Results 31 to 40 of about 957,336 (307)
Embedding Properties of sets with finite box-counting dimension [PDF]
, 2019 In this paper we study the regularity of embeddings of finite--dimensional subsets of Banach spaces into Euclidean spaces. In 1999, Hunt and Kaloshin [Nonlinearity 12 1263-1275] introduced the thickness exponent and proved an embedding theorem for ...
Margaris, Alexandros, Robinson, James C.
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Some Dimensional Results of a Class of Homogeneous Moran Sets
Journal of Mathematics, 2021 In this paper, we construct a class of special homogeneous Moran sets: mk-quasi-homogeneous perfect sets, and obtain the Hausdorff dimension of the sets under some conditions.
Jingru Zhang, Yanzhe Li, Manli Lou
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Almost Sure Frequency Independence of the Dimension of the Spectrum of Sturmian Hamiltonians [PDF]
, 2014 We consider the spectrum of discrete Schr\"odinger operators with Sturmian potentials and show that for sufficiently large coupling, its Hausdorff dimension and its upper box counting dimension are the same for Lebesgue almost every value of the ...
A. Girand +18 more
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On the equality of Hausdorff and box counting dimensions [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 1993 By viewing the covers of a fractal as a statistical mechanical system, the exact capacity of a multifractal is computed. The procedure can be extended to any multifractal described by a scaling function to show why the capacity and Hausdorff dimension are expected to be equal.
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Box dimension for graphs of fractal functions [PDF]
Proceedings of the Edinburgh Mathematical Society, 1997 We calculate the box-dimension for a class of nowhere differentiable curves defined by Markov attractors of certain iterated function systems of affine maps.
Gavin Brown, Qinghe Yin
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Some typical properties of dimensions of sets and measures
Abstract and Applied Analysis, 2005 This paper contains a review of recent results concerning typical properties of dimensions of sets and dimensions of measures. In particular, we are interested in the Hausdorff dimension, box dimension, and packing dimension of sets and in the Hausdorff ...
Józef Myjak
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Approximate resolutions and box-counting dimension
Topology and its Applications, 2003 The notion of approximate resolution was introduced and investigated in earlier papers of S. Mardešić and the authors [\textit{S. Mardešić} and \textit{T. Watanabe}, Glas. Mat., III. Ser. 24(44), 587--637 (1989; Zbl 0715.54009); \textit{T. Miyata} and \textit{T. Watanabe}, Topology Appl. 113, No. 1--3, 211--241 (2001; Zbl 0986.54033); \textit{T. Miyata}
Miyata, Takahisa, Watanabe, Tadashi
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Dimension and product structure of hyperbolic measures [PDF]
, 1999 We prove that every hyperbolic measure invariant under a C^{1+\alpha} diffeomorphism of a smooth Riemannian manifold possesses asymptotically ``almost'' local product structure, i.e., its density can be approximated by the product of the densities on ...
Barreira, Luis +2 more
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Fractal Analysis of Overlapping Box Covering Algorithm for Complex Networks
IEEE Access, 2020 Due to extensive research on complex networks, fractal analysis with scale invariance is applied to measure the topological structure and self-similarity of complex networks. Fractal dimension can be used to quantify the fractal properties of the complex
Wei Zheng +4 more
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The multifractal box dimensions of typical measures [PDF]
Fundamenta Mathematicae, 2012 We compute the typical (in the sense of Baire's category theorem) multifractal box dimensions of measures on a compact subset of $\mathbb R^d$. Our results are new even in the context of box dimensions of measures.
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