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A note on the Hausdorff dimension of uniformly non flat sets with plenty\n of big projections [PDF]
, 2021 Michele Villa
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Hausdorff dimension of wild fractals [PDF]
Transactions of the American Mathematical Society, 1992 We show that for every s ∈ [ n − 2 , n ] s \in [n - 2,n] there exists a homogeneously embedded wild Cantor set C s {C^s} in R n , n ≥ 3
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Noncommutative space–time and Hausdorff dimension [PDF]
International Journal of Modern Physics A, 2017 We study the Hausdorff dimension of the path of a quantum particle in noncommutative space–time. We show that the Hausdorff dimension depends on the deformation parameter [Formula: see text] and the resolution [Formula: see text] for both nonrelativistic and relativistic quantum particle.
Anjana, V., Harikumar, E., Kapoor, A. K.
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Numerical estimates of Hausdorff dimension [PDF]
Journal of Computational Physics, 1982 Numerical methods for estimating Hausdorff dimension, useful in the analysis of turbulence, are explained and applied to a specific example. In particular, methods involving rescaling and approximation by Cantor sets are discussed.
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Hidden Positivity and a New Approach to Numerical Computation of Hausdorff Dimension: Higher Order Methods [PDF]
, 2020 Richard S. Falk, Roger D. Nussbaum
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Harmonic Measure Is Absolutely Continuous with Respect to the Hausdorff Measure on All Low-Dimensional Uniformly Rectifiable Sets [PDF]
, 2022 Guy David, Svitlana Mayboroda
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Hausdorff Dimension of Centered Sets
Real Analysis Exchange, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Hausdorff Dimension and Gaussian Fields
The Annals of Probability, 1977 Let $X(t)$ be a Gaussian process taking values in $R^d$ and with its parameter in $R^N$. Then if $X_j$ has stationary increments and the function $\sigma^2(t) = E\{|X_j(s + t) - X_j(s)|^2\}$ behaves like $|t|^{2\alpha}$ as $|t| \downarrow 0, 0 < \alpha < 1$, the graph of $X$ has Hausdorff dimension $\min \{N/\alpha, N + d(1 - \alpha)\}$ with ...
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Hausdorff Dimension in Stochastic Dispersion
Journal of Statistical Physics, 2002 26 ...
Dolgopyat, D., Kaloshin, V., Koralov, L.
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Singular dimension of spaces of real functions
Le Matematiche, 2007 Let X be a space of measurable real functions defined on a fixed open set Ω ⊆ R^N . It is natural to define the singular dimension of X as the supremum of Hausdorff dimension of singular sets of all functions in X.We say that f ∈ X is a maximally ...
Darko Žubrinić
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