共查询到18条相似文献,搜索用时 187 毫秒
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本文证明了两个正则齐次均匀Moran集拟Lipschitz等价当且仅当它们的Hausdorff维数相等. 相似文献
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《数学物理学报(A辑)》2016,(5)
该文构造了一类特殊的齐次Moran集,称为{m_k}-拟齐次Cantor集,并讨论了它们的packing维数.通过调整序列{m_k}_(k≥1)的值,构造性证明了齐次Moran集packing维数的介值定理.此外,还得到了齐次Moran集的packing维数取得最小值的一个充分条件. 相似文献
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本文研究了随机压缩向量满足一定条件下的随机Moran集的分形维数.利用计算上盒维数的上界和分形维数之间的性质,得到Moran集各种分形维数. 并在一般情形下,给出随机Moran集的上盒维数的上界. 相似文献
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《数学物理学报(A辑)》2020,(3)
该文利用连通分支与其间隔构造了一类特殊的齐次Moran集:{m_k}-拟齐次完全集,并证明该集合在sup{m_k}有限的条件下其上盒维数与packing维数可以达到所有齐次Moran集的最小值,并得到该集合在一定条件下上盒维数取值范围,并找到了上盒维数取到精确表达式所需的一个充分条件. 相似文献
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丰德军等人在他们的相关的论文中介绍了齐次均匀康托集和偏齐次均匀康托集,在本文中我们构造介于两者之间的一类齐次Moran集,给出其豪斯多夫维数的精确计算公式,并讨论维数关于参数的不连续性. 相似文献
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本文研究了填充维数与上盒维数的关系.利用Cantor-Bendixson定理的方法,得到了由上盒维数给出的填充维数的等价定义.并证明了齐次Moran集对上盒维数和填充维数的连续性. 相似文献
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作为Cantor型集的推广,文志英和吴军引入了齐次完全集的概念,并基于齐次完全集的基本区间的长度以及基本区间之间的间隔的长度,得到了齐次完全集的Hausdorff维数.本文研究齐次完全集的拟对称极小性,证明在某些条件下Hausdorff维数为1的齐次完全集是1维拟对称极小的. 相似文献
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In the paper, we try to classify Moran fractals by using the quasi-Lipschitz equivalence, and prove that two regular homogeneous Moran sets are quasi-Lipschitz equivalent if and only if they have the same Hausdorff dimension. 相似文献
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Yi Wang 《Journal of Mathematical Analysis and Applications》2009,354(2):445-450
In this paper, we consider a class of fractals generated by the Cantor series expansions. By constructing some homogeneous Moran subsets, we prove that these sets have full dimension. 相似文献
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This paper provides an explicit formula for the Hausdorff measures of a class of regular homogeneous Moran sets. In particular, this provides, for the first time, an example of an explicit formula for the Hausdorff measure of a fractal set whose Hausdorff dimension is greater than 1. 相似文献
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We give a general construction of the probability measure for describing stochastic fractals that model fractally disordered
media. For these stochastic fractals, we introduce the notion of a metrically homogeneous fractal Hansdorff-Karathéodory measure
of a nonrandom type. We select a classF[q] of random point fields with Markovian refinements for which we explicitly construct the probability distribution. We prove
that under rather weak conditions, the fractal dimension D for random fields of this class is a self-averaging quantity and
a fractal measure of a nonrandom type (the Hausdorff D-measure) can be defined on these fractals with probability 1.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 3, pp. 490–505, September, 2000. 相似文献
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We solve Gromov's dimension comparison problem for Hausdorff and box counting dimension on Carnot groups equipped with a Carnot-Carathéodory metric and an adapted Euclidean metric. The proofs use sharp covering theorems relating optimal mutual coverings of Euclidean and Carnot-Carathéodory balls, and elements of sub-Riemannian fractal geometry associated to horizontal self-similar iterated function systems on Carnot groups. Inspired by Falconer's work on almost sure dimensions of Euclidean self-affine fractals we show that Carnot-Carathéodory self-similar fractals are almost surely horizontal. As a consequence we obtain explicit dimension formulae for invariant sets of Euclidean iterated function systems of polynomial type. Jet space Carnot groups provide a rich source of examples. 相似文献
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Xiaomei Hu 《Czechoslovak Mathematical Journal》2016,66(1):127-135
We construct a class of special homogeneous Moran sets, called {mk}-quasi homogeneous Cantor sets, and discuss their Hausdorff dimensions. By adjusting the value of {mk}k?1, we constructively prove the intermediate value theorem for the homogeneous Moran set. Moreover, we obtain a sufficient condition for the Hausdorff dimension of ho- mogeneous Moran sets to assume the minimum value, which expands earlier works. 相似文献
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In this paper, we shall study the multifractal decomposition behavior for a family of sets E known as Moran fractals. For each value of the parameter α ∈ (αmin, αmax), we define “multifractal components” Eα of E, and show that they are non-regularity fractals (in the sense of Taylor). By obtaining the new sufficient conditions for the valid multifractal formalisms of non-regularity Moran measures, we give explicit formula for the Hausdorff dimension and Packing dimension of Eα respectively. In particular, we describe a large class of non-regularity Moran measure satisfying the explicit formula. 相似文献
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There exist several sets having similar structure on arbitrarily small scales. Mandelbrot called such sets fractals, and defined a dimension that assigns non-integer numbers to fractals. On the other hand, a dynamical system yielding a fractal set referred to as a strange attractor is a chaotic map. In this paper, a characterization of self-similarity for attractors is attempted by means of conditional entropy. 相似文献