Results 241 to 250 of about 144,663 (264)

Packing dimensions of projections and dimension profiles

Mathematical Proceedings of the Cambridge Philosophical Society, 1997
Let \(E\subset\mathbb{R}^n\) be an analytic set and \(\mu\in{\mathfrak M}^+_c(E)\) a finite Borel measure on \(E\) with compact support. For a real number \(s\) with \(0\leq s\leq n\) put \[ F^\mu_s(x,r)= \int_{\mathbb{R}^n}\min\{1,r^s|y-x|^{-s}\}d\mu(y).
J. D. Howroyd, Kenneth J. Falconer
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Packing dimensions of sections of sets

Mathematical Proceedings of the Cambridge Philosophical Society, 1999
We obtain a formula for the essential supremum of the packing dimensions of the sections of sets parallel to a given subspace. This depends on a variant of packing dimension defined in terms of local projections of sets.
Kenneth J. Falconer, M. Järvenpää
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Packing Measure and Dimension of Random Fractals

Journal of Theoretical Probability, 2002
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R. Daniel Mauldin, Artemi Berlinkov
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Packing dimension, Hausdorff dimension and Cartesian product sets [PDF]

Mathematical Proceedings of the Cambridge Philosophical Society, 1996
AbstractWe show that the dimension adim introduced by R. Kaufman (1987) coincides with the packing dimension Dim, but the dimension aDim introduced by Hu and Taylor [7] is different from the Hausdorff dimension. These results answer questions raised by Hu and Taylor.
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Box and packing dimensions of projections and dimension profiles

Mathematical Proceedings of the Cambridge Philosophical Society, 2001
For E a subset of ℝn and s ∈ [0, n] we define upper and lower box dimension profiles, B-dimsE and B-dimsE respectively, that are closely related to the box dimensions of the orthogonal projections of E onto subspaces of ℝn. In particular, the projection of E onto almost all m-dimensional subspaces has upper box dimension B-dimmE and lower box ...
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Species Packing in Two Dimensions

The American Naturalist, 1977
The two-dimensional case for invasion by a species into a resource space occupied by two resident species is considered. Numerical solutions for the condition for invasion were obtained, and invisibility spaces constructed for certain sets of values for the parameters of the system.
Jonathan Roughgarden, Ronald M. Yoshiyama   +1 more
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The regular packing of fibres in three dimensions

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1998
The possible tightest packing of bars of variously shaped cross–sections is investigated in detail. The bars are taken to lie along well–defined directions, e.g. cube edges, face diagonals, etc. The results are used to explore the feasibility of designing a fibrous composite which is both elastically isotropic and contains an appreciable volume ...
J. G. Parkhouse, Anthony Kelly
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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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Fractional Brownian motion and packing dimension [PDF]

Journal of Theoretical Probability, 1996
Let \(X\) be a fractional Brownian motion of index \(\alpha\in]0,1[\), from \(\mathbb{R}\) into \(\mathbb{R}^d\), with \(1>\alpha d\), and let \(\text{Dim }F\) denote the packing dimension of any set \(F\) in \(\mathbb{R}^N\). A compact set \(E\) of \([0,1]\) is constructed, such that \(\text{Dim }X(E)
Michel Talagrand, Yimin Xiao
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Packing dimension estimation for exceptional parameters [PDF]

Israel Journal of Mathematics, 2002
Let \(V\) be an open and bounded subset of \(\mathbb{R}^d\). For each parameter \(t\in \overline{V}\) we consider a conformal iterated function system (IFS) \((f_i(\cdot, t))_{i=1}^k\) in \(\mathbb{R}^d\) depending on the parameter \(t\). By assuming this dependence to be smooth, the author proves: For each \(p\), let \(G_p= \{t\in \overline{V}: \dim_H
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