云南高校图书馆联盟文献共享服务平台- HAUSDORFF

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>>

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

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

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

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

HITTING PROBABILITIES AND INTERSECTIONS OF TIME-SPACE ANISOTROPIC RANDOM FIELDS被引量：1: 《Acta Mathematica Scientia》2022年第2期653-670,共18页Jun WANG Zhenlong CHEN; supported by National NaturalScience Foundation of China(11971432);Natural Science Foundation of Zhejiang Province(LY21G010003);First Class Discipline of Zhejiang-A(Zhejiang Gongshang University-Statistics);the Natural Science Foundation of Chuzhou University(zrjz2019012)。; Let X^(H)={X^(H)(s),s∈R^(N_(1))}and X^(K)={X^(K)(t),t∈R^(N_(2))}be two independent time-space anisotropic random fields with indices H∈(0,1)^(N_(1)) and K∈(0,1)^(N_(2)),which may not possess Gaussianity,and which ...; 关键词：Hitting probability multiple intersection anisotropic random field capacity Hausdorff dimension stochastic fractional heat equations

AN UPBOUND OF HAUSDORFF’S DIMENSION OF THE DIVERGENCE SET OF THE FRACTIONAL SCHRODINGER OPERATOR ON H^(s)(R^(n))被引量：1: 《Acta Mathematica Scientia》2021年第4期1223-1249,共27页Dan LI Junfeng LI Jie XIAO; Li Dan and Li Junfeng were supported by NSFC-DFG(11761131002);NSFC(12071052);Xiao Jie was supported by NSERC of Canada(202979463102000).; Given n≥2 and α≥1/2,we obtained an improved upbound of Hausdorff's dimension of the fractional Schrodinger operator;that is,supf∈H^(s)(R^(n)) dim_(H){x∈R^(n):limt→0 e^(it)(-△)^(α) f(x)≠f(x)}≤n+1-2(n+1)s/n fo...; 关键词：The Carleson problem divergence set the fractional Schrodinger operator Hausdorff dimension Sobolev space

REGULARITY OF WEAK SOLUTIONS TO A CLASS OF NONLINEAR PROBLEM: 《Acta Mathematica Scientia》2021年第4期1333-1365,共33页Jianfeng ZHOU Zhong TAN; The first author is partially supported by the Postdoctoral Science Foundation of China(2019TQ0006);the second author is partially supported by the National Natural Science Foundation of China(11726023,11531010).; We study the regularity of weak solutions to a class of second order parabolic system under only the assumption of continuous coefficients.We prove that the weak solution u to such system is locally Holder continuous ...; 关键词：Parabolic system REGULARITY weak solution HausdorfF dimension

ON POINTS CONTAIN ARITHMETIC PROGRESSIONS IN THEIR LROTH EXPANSION被引量：1: 《Acta Mathematica Scientia》2016年第1期257-264,共8页张振亮曹春云; supported by NSFC(11326206,11426111); For any x ∈ （0, 1] （except at most countably many points）, there exists a unique sequence {dn（x）}n≥1 of integers, called the digit sequence of x, such that x =∞ ∑j=1 1/d1（x）（d1（x）-1）……dj-1（x）（dj-1...; 关键词：Luroth expansion arithmetic progression Hausdorff dimension

ARBITRARILY LONG ARITHMETIC PROGRESSIONS FOR CONTINUED FRACTIONS OF LAURENT SERIES被引量：3: 《Acta Mathematica Scientia》2013年第4期943-949,共7页胡动刚胡学海; supported by NSFC(11001093,10901066); A famous theorem of Szemer＇edi asserts that any subset of integers with posi- tive upper density contains arbitrarily arithmetic progressions. Let Fq be a finite field with q elements and Fq（（X^-1）） be the power ...; 关键词：Szemeredi theorem continued fractions Laurent series Hausdorff dimension

FRACTAL PROPERTIES OF POLAR SETS OF RANDOM STRING PROCESSES被引量：1: 《Acta Mathematica Scientia》2011年第3期969-992,共24页陈振龙; supported by the Natural Science Foundation of Zhejiang Province(Y6100663); This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary condition...; 关键词：random string process hitting probability polar set Hausdorff dimension

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