Results 301 to 310 of about 325,035 (334)

Scaling properties of Hausdorff and packing measures

Mathematische Annalen, 2001
Let \(\theta \) 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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The measurement of packing and contraction in chromosomes

Chromosoma, 1939
The observations of lengths of chromosomes in salivary glands at pachytene and in mitotic and meiotic metaphases are consistent with the observed coiling of the chromosomes in mitosis and meiosis in plants, animals and Protista, and with the doubly-refractive properties of the chromomeres and chromosomes, on various possible assumptions with regard to ...
C. D. Darlington, M. B. Upcott
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Hausdorff and packing dimensions and sections of measures

Mathematika, 1998
Summary: 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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The packing dimension of projections and sections of measures

Mathematical Proceedings of the Cambridge Philosophical Society, 1996
AbstractWe show that for a probability measure μ on ℝnfor almost all m–dimensional subspaces V, provided dimH μ≤m. Here projv denotes orthogonal projection onto V, and dimH and dimp denote the Hausdorff and packing dimension of a measure. In the case dimH μ > m we show that at μ-almost all points x the slices of μ by almost all (n − m)-planes Vx ...
Pertti Mattila, Kenneth J. Falconer
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The packing measure of rectifiable subsets of the plane

Mathematical Proceedings of the Cambridge Philosophical Society, 1986
It is usual to define Lebesgue outer measure in ℝ by using economical coverings by a sequence of open intervals. We start by outlining a different definition which gives the same answer for a bounded measurable E ⊂ ℝ. PutThen λ0 defines a pre-measure, but is not an outer measure because it is not countably sub-additive.
S. James Taylor, Claude Tricot
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Packing dimension, intersection measures, and isometries

Mathematical Proceedings of the Cambridge Philosophical Society, 1997
Let \(\mu\) and \(\nu\) be Radon probability measures on \(\mathbb{R}^n\). If \(f:\mathbb{R}^n\to \mathbb{R}^n\) is some isometry then \(f_\#\nu\) denotes the image measure of \(\nu\) with respect to \(f\). The intersection measure \(\mu\cap f_\#\nu\) of \(\mu\) and \(f_\#\nu\) is defined as follows: Let \(f=\tau_z\circ g\) be the representation of \(f\
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The packing measure of self-affine carpets

Mathematical Proceedings of the Cambridge Philosophical Society, 1994
AbstractWe show that the seif-affine sets considered by McMullen [15] and Bedford [2] have infinite packing measure in their packing dimension θ except when all non-empty rows of the initial pattern have the same number of rectangles. More precisely, the packing measure is infinite in the gauge tθ|logt|−1 and zero in the gauge tθ|logt|−1−δ for any δ ...
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Concerning the packing dimension of intersection measures

Mathematical Proceedings of the Cambridge Philosophical Society, 1997
Summary: For a Radon probability measure \(\mu\) on \(\mathbb{R}^n\) we can use the Hausdorff dimension \(\dim_{\text{H}}\) and the packing dimension \(\dim_{\text{p}}\) to define lower indices \[ \dim_{\text{H}}\mu= \inf\{\dim_{\text{H}}A:A\text{ is a Borel set and }\mu(A)>0\} \] and \[ \dim_{\text{p}}\mu= \inf\{\dim_{\text{p}}A:A\text{ is a Borel set
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Time to add screening for financial hardship as a quality measure?

Ca-A Cancer Journal for Clinicians, 2021
Cathy J Bradley, K Robin Yabroff, Ya-Chen Tina Shih   +2 more
exaly  

A minimal common outcome measure set for COVID-19 clinical research

Lancet Infectious Diseases, The, 2020
Srinivas Murthy, Derek C Angus, Yaseen M Arabi   +2 more
exaly