Results 241 to 250 of about 65,125 (273)

The fiber of persistent homology for trees. [PDF]

J Appl Comput Topol
Beers D, Leygonie J.
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Local Hausdorff dimension

Acta Informatica, 1995
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Helmut Jürgensen, Ludwig Staiger
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On the Hausdorff dimension of fibres

Israel Journal of Mathematics, 1991
The unit square is partitioned into four congruent subsquares, and an arbitrary one of them is deleted. This operation will be applied to all remaining squares ad infinitum. The authors prove that for the resulting limit set \(F\) its fibre sets \(F_ x=\{y\in[0,1]\mid(x,y)\in F\}\) satisfy \(\dim(F_ x)\geq 1/2\) for almost all \(x\in[0,1]\) with ...
Yuval Peres, Itai Bejamini
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Generalized Hausdorff dimension

Mathematika, 1970
It is natural to say that a set S in a metric space has infinite generalized Hausdorff dimension if there is no Hausdorff measure Λh with Λh(S) = 0. In this note we study such sets. We first need some definitions.We say that h(x) is a Hausdorff measure function if it satisfies the conditions:
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On Hausdorff dimension of projections

Mathematika, 1968
Let E be a compact subset of R2, of Hausdorff dimension s > 0 and for each real number t let Ft be the linear set {x1 + tx2: (x1x2) ∈ E}. In this note we shall proveTHEOREM. If s ≤ 1 then Ft has dimension ≥ s, excepting numbers t in a set of dimension ≤ s. If s > 1 then Ft, has positive Lebesgue measure, excepting numbers t in a set of Lebesgue measure
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On the Hausdorff dimensions of distance sets

Mathematika, 1985
The distance set of a subset E of \(R^ n\) is \(D(E)=\{| x- y|:x,y\in E\}.\) If E is analytic (i.e. Suslin), the author uses Fourier transform to derive the following lower bound for the Hausdorff dimension of \(E\): \[ \dim D(E)\geq \min \{1,(\dim E)-(n-1)/2\}. \] Moreover, \(D(E)\) has positive Lebesgue measure if \(\dim E>(n+1)/2\).
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On Hausdorff dimensions of quasiconformal curves

Siberian Mathematical Journal, 1993
The author establishes that a curve \(\Gamma\) is quasiconformal (i.e. the quasiconformal image of a segment) iff it satisfies Ahlfors' condition (that is there exists a constant \(C>1\) such that \[ | z_ 1- z_ 2|+ | z_ 2- z_ 3|\leq C| z_ 1- z_ 3|\quad\text{for all points } z_ 1,z_ 2,z_ 3\in \Gamma \] so that \(z_ 2\) separates \(z_ 1\) and \(z_ 3 ...
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Unitary Transformation of the Electronic Hamiltonian with an Exact Quadratic Truncation of the Baker-Campbell-Hausdorff Expansion

Journal of Chemical Theory and Computation, 2021
Robert A Lang, Ilya G Ryabinkin, Artur F Izmaylov   +2 more
exaly  

A fuzzy rough set approach to hierarchical feature selection based on Hausdorff distance

Applied Intelligence, 2022
Hong Zhao
exaly