Results 41 to 50 of about 65,125 (273)
Rigidity, Graphs and Hausdorff Dimension [PDF]
, 2021 For a compact set $E \subset \mathbb R^d$ and a connected graph $G$ on $k+1$ vertices, we define a $G$-framework to be a collection of $k+1$ points in $E$ such that the distance between a pair of points is specified if the corresponding vertices of $G$ are connected by an edge.
Nikolaos Chatzikonstantinou +3 more
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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
doaj +1 more source
Extremal manifolds and Hausdorff dimension [PDF]
Duke Mathematical Journal, 2000 Let \(U\) be an open set in \(\mathbb{R}^n\) where \(m\leq n\). \textit{V. G. Sprindzhuk} conjectured that if the functions \(\theta_j: U\to \mathbb{R}\), \(j= 1,\dots, n\), are analytic and together with 1, independent over \(\mathbb{R}\), then the manifold \[ \{[\theta_1(u),\dots, \theta_n(u)]: u\in U\}= \theta(U) \subset \mathbb{R}^n \] is extremal.
Dickinson, H., Dodson, M. M.
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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
doaj
Automated Segmentation of the Pituitary and Pineal Glands. [PDF]
Hum Brain MappThis work presents a deep‐learning‐based tool for automatic segmentation of the pituitary and pineal glands. It has two novel aspects: it considers the anterior and posterior lobes as separate labels rather than a single, combined structure, and it is also the first deep‐learning protocol for pineal gland segmentation. ABSTRACT The pituitary and pineal
Larson KE +6 more
europepmc +2 more sources
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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Univoque bases and Hausdorff dimension
Monatshefte für Mathematik, 2017 Given a positive integer $M$ and a real number $q >1$, a \emph{$q$-expansion} of a real number $x$ is a sequence $(c_i)=c_1c_2\cdots$ with $(c_i) \in \{0,\ldots,M\}^\infty$ such that \[x=\sum_{i=1}^{\infty} c_iq^{-i}.\] It is well known that if $q \in (1,M+1]$, then each $x \in I_q:=\left[0,M/(q-1)\right]$ has a $q$-expansion.
Fan Lü +4 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 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
core +5 more sources