Results 21 to 30 of about 3,791,283 (277)
On the Hausdorff dimension of pinned distance sets [PDF]
Israel Journal of Mathematics, 2017 We prove that if A is a Borel set in the plane of equal Hausdorff and packing dimension s > 1, then the set of pinned distances {|x − y| : y ∈ A} has full Hausdorff dimension for all x outside of a set of Hausdorff dimension 1 (in particular, for many x ∈
Pablo Shmerkin
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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
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Dimensions and singular traces for spectral triples, with applications to fractals [PDF]
, 1992 Given a spectral triple (A,D,H), the functionals on A of the form a -> tau_omega(a|D|^(-t)) are studied, where tau_omega is a singular trace, and omega is a generalised limit.
Guido, Daniele, Isola, Tommaso
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Hausdorff dimension of unions of affine subspaces and of Furstenberg-type sets [PDF]
Journal of Fractal Geometry, 2017 We prove that for any $1 \le ...
K. Héra, Tam'as Keleti, András Máthé
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Physically based method for determining the Hausdorff’s topological dimension of capillary-porous media [PDF]
BIO Web of ConferencesThe soil structure the solid phase and pore space of the soils are a set of self-similar parts of each other at different levels ( for example, on level aggregates, micro-aggregates or elementary particles of soil).
Moiseev Kirill +3 more
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On the construction, properties and Hausdorff dimension of random Cantor one pth set
AIMS Mathematics, 2020 In 1883, German Mathematician George Cantor introduced Cantor ternary set which is a self-similar fractal. K. J. Falconer (1990) defined random Cantor set with statistical self-similarity.
Sudesh Kumari +3 more
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International Journal of Mathematics and Mathematical Sciences, 1995 We define the coordinate d-dimension print to distinguish sets of same fractal dimension, and investigate its geometrical properties.
Hung Hwan Lee, In Soo Baek
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Exceptional directions for the Teichmüller geodesic flow and Hausdorff dimension [PDF]
Journal of the European Mathematical Society (Print), 2017 We prove that for every flat surface $\omega$, the Hausdorff dimension of the set of directions in which Teichmuller geodesics starting from $\omega$ exhibit a definite amount of deviation from the correct limit in Birkhoff's and Oseledets' Theorems is ...
Hamid Al-Saqban +5 more
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Analysis and Geometry in Metric Spaces, 2020 This paper studies the Hausdorff dimension of the intersection of isotropic projections of subsets of ℝ2n, as well as dimension of intersections of sets with isotropic planes. It is shown that if A and B are Borel subsets of ℝ2n of dimension greater than
Román-García Fernando
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Hausdorff dimension of random limsup sets [PDF]
Journal of the London Mathematical Society, 2016 We prove bounds for the almost sure value of the Hausdorff dimension of the limsup set of a sequence of balls in Rd whose centres are independent, identically distributed random variables.
Fredrik Ekström, T. Persson
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