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MRI parcellation of ex vivo medial temporal lobe. [PDF]
Augustinack JC +5 more
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Conserved structural chemistry for incision activity in structurally non-homologous apurinic/apyrimidinic endonuclease APE1 and endonuclease IV DNA repair enzymes. [PDF]
Tsutakawa SE +15 more
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ESICM LIVES 2024. Barcelona, Spain. 5–9 October 2024. [PDF]
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Hausdorff and packing measure for solenoids
Ergodic Theory and Dynamical Systems, 2003Summary: We prove that the solenoid with two different contraction coefficients has zero Hausdorff and positive packing measure in its own dimension and the SBR measure is equivalent to the packing measure on the attractor. Further, we prove similar statements for Slanting Baker maps with intersecting cylinders (in \(\mathbb{R}^{2}\)).
Károly Simon, Michał Rams
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Hausdorff and packing dimensions and sections of measures
Mathematika, 1998Summary: Let \(m\) and \(n\) be integers with \(0< m< n\) and let \(\mu\) be a Radon measure on \(\mathbb{R}^n\) with compact support. For the Hausdorff dimension, \(\dim_H\), of sections of measures we have the following equality: for almost all \((n- m)\)-dimensional linear subspaces \(V\) \[ \text{ess inf}\{\dim_H \mu_{V,a}: a\in V^{\perp}\text ...
Maarit Järvenpää, Pertti Mattila
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Scaling properties of Hausdorff and packing measures
Mathematische Annalen, 2001Let \(\theta \) be a continuous increasing function defined on the nonnegative number line with some restriction. Among other results, the authors characterize those function \(\theta \) such that the corresponding Hausdorff or packing measure with gauge function \(\theta \) scales with exponent \(\alpha \) by showing it must be a product of a power ...
Marianna Csörnyei, R. D. Mauldin
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Comparing Packing Measures to Hausdorff Measures on the Line [PDF]
In this paper the author compare packing measures to Hausdorff measures on the line. The main result of this paper is as follows.
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Hausdorff and packing dimensions of Mandelbrot measure
International Journal of Mathematics, 2020We develop, in the context of the boundary of a supercritical Galton–Watson tree, a uniform version of large deviation estimate on homogeneous trees to estimate almost surely and simultaneously the Hausdorff and packing dimensions of the Mandelbrot measure over a suitable set [Formula: see text].
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