Cantor尘的Hausdorff测度估计

Cantor dust is a classical fractal set .It is very important to compute its Hausdorff measure.In this Paper,we obtained the expression and approximation of Hausdorff measure of Cantor dust through the analysis of interpolation function of a certain of mass distribution defined on Cantor dust.     

THE MULTIFRACTAL HAUSDORFF AND PACKING MEASURE OF GENERAL SIERPINSKI CARPETS

1 IntroductionThe self-affine sets include self-similar sets as their special case. Although the fractalproperties of self-similar sets are well understood, little is known about self-affine sets in general.McMullen[1] studied a class of self~affine sets called generlized Sierpinski carpets, and got theirHausdorff and box dimensions. King[2] got the singular spectrum of general Sierpinski carpets.In [3] Olsen introduced the multifratal Hausdorff ajnd packing measure. and use them tostudy th…     

两条相互独立的非对称Cauchy过程轨道的乘积集的分形性质

设Ｘ１,Ｘ２是Ｒ＾ｄ上两条相互独立的非对称Ｃａｕｃｈｙ过程,我们求出了,两条轨道的乘积集的确切Ｈａｕｓｄｏｒｆｆ测度函数ψ（ｈ）＝ｈ＾２／ｌｏｇ＾ｈ,同时ψ（ｈ）,同时ψ（ｈ）也是图集的乘积集的确切Ｈａｕｓｄｏｒｆｆ测度函数,另外,我们还求出了乘积集的Ｈａｕｓｄｏｒｆｆ维数和Ｐａｃｋｉｎｇ维数均为２,从而证明了乘 集仍然是分形集。     

关于广义齐次自相似集上Hausdorff测度的一个特征

设E是Hausdorff测度正有限的广义齐次自相似集,本文证明了s维Hausdorff测度是E上唯一的非扩张概率测度.     

THE HAUSDORFF MEASURE OF SIERPINSKI CARPETS BASING ON REGULAR PENTAGON

In this paper,we address the problem of exact computation of the Hausdorff measure of a class of Sierpinski carpets E the self-similar sets generating in a unit regular pentagon on the plane.Under some conditions,we show the natural covering is the best one,and the Hausdorff measures of those sets are euqal to | E | s,where s=dim H E.     

含参变量Cantor集的Hausdorff测度

本文研究了菱形为基本集所构成的的广义Cantor集的Hausdorff测度问题.利用菱形几何结构的相关证明方法,获得了此类广义Cantor集的Hausdorff测度准确值,推广了曾超益和许绍元等人的已有结果.     

Cantor集的自乘积集的Hausdorff测度的下界

证明了三分Cantor集C的自乘积集C×C的Hausdorff测度满足 H~(log_3)~4(C×C)≥1.48329。     

有限型子集的Hausdorff测度

给出了有限型子集的Hausdorff测度的一个估计,改进了已有的结果。     

HAUSDORFF DIMENSION OF THE DOUBLE POINT SET OF THE WESTWATER PROCESS

Let X={X_i}_(t∈[0,1])be the Westwater process which is the coordinate process under3-dimensional polymer measure v(g)constructed by J.Westwater.In this paper,theHausdorff dimension problem for the double point set of X is investigated.As a result,it is proved thatdim D_2=1,v(g)-a.e.,where D_2={x∈R~3:X=X_(?)=x for some s相似文献   

THE HAUSDORFF DIMENSION AND MEASURE IN GENERALIZED GEOMETRIC GRAPH DIRECTED CONSTRUCTION

1GeneralizedGeometricGraphDirectedContructionAgenera1izedgeometricgraphdirectedconstructioninR"consistof(1)afinitesequence0fnonoverlapping,compactsubsetsofRm:J1,J2,''tJn.SuchthateachJihasanonemptyinterior,(2)adirectedgeaPh{G}withvertexsetconsistingoftheintegers1,'',n,andsiAn-laritymapsTf?)ofR".where(i,j)EG,withratiost::),suchthat(a)foreachi,1Si5n.thereissomejsuchthat(i,j)EG.(b)foreachi,{ri:)(J,)I(i,i)EG}isanon0verlappingfandlyand(c)ifthepathc0mponentofGr0tedattheyertexi1isacycIe:Fo…     

一类均匀康托集的Hausdorff中心测度

本文研究了均匀2n部分康托集的Hausdorff中心测度.利用极大中心密度与Hausdorff 中心测度之间的关系,确定了均匀2n部分康托集Hausdorff中心测度的精确值.     

经典分形集测度上估的计算机搜索Ⅱ──对典型例子Sierpinski垫片计数技术和格点跟踪技术的剖析

A upper estimate function ν(x) of Hausdorff measure Hs (S) ofSierpinski Gasket is given. A mathematical representation of the upperapproximate value νN (x) to ν(x) and a simple algorithm ofνN (x) based on lattice tracing technique are also derived. As asimple corollary, the estimation Hs(S)≤ min ν15 (n·10-5)=ν15 (0.50783)=0.81794 …is obtained.     

The HAUSDORFF DIMENSION AND MEASURE OF THE GENERALIZED MORAN FRACTALS AND FOURIER SERIES

ＴｈｅＨＡＵＳＤＯＲＦＦＤＩＭＥＮＳＩＯＮＡＮＤＭＥＡＳＵＲＥＯＦＴＨＥＧＥＮＥＲＡＬＩＺＥＤＭＯＲＡＮＦＲＡＣＴＡＬＳＡＮＤＦＯＵＲＩＥＲＳＥＲＩＥＳ￥ＲＥＮＦＵＴｈＯ；ＬＩＡＮＧＪＩＮＲＯＮＧＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒｓｔｕｄｉｅｓｔｈ...     

一类齐次Moran集的Hausdorff测度

本文研究了一类新的齐次Moran集.利用x~s(0s1)的凸性方法,获得了它的Hausdorff测度,推广了齐次cantor集的结果.     

一类广义Sierpinski海绵的填充测度

对于m2的任何整数m,本文定义了R~m中的一类广义 Sierpinski海绵,同时给出了该类海绵的填充测度的计算公式.     

N指标d维广义Wiener过程像集的一致维数

研究了N指标d维广义Wiener过程像集的一致维数和测度，得到了其像集的致Hausdorff维数和一致Packing维数。     

ON THE STRUCTURES OF RANDOM MEASURE AND POINT PROCESS CONVOLUTION SEMIGROUPS

§0.ＩｎｔｒｏｄｕｃｔｉｏｎＫｅｎｄａｌｌ[1]ｆｏｕｎｄｅｄｔｈｅＤｅｌｐｈｉｃｓｅｍｉｇｒｏｕｐｔｈｅｏｒｙａｎｄｕｓｅｄｔｈｉｓｔｈｅｏｒｙｔｏｓｔｕｄｙｔｈｅｓｔｒｕｃｔｕｒｅｓｏｆｔｈｅｒｅｎｅｗａｌｓｅｑｕｅｎｃｅｓｅｍｉｇｒｏｕｐａｎｄｔｈｅｓｔａｎｄａｒｄｐ-ｆｕｎｃｔｉｏｎｓｅｍｉｇｒｏｕｐ.Ｄａｖｉｄｓｏｎ[2,3],ＲｕｚｓａａｎｄＳｚ啨ｋｅｌｙ[4]ａｎｄＨｅ[5,6]ｇｅｎｅｒａｌｉｚｅｄｔｈｅＤｅｌｐｈｉｃｓｅｍｉｇｒｏｕｐｔｈｅｏｒｙａｎｄｕｓｅｄｔｈｅｉｒｒｅｓｕｌｔｓｔｏｓｔｕｄ…