Results 41 to 50 of about 3,791,283 (277)
On the Hausdorff Dimension of CAT(κ) Surfaces
Analysis and Geometry in Metric Spaces, 2016 We prove that a closed surface with a CAT(κ) metric has Hausdorff dimension = 2, and that there are uniform upper and lower bounds on the two-dimensional Hausdorff measure of small metric balls.
Constantine David, Lafont Jean-François
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Gaussian Random Particles with Flexible Hausdorff Dimension [PDF]
Advances in Applied Probability, 2015 Gaussian particles provide a flexible framework for modelling and simulating three-dimensional star-shaped random sets. In our framework, the radial function of the particle arises from a kernel smoothing, and is associated with an isotropic random field
L. V. Hansen +4 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 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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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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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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Advanced Intelligent Systems, EarlyView.Soft robots capable of morphing into various 3D shapes are crucial for applications like human‐machine interfaces and biological manipulation. However, controlling 3D shape‐morphing robots with soft actuators remains a challenge. This work introduces a machine learning model that maps complex 3D deformations to control inputs, enabling robots to mimic ...
Jue Wang +3 more
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Fractional dimension of some exceptional sets in continued fractions
Comptes Rendus. MathématiqueIn this paper, we calculate the Hausdorff dimension of some exceptional sets that emerge from specific constraints imposed on the partial quotients of continued fractions.
Hussain, Mumtaz +2 more
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On sets containing a unit distance in every direction
Discrete Analysis, 2021 On sets containing a unit distance in every direction, Discrete Analysis 2021:5, 13 pp. A _Kakeya set_ in $\mathbb R^d$ is a subset $A\subset\mathbb R^d$ that contains a line in every direction. Besicovitch famously proved that a Kakeya set in $\mathbb
Pablo Shmerkin, Han Yu
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