Results 41 to 50 of about 66,461 (287)
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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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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Irrationality exponent, Hausdorff dimension and effectivization [PDF]
, 2017 We generalize the classical theorem by Jarnik and Besicovitch on the irrationality exponents of real numbers and Hausdorff dimension and show that the two notions are independent. For any real number a greater than or equal to 2 and any non-negative real
Becher, Veronica Andrea +2 more
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Axioms, 2021 In this speculative analysis, interdimensionality is introduced as the (co)existence of universes embedded into larger ones. These interdimensional universes may be isolated or intertwined, suggesting a variety of interdimensional intrinsic phenomena ...
Karl Svozil
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Hausdorff Dimension and Quasiconformal Mappings [PDF]
Journal of the London Mathematical Society, 1973 Peer Reviewed ; http://deepblue.lib.umich.edu/bitstream/2027.42/135677/1/jlms0504 ...
Gehring, F. W., Väisälä, J.
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Hausdorff dimension of some groups acting on the binary tree
, 2006 Based on the work of Abercrombie, Barnea and Shalev gave an explicit formula for the Hausdorff dimension of a group acting on a rooted tree. We focus here on the binary tree T.
Aleshin S. V. +2 more
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ON THE MUTUAL MULTIFRACTAL ANALYSIS FOR SOME NON-REGULAR MORAN MEASURES
Проблемы анализа, 2023 In this paper, we study the mutual multifractal Hausdorff dimension and the packing dimension of level sets 𝐾(𝛼, 𝛽) for some non-regular Moran measures satisfying the so-called Strong Separation Condition.We obtain sufficient conditions for the valid ...
B. Selmi, N. Yu. Svetova
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Hausdorff dimension of three-period orbits in Birkhoff billiards
, 2011 We prove that the Hausdorff dimension of the set of three-period orbits in classical billiards is at most one. Moreover, if the set of three-period orbits has Hausdorff dimension one, then it has a tangent line at almost every point.Comment: 10 pages, 1 ...
Falconer K J +6 more
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Anyons and fractional quantum Hall effect in fractal dimensions
Physical Review Research, 2020 The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. Here, we construct a different type of fractional quantum Hall system, which has the special property that it lives in fractal ...
Sourav Manna +3 more
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Hausdorff Dimension and mean porosity [PDF]
Mathematische Annalen, 1997 Let \(E \subset R^n\) be a compact set and assume that there exists \(c \in (0, 1/2)\) such that for every \(x \in E\) and all \(r \in (0, d(E)/2),\) the ball \(B^n(x,r)\) contains a ball of radius \(cr\) not meeting \(E \). Then no point of \(E\) can be a point of density and hence \(E \) has \(n\)-dimensional Lebesgue measure equal to \(0\). In fact,
Koskela, Pekka, Rohde, Steffen
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