Results 291 to 300 of about 325,035 (334)
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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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A Packing Problem for Measurable Sets
Canadian Journal of Mathematics, 1967Given a probability measure space (Ω,,P)consider the followingpacking problem.What is the maximum number,b(K,Λ), of sets which may be chosen fromso that each set has measureKand no two sets have intersection of measure larger than Λ <K?In this paper the packing problem is solved for any non-atomic probability measure space. Rather than obtaining the
David Sankoff, Donald A. Dawson
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Some Relations Between Packing Premeasure and Packing Measure
Bulletin of the London Mathematical Society, 1999Summary: Let \(K\) be a compact subset of \(\mathbb{R}^n\), \(0\leq s\leq n\). Let \(P^s_0\), \({\mathcal P}^s\) denote \(s\)-dimensional packing premeasure and measure, respectively. We discuss in this paper the relation between \(P^s_0\) and \({\mathcal P}^s\). We prove: if \(P^s_0(K)< \infty\), then \({\mathcal P}^s(K)= P^s_0(K)\); and if \(P^s_0(K)=
Zhi-Ying Wen, De-Jun Feng, Su Hua
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Comparing Packing Measures to Hausdorff Measures on the Line [PDF]
Mathematische Nachrichten, 2002 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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Packing Measure Analysis of Harmonic Measure
Journal of the London Mathematical Society, 1995We prove a conjecture of James Taylor that for any simply connected domain \(\Omega \subset R^2\) there is a subset \(E \subset \partial \Omega\) of full harmonic measure such that \(E\) has packing dimension 1. The results of Markov ensure that there exists a subset \(E\) of full harmonic measure with Hausdorff dimension 1.
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Packing Measure and Dimension of Random Fractals
Journal of Theoretical Probability, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
R. Daniel Mauldin, Artemi Berlinkov
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Measurement of Granular Material Packing
AIP Conference Proceedings, 2009Granular material packing is of considerable importance when considering the stability and shear strength of granular media. It has been shown in various studies that the shear strength of granular media is influenced by inherent particle characteristics such as shape, angularity, surface texture and mineralogy. In this study, granular material packing
Michael Bloom +7 more
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Some Measure-Theoretic Properties of Packing Measure
Periodica Mathematica Hungarica, 1998This paper is an informal discussion of some fundamental measure-theoretic differences between the families of measures known as packing measures and Hausdorff measures. Two main issues of focus are, whether or not a set of infinite measure necessarily contains a subset of positive finite measure, and the question of Borel regularity.
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Measurement of Packing and Spacing of Photoreceptors
Imaging and Applied Optics, 2011We developed two automated methods for measuring the hexagon size and the fraction of hexagonally packed cones. Density is mostly set by adjacent cones, decreasing with eccentricity. High frequencies are also being sampled in the periphery.
Erez N. Ribak, Nizan Meitav
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Radiography Measurements of Particle Packing
Nature, 1969Measurements of particle packing by radiography have been analysed in terms of a general geometrical model.
J. R. F. Arthur, T. Dunstan
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