martin boundary Markov chain Green function harmonic function FRACTAL Sierpinski gasket

Quasi-Lipschitz equivalence of quasi Ahlfors-David regular sets被引量：3: 《Science China Mathematics》2011年第12期2573-2582,共10页WANG Qin XI LiFeng; supported by the Program for New Century Excellent Talents in University of China;National Natural Science Foundation of China (Grant No. 11071224); Suppose compact sets E and F are quasi uniformly disconnected and quasi Ahlfors-David regular.This paper proves that E and F are quasi-Lipschitz equivalent if and only if they have the same Hausdorff dimension.; 关键词：FRACTAL quasi-Lipschitz equivalence Ahlfors-David regularity

Lipschitz equivalence of self-similar sets with triangular pattern: 《Science China Mathematics》2011年第5期1019-1026,共8页ZHU ZhiYong XIONG Ying XI LiFeng; supported by National Natural Science of China (Grant Nos. 11071224, 11071082, 11071090, 10671180, 10631040);Natural Science Foundation of Ningbo (Grant No. 2009A610077);the Fundamental Research Funds for the Central Universities, SCUT;the Science Foundation for the Youth of South China University of Technology (Grant No. E5090470); In this paper, we discuss the Lipschitz equivalence of self-similar sets with triangular pattern. This is a generalization of {1, 3, 5}-{1, 4, 5} problem proposed by David and Semmes. It is proved that if two such sel...; 关键词：FRACTAL Lipschitz equivalence triangular pattern self-similar set

Sharp Lipschitz constant of bi-Lipschitz automorphism on Cantor set被引量：1: 《Science China Mathematics》2009年第4期709-719,共11页XIONG Ying WANG LiSha XI LiFeng; supported by National Natural Science Foundation of China (Grant Nos. 10671180, 10571140,10571063, 10631040, 11071164);Morningside Center of Mathematics; Suppose C r = (r C r ) ∪ (r C r + 1 ? r) is a self-similar set with r ∈ (0, 1/2), and Aut(C r ) is the set of all bi-Lipschitz automorphisms on C r . This paper proves that there exists f* ∈ Aut(C r ) such that $$ ...; 关键词：FRACTAL bi-Lipschitz automorphism Cantor set 28A80

Sliding of self-similar sets被引量：7: 《Science China Mathematics》2007年第3期351-360,共10页Li-feng XI Huo-jun RUAN Qiu-li GUO; This work Was partially supported by the National Natural Science Foundation of China(Grant Nos.10301029,10671180,10571063,10601049); This paper deals with the Lipschitz equivalence of slidings of self-similar sets by graph-directed construction and martingale theory.; 关键词：FRACTAL self-similar set Lipschitz equivalence 28A80

Comparison of fractal measures: 《Science China Mathematics》2005年第11期1545-1553,共9页QU Yanhui,WEN Shengyou & WEN Zhiying Department of Mathematics,Tsinghua University,Beijing 100084,China Department of Mathematics,Hubei University, Wuhan 430062, China; In this paper, the relationship between the s-dimensional Hausdorff measures and the g-measures in Rd is discussed, where g is a gauge function which is equivalent to ts and 0 < s≤d. It shows that if s=d, then Hg = c...; 关键词：gauge function Hausdorff measure central Hausdorff measure packing measure.

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