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On the equality of Hausdorff measure and Hausdorff content [PDF]
Journal of Fractal Geometry, Mathematics of Fractals and Related Topics, 2014 We are interested in situations where the Hausdorff measure and Hausdorff content of a set are equal in the critical dimension. Our main result shows that this equality holds for any subset of a self-similar set corresponding to a nontrivial cylinder of ...
Farkas, Ábel, Fraser, Jonathan M.
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A cohomology-based Gromov–Hausdorff metric approach for quantifying molecular similarity [PDF]
Scientific ReportsWe introduce a cohomology-based Gromov–Hausdorff ultrametric method to analyze 1-dimensional and higher-dimensional (co)homology groups, focusing on loops, voids, and higher-dimensional cavity structures in simplicial complexes, to address typical ...
JunJie Wee +3 more
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Hausdorff Measures on Generalized Set Valued Neutrosophic Quadruple Numbers and Decision Making Applications for Adequacy of Online Education [PDF]
Neutrosophic Sets and Systems, 2021 In this paper, we develop a new method of decision-making algorithm with Hausdorff distance and Hausdorff similarity measures based on generalized set-valued neutrosophic quadruple numbers.
Sevilay Şahin +2 more
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Hausdorff measure of quasicircles [PDF]
Advances in Mathematics, 2012 15 ...
Prause, István +2 more
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On intersections of Cantor sets: Hausdorff measure [PDF]
Opuscula Mathematica, 2013 We establish formulas for bounds on the Haudorff measure of the intersection of certain Cantor sets with their translates. As a consequence we obtain a formula for the Hausdorff dimensions of these intersections.
Steen Pedersen, Jason D. Phillips
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A Hausdorff Measure Inequality [PDF]
Transactions of the American Mathematical Society, 1976 We prove that the Hausdorff ( m + k ) (m + k) -measure of a product set is no less than the product of the Hausdorff m-measure of the (measurable) first component set in R m {{\mathbf {R}}^m} and the ...
Gerald Freilich, Lawrence R. Ernst
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The Second Generalization of the Hausdorff Dimension Theorem for Random Fractals
Mathematics, 2022 In this paper, we present a second partial solution for the problem of cardinality calculation of the set of fractals for its subcategory of the random virtual ones.
Mohsen Soltanifar
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Determining the Hausdorff Distance Between Trees in Polynomial Time [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 The Hausdorff distance is a relatively new measure of similarity of graphs. The notion of the Hausdorff distance considers a special kind of a common subgraph of the compared graphs and depends on the structural properties outside of the common subgraph.
Aleksander Kelenc
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European Radiology Experimental, 2021 Average Hausdorff distance is a widely used performance measure to calculate the distance between two point sets. In medical image segmentation, it is used to compare ground truth images with segmentations allowing their ranking.
Orhun Utku Aydin +7 more
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A Generalization of the Hausdorff Dimension Theorem for Deterministic Fractals
Mathematics, 2021 How many fractals exist in nature or the virtual world? In this paper, we partially answer the second question using Mandelbrot’s fundamental definition of fractals and their quantities of the Hausdorff dimension and Lebesgue measure.
Mohsen Soltanifar
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