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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.
Berlinkov, Artemi, Mauldin, R. Daniel
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Hausdorff, Similarity, and Packing Dimensions
2020In this chapter we consider three fractal dimensions of a geometric object \({\varOmega } \subset {\mathbb {R}}^E\):
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1988
We propose and motivate a new variant of the wellknown two-dimensional binpacking problem (orthogonal and oriented rectangle packing). In our model, we are allowed to cut a rectangle and move the parts horizontally. We describe two relatively simple algorithms for this problem and determine their asymptotic performance ratios.
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We propose and motivate a new variant of the wellknown two-dimensional binpacking problem (orthogonal and oriented rectangle packing). In our model, we are allowed to cut a rectangle and move the parts horizontally. We describe two relatively simple algorithms for this problem and determine their asymptotic performance ratios.
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Hermitian widths, mean dimension, and multiple packings
Sbornik: Mathematics, 1996The paper deals with problems of approximation in the space \(H^\mu_p\) with the norm \(|u|_{p,\mu} =|\mu {\mathcal F} u|_{L_p (E_n)}\) where \(\mu\) is a weight function, \(1\leq p\leq \infty\) and \({\mathcal F}\) is the Fourier transform. The approximating subspaces are the closed linear hull of the shifts of \(N\) fixed functions with respect to a ...
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Packing dimensions of homogeneous perfect sets
Acta Mathematica Hungarica, 2007A class of Cantor-like sets on the line, the homogeneous perfect sets, were defined by \textit{Z.-Y.~Wen} and \textit{J.~Wu} [Acta Math. Hungar. 107, 35--44 (2005; Zbl 1082.28008)] where their Hausdorff and lower box-counting dimensions were computed under certain conditions in terms of the basic parameters of the construction.
Wang, X.-Y., Wu, Jun
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Packing dimensions of sections of sets
Mathematical Proceedings of the Cambridge Philosophical Society, 1999We 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.
Falconer, K. J., Järvenpää, M.
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Box and packing dimensions of projections and dimension profiles
Mathematical Proceedings of the Cambridge Philosophical Society, 2001For 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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Packing dimension, intersection measures, and isometries
Mathematical Proceedings of the Cambridge Philosophical Society, 1997Let \(\mu\) 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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Packing dimension estimation for exceptional parameters
Israel Journal of Mathematics, 2002Let \(V\) 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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