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HAUSDORFF_DIMENSION: 作品数：158被引量：118H指数：5; 导出分析报告; 相关作者：王贺元钟婷姜海益陆式盘杨竹莘更多>>; 相关机构：辽宁工业大学东北财经大学浙江大学武汉大学更多>>; 相关期刊：《Journal of Partial Differential Equations》《Applied Mathematics》《Communications in Mathematical Research》《Acta Mathematica Sinica,English Series》更多>>; 相关基金：国家自然科学基金上海市自然科学基金广东省自然科学基金武汉大学校科研和教改项目更多>>

Hausdorff Dimension of Range and Graph for General Markov Processes: 《应用概率统计》2024年第6期942-956,共15页CHEN Zhi-He; supported by Leshan Normal University Scientific Research Start-up Project for Introducing High-level Talents(Grand No.RC2024001).; We establish the Hausdorff dimension of the graph of general Markov processes on Rd based on some probability estimates of the processes staying or leaving small balls in small time.In particular,our results indicate ...; 关键词：Markov process Hausdorff dimension RANGE GRAPH

MULTIFRACTAL ANALYSIS OF CONVERGENCE EXPONENTS FOR PRODUCTS OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS: 《Acta Mathematica Scientia》2024年第4期1594-1608,共15页Lulu FANG Jihua MA Kunkun SONG Xin YANG; supported by the Scientific Research Fund of Hunan Provincial Education Department(21B0070);the Natural Science Foundation of Jiangsu Province(BK20231452);the Fundamental Research Funds for the Central Universities(30922010809);the National Natural Science Foundation of China(11801591,11971195,12071171,12171107,12201207,12371072)。; For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction expansion.We study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflects t...; 关键词：continued fractions product of partial quotients Hausdorff dimension

The Global Attractor and Its Dimension Estimation of Generalized Kolmogorov-Petrovlkii-Piskunov Equation: 《Journal of Applied Mathematics and Physics》2024年第4期1178-1187,共10页Yuhuai Liao; In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set ar...; 关键词：Generalized Kolmogorov-Petrovlkii-Piskunov Equation Existence of Solution Hausdorff Dimension Fractal Dimension

ON THE GRAPHS OF PRODUCTS OF CONTINUOUS FUNCTIONS AND FRACTAL DIMENSIONS: 《Acta Mathematica Scientia》2023年第6期2483-2492,共10页刘佳石赛赛张远; supported by the NSFC (11701001,11626030);the Support Plan for Outstanding Young Talents in Colleges in Anhui Province (Key project) (gxyqzD2020021);the Scientific Research Project of Colleges and Universities in Anhui Province,2023。; In this paper,we consider the graph of the product of continuous functions in terms of Hausdorff and packing dimensions.More precisely,we show that,given a real number 1≤β≤2,any real-valued continuous function in C...; 关键词：Hausdorff dimension packing dimension graph of function product of functions

Partial Regularity of Suitable Weak Solutions of the Model Arising in Amorphous Molecular Beam Epitaxy: 《Acta Mathematica Sinica,English Series》2023年第11期2219-2246,共28页Yan Qing WANG Yi Ke HUANG Gang WU Dao Guo ZHOU; the National Natural Science Foundation of China(Grant Nos.11971446,11601492,11771423 and12071113);Natural Science Foundation of He’nan(Grant No.232300421077);Research Start-up Funding Program of Hangzhou Normal University(Grant No.4235C50223204065)。; In this paper,we are concerned with the precise relationship between the Hausdorff dimension of possible singular point set S of suitable weak solutions and the parameterαin the nonlinear term in the following parabo...; 关键词：Surface growth model modified Navier–Stokes equations partial regularity Hausdorff dimension

THE HAUSDORFF DIMENSION OF THE SPECTRUM OF A CLASS OF GENERALIZED THUE-MORSE HAMILTONIANS: 《Acta Mathematica Scientia》2023年第5期1997-2004,共8页刘庆晖唐志毅; supported by the National Natural ScienceFoundation of China(11871098)。; Letτbe a generalized Thue-Morse substitution on a two-letter alphabet{a,b}:τ(a)=ambm,τ(b)=bmam for the integer m≥2.Letξbe a sequence in{a,b}Z that is generated byτ.We study the one-dimensional Schr?dinger operat...; 关键词：one-dimensional Schrodinger operator generalized Thue-Morse sequence Hausdorff dimension

Dimension Estimate of the Global Attractor for a 3D Brinkman-Forchheimer Equation被引量：1: 《Wuhan University Journal of Natural Sciences》2023年第1期1-10,共10页SONG Xueli DENG Xi QIAO Baoming; Supported by the National Natural Science Foundation of China(12001420)。; In this paper,we study the dimension estimate of global attractor for a 3D Brinkman-Forchheimer equation.Based on the differentiability of the semigroup with respect to the initial data,we show that the global attract...; 关键词：Brinkman-Forchheimer equation global attractor Hausdorff dimension fractal dimension

A Carleson Problem for the Boussinesq Operator: 《Acta Mathematica Sinica,English Series》2023年第1期119-148,共30页Dan LI Jun Feng LI; supported by NSFC(Grant No.12071052);the Fundamental Research Funds for the Central Universities;supported by the Research Initiation Fund for Young Teachers of Beijing Technology and Business University(Grant No.QNJJ2021-02)。; In this paper,we show that the Boussinesq operator B_(t)f converges pointwise to its initial data.f∈H^(s)(R)as t→0 provided s≥1/4-more precisely-on one hand,by constructing a counterexample in R we discover that th...; 关键词：Carleson problem Boussinesq operator pointwise convergence Hausdorff dimension Sobolev space

Trigonometric multiplicative chaos and applications to random distributions: 《Science China Mathematics》2023年第1期3-36,共34页Aihua Fan Yves Meyer; supported by National Natural Science Foundation of China (Grant No.11971192)。; The random trigonometric series∑∞n=1ρn cos(nt+ωn)on the circle T are studied under the conditions∑|ρn|^(2)=∞andρn→0,where{ωn}are independent and uniformly distributed random variables on T.They are almost su...; 关键词：multiplicative chaos random Fourier series Hausdorff dimension Riesz potential

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

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