Results 21 to 30 of about 64,955 (216)
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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A Note on Topological Properties of Non-Hausdorff Manifolds
International Journal of Mathematics and Mathematical Sciences, 2009 The notion of compatible apparition points is introduced for non-Hausdorff manifolds, and properties of these points are studied. It is well known that the Hausdorff property is independent of the other conditions given in the standard definition of a ...
Steven L. Kent +2 more
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On the Fractal Measures and Dimensions of Image Measures on a Class of Moran Sets
Mathematics, 2023 In this work, we focus on the centered Hausdorff measure, the packing measure, and the Hewitt–Stromberg measure that determines the modified lower box dimension Moran fractal sets. The equivalence of these measures for a class of Moran is shown by having
Najmeddine Attia, Bilel Selmi
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Topological Conformal Dimension [PDF]
, 2015 We investigate a quasisymmetrically invariant counterpart of the topological Hausdorff dimension of a metric space. This invariant, called the topological conformal dimension, gives a lower bound on the topological Hausdorff dimension of quasisymmetric ...
DiMarco, Claudio A.
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Hausdorff–Lebesgue Dimension of Attractors [PDF]
International Journal of Bifurcation and Chaos, 2017 Definitions of Hausdorff–Lebesgue measure and dimension are introduced. Combination of Hausdorff and Lebesgue ideas are used. Methods for upper and lower estimations of attractor dimensions are developed.
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Random trees constructed by aggregation [PDF]
, 2016 We study a general procedure that builds random $\mathbb R$-trees by gluing recursively a new branch on a uniform point of the pre-existing tree.
Curien, Nicolas, Haas, Bénédicte
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Topological Hausdorff dimension and Poincaré inequality
Extracta Mathematicae, 2022 A relationship between Poincaré inequalities and the topological Hausdorff dimension is exposed—a lower bound on the dimension of Ahlfors regular spaces satisfying a weak (1, p)-Poincaré inequality is given.
C.A. DiMarco
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On Simon’s Hausdorff Dimension Conjecture [PDF]
, 2021 Barry Simon conjectured in 2005 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 - $. Three of the authors recently proved
Damanik, David +3 more
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Hausdorff dimension of the range and the graph of stable-like processes [PDF]
, 2017 We determine the Hausdorff dimension for the range of a class of pure jump Markov processes in $\mathbb{R}^d$, which turns out to be random and depends on the trajectories of these processes. The key argument is carried out through the SDE representation
Yang, Xiaochuan
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Representations of real numbers induced by probability distributions on $\mathbb{N}$
, 2021 We observe that a probability distribution supported by $\mathbb{N}$, induces a representation of real numbers in [0, 1) with digits in $\mathbb{N}$.
Neunhäuserer, Jörg
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