The density theorem and Hausdorff inequality for packing measure in general metric spaces
Illinois Journal of Mathematics, 1995 There are two basic mechanisms (diameter method and radius method) for extending the definition of Euclidean packing measure to general metric spaces. Although the diameter method has received the most attention in the literature, we show that it is generally inferior to the radius method in preserving the desirable properties of Euclidean packing ...
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On entropy and Hausdorff dimension of measures defined through a non-homogeneous Markov process
, 2003 13 pagesIn this work we study the Hausdorff dimension of measures whose weight distribution satisfies a markov non-homogeneous property. We prove, in particular, that the Hausdorff dimensions of this kind of measures coincide with their lower Rényi ...
Batakis, Athanasios
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Self-Conformal Multifractal Measures
, 1997 A self-conformal measure is a measure invariant under a set of conformal mappings. In this paper we describe the local structure of self-conformal measures.
Patzschke, Norbert
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A multiscale generative model to understand disorder in domain boundaries. [PDF]
Sci Adv, 2023 Dan J +6 more
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The Multifractal Spectrum of Quasi Self-Similar Measures
, 1997 We define the notion of quasi self-similar measures and show that for such measures their generalised Hausdorff and packing measures are positive and finite at the critical exponent.
O'Neil, Toby C
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Neural network-assisted automated image registration for MRI-guided adaptive brachytherapy in cervical cancer. [PDF]
Z Med Phys, 2022 Ecker S +8 more
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Conical upper density theorems and porosity of measures
, 2008 We study how measures with finite lower density are distributed around (n−m)-planes in small balls in Rn. We also discuss relations between conical upper density theorems and porosity.
Käenmäki, Antti, Suomala, Ville
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A Comprehensive Survey with Quantitative Comparison of Image Analysis Methods for Microorganism Biovolume Measurements. [PDF]
Arch Comput Methods Eng, 2023 Zhang J +8 more
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Hausdorff measures and packing premeasures
Hausdorff measures and packing premeasuresWe estimate the HausdorR measures and the packing premeasures of symmetric generalized Cantor sets in the d-dimensional Euclidean space R^d. Two simple estimations will be obtained. Let φ_1 and φ_2 be two measure functions. Suppose limt_(t→0) φ_2(t)/φ_1(t) = 0, limt_(t→0) φ_2(t)/t^d = ∞, and φ_1(t)/t^d is strictly decreasing as t increases. Then we can
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Graph fractal dimension and the structure of fractal networks. [PDF]
J Complex Netw, 2020 Skums P, Bunimovich L.
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