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1.
满足强分离条件的自相似集的填充测度 总被引:1,自引:0,他引:1
对满足强分离条件的自相似集,本文给出一种估计填充测度下界的方法,称为部分估计原理.利用这种估计方法得出的某些自相似集的填充测度的下界,往往和准确的填充测度值相等. 相似文献
2.
对满足强分离条件的自相似集,本文给出一种估计填充测度下界的方法,称为部分估计原理。利用这种估计方法得出的某些自相似集的填充测度的下界,往往和准确的填充测度值相等 相似文献
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该文讨论满足开集条件的自相似集上的马尔科夫测度,给出了马尔科夫测度具有加倍性质的一个充分必要条件.作为应用,刻画了几个具体的自相似集上具有加倍性质的马尔科夫测度. 相似文献
5.
讨论自相似迭代系统的等价性,在满足开集条件与等缩条件的情况下,除了平凡情形之外,我们给出了迭代系统的等价性的一个十分简洁的充要条件。 相似文献
6.
余旌胡 《数学物理学报(A辑)》2001,21(4):443-452
定义了一类广泛的随机自仿射集,得到了此类集合的Hausdorff维数估计.此前的随机自相似(包括Graf,Mauldin与Falconer等定义的随机自相似情形)和Falconer定义的(严格)自仿射以及作者定义的μ 统计自仿射情形均成为该文结果的特例. 相似文献
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本文研究了Cantor集和其并的自相似性.利用Cantor展式的方法,得到了关于Cantor集和迭代函数系的一个基本关系:T∪(T+α)为自相似的当且仅当存在一个非负整数n使得α=±(k2-k1)dn.进一步,若T∪(T+α)是自相似的,则它满足开集条件. 相似文献
8.
μ-统计自仿射集的Hausdorff维数估计 总被引:1,自引:0,他引:1
本文定义了一类μ-统计自仿射集,得到了其Hausdorff维数的上下估计Falconer定义的(严格)自仿射集及Graf定义的统计自相似情形均为本文特例 相似文献
9.
关于满足强分离开集条件的自相似集的Hausdorff测度 总被引:6,自引:0,他引:6
设E是Rn中由相似压缩S1,S2,…,Sm所确定的满足开集条件的自相似集,其Hausdorff维数为s,其s-维Hausdorff测度记为Hs(E).利用部分估计原理得到了本文的主要结果:若E满足强分离开集条件,则在E中存在一个压缩拷贝串序列{Ui}和紧集U(|U|>0),使得Hs(U)等于|U|s,并且{Ui}按Hausdorff度量收敛到U,进而证明了由U可以构造一个数列,使得该数列正好收敛到Hs(E);另外,引入了自相似集的相似压缩不动点,得到了等式Hs(E∩U)=|U|s 成立的一个必要条件. 相似文献
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本文证明对于满足强分离条件的自相似集E,存在一个闭凸集达到它的最大密度.即存在一个闭凸集V■E0(|V|0),使得sup{μ(U)/|U|s:U■E0}=μ(V)/|V|s,其中U为闭集,E0表示自相似集E的闭凸壳,μ表示E上的唯一自相似概率测度.作为应用,我们给出命题"满足强分离开集条件的自相似集具有最优几乎处处覆盖"的一个新证明. 相似文献
11.
Shaoyuan Xu Weiyi Su 《分析论及其应用》2007,23(4):334-342
Falconer[1] used the relationship between upper convex density and upper spherical density to obtain elementary density bounds for s-sets at H S-almost all points of the sets. In this paper, following Falconer[1], we first provide a basic method to estimate the lower bounds of these two classes of set densities for the self-similar s-sets satisfying the open set condition (OSC), and then obtain elementary density bounds for such fractals at all of their points. In addition, we apply the main results to the famous classical fractals and get some new density bounds. 相似文献
12.
陈振龙 《数学物理学报(B辑英文版)》2011,31(3):969-992
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 conditions for compact sets to be polar for the random string process. Moreover, we also determine the smallest Hausdorff dimensions of non-polar sets by constructing a Cantor-type set to connect its Hausdorff dimension and capacity. 相似文献
13.
N指标d维广义Brownian Sheet的像集及图集的Hausdorff测度 总被引:2,自引:0,他引:2
本文得到了N指标d维广义Brownian Sheet的像集及图集的Hausdorff测度的上、下界. 相似文献
14.
An original algorithm is presented that generates both restricted integer compositions and restricted integer partitions that
can be constrained simultaneously by (a) upper and lower bounds on the number of summands (“parts”) allowed, and (b) upper
and lower bounds on the values of those parts. The algorithm can implement each constraint individually, or no constraints
to generate unrestricted sets of integer compositions or partitions. The algorithm is recursive, based directly on very fundamental
mathematical constructs, and given its generality, reasonably fast with good time complexity. A general, closed form solution
to the open problem of counting the number of integer compositions doubly restricted in this manner also is presented; its
formulaic link to an analogous solution for counting doubly-restricted integer partitions is shown to mirror the algorithmic
link between these two objects. 相似文献
15.
Lilia Yu. Kolotilina 《Numerical Algorithms》2006,42(3-4):247-280
Using a unified approach based on the monotonicity property of the Perron root and its circuit extension, a series of exact two-sided bounds for the Perron root of a nonnegative matrix in terms of paths in the associated directed graph is obtained. A method for deriving the so-called mixed upper bounds is suggested. Based on the upper bounds for the Perron root, new diagonal dominance type conditions for matrices are introduced. The singularity/nonsingularity problem for matrices satisfying such conditions is analyzed, and the associated eigenvalue inclusion sets are presented. In particular, a bridge connecting Gerschgorin disks with Brualdi eigenvalue inclusion sets is found. Extensions to matrices partitioned into blocks are proposed. 相似文献
16.
Mrinal Kanti Roychowdhury 《Israel Journal of Mathematics》2014,201(2):507-523
In this paper, under the open set condition we have determined the lower and upper bounds of the Hausdorff dimensions and the upper box-counting dimensions of the limit sets of hyperbolic recurrent iterated function systems in terms of the unique zeros h and H of the two pressure functions. In addition, we have estimated the bounds of h, H-dimensional Hausdorff and packing measures. The result in this paper generalizes existing results about fractal dimensions of many other iterated function systems. 相似文献
17.
《Applied Mathematics Letters》2000,13(5):47-51
Introducing the concept of extremal subset to solve one open problem raised in [1]: find the conditions for a lower and upper bounds version of a variational inequality. A few applications are given. 相似文献
18.
Doklady Mathematics - Methods for improving upper and lower bounds for various coverings of planar sets are proposed. New bounds for various numbers of partition constituents are presented, and... 相似文献
19.
一类具有上下界的均衡问题 总被引:1,自引:0,他引:1
本文获得一类具有上、下界的抽象均衡问题解的存在性条件, 回答了Isac, Sehgal和Singh提出的一个公开问题,进一步研究了具上、下界及约束条件的抽象均 衡问题,获得了更为深刻的结果. 最后,把上述公开问题推广到两个空间的情形. 相似文献