Results 11 to 20 of about 66,461 (287)
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
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A Survey on the Hausdorff Dimension of Intersections [PDF]
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
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Levy processes: Capacity and Hausdorff dimension
The Annals of Probability, 2005 We use the recently-developed multiparameter theory of additive Levy processes to establish novel connections between an arbitrary Levy process $X$ in $\mathbf{R}^d$, and a new class of energy forms and their corresponding capacities. We then apply these
Khoshnevisan, Davar, Xiao, Yimin
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Simon’s OPUC Hausdorff dimension conjecture [PDF]
Mathematische Annalen, 2021 We show that the Szeg matrices, associated with Verblunsky coefficients $\{ _n\}_{n\in\mathbb{Z}_+}$ obeying $\sum_{n = 0}^\infty n^ | _n|^2 < \infty$ for some $ \in (0,1)$, are bounded for values $z \in \partial \mathbb{D}$ outside a set of Hausdorff dimension no more than $1 - $.
David Damanik +2 more
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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
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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
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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
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Unimodular Hausdorff and Minkowski dimensions [PDF]
Electronic Journal of Probability, 2021 This work introduces two new notions of dimension, namely the unimodular Minkowski and Hausdorff dimensions, which are inspired from the classical analogous notions. These dimensions are defined for unimodular discrete spaces, introduced in this work, which provide a common generalization to stationary point processes under their Palm version and ...
Baccelli, François +2 more
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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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GAN‐LSTM‐3D: An efficient method for lung tumour 3D reconstruction enhanced by attention‐based LSTM
CAAI Transactions on Intelligence Technology, EarlyView., 2023 Abstract Three‐dimensional (3D) image reconstruction of tumours can visualise their structures with precision and high resolution. In this article, GAN‐LSTM‐3D method is proposed for 3D reconstruction of lung cancer tumours from 2D CT images. Our method consists of three phases: lung segmentation, tumour segmentation, and tumour 3D reconstruction. Lung
Lu Hong +12 more
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