Results 11 to 20 of about 3,079 (209)
Hausdorff Dimension and Topological Entropies of a Solenoid [PDF]
Entropy, 2020 The purpose of this paper is to elucidate the interrelations between three essentially different concepts: solenoids, topological entropy, and Hausdorff dimension.
Andrzej Biś, Agnieszka Namiecińska
doaj +2 more sources
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
exaly +3 more sources
A Survey on the Hausdorff Dimension of Intersections
Mathematical and Computational Applications, 2023 Let A and B be Borel subsets of the Euclidean n-space with dimA+dimB>n. This is a survey on the following question: what can we say about the Hausdorff dimension of the intersections A∩(g(B)+z) for generic orthogonal transformations g and translations by
Pertti Mattila
doaj +4 more sources
Comparing Two Novel LiDAR‐Based Indices for Quantifying Forest Structural Complexity [PDF]
Ecology and EvolutionForest structural complexity is critical for ecosystem functions, yet standardized metrics for its quantification remain elusive. This study compares two LiDAR‐derived three‐dimensional indices, the box dimension (Db) as a fractal‐based measure, and ...
Tillman Reuter +2 more
doaj +2 more sources
Quantum error correction with fractal topological codes [PDF]
Quantum, 2023 Recently, a class of fractal surface codes (FSCs), has been constructed on fractal lattices with Hausdorff dimension $2+\epsilon$, which admits a fault-tolerant non-Clifford CCZ gate \cite{zhu2021topological}.
Arpit Dua +2 more
doaj +1 more source
The Hausdorff Dimension and Capillary Imbibition
Fractal and Fractional, 2022 The time scaling exponent for the analytical expression of capillary rise ℓ∼tδ for several theoretical fractal curves is derived. It is established that the actual distance of fluid travel in self-avoiding fractals at the first stage of imbibition is in ...
Didier Samayoa +4 more
doaj +1 more source
A Simple Proof of Dvoretzky-Type Theorem for Hausdorff Dimension in Doubling Spaces
Analysis and Geometry in Metric Spaces, 2022 The ultrametric skeleton theorem [Mendel, Naor 2013] implies, among other things, the following nonlinear Dvoretzky-type theorem for Hausdorff dimension: For any 0 < β < α, any compact metric space X of Hausdorff dimension α contains a subset which is ...
Mendel Manor
doaj +1 more source
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
doaj +1 more source
Lowness for effective Hausdorff dimension [PDF]
Journal of Mathematical Logic, 2014 We examine the sequences A that are low for dimension, i.e. those for which the effective (Hausdorff) dimension relative to A is the same as the unrelativized effective dimension. Lowness for dimension is a weakening of lowness for randomness, a central notion in effective randomness.
Steffen Lempp +4 more
openaire +2 more sources
On the Hausdorff dimension of the mather quotient [PDF]
Communications on Pure and Applied Mathematics, 2008 AbstractUnder appropriate assumptions on the dimension of the ambient manifold and the regularity of the Hamiltonian, we show that the Mather quotient is small in term of the Hausdorff dimension. Then we present applications in dynamics. © 2008 Wiley Periodicals, Inc.
Fathi, Albert +2 more
openaire +3 more sources