Results 1 to 10 of about 144,663 (264)
Packing dimension of mean porous measures [PDF]
Journal of the London Mathematical Society, 2009 We prove that the packing dimension of any mean porous Radon measure on $\mathbb R^d$ may be estimated from above by a function which depends on mean porosity. The upper bound tends to $d-1$ as mean porosity tends to its maximum value.
Beliaev, D. +6 more
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On the densest packing of polycylinders in any dimension [PDF]
Discrete & Computational Geometry, 2016 Using transversality and a dimension reduction argument, a result of A. Bezdek and W. Kuperberg is applied to polycylinders $\mathbb{D}^2\times \mathbb{R}^n$, showing that the optimal packing density is $\pi/\sqrt{12}$ in any dimension.Comment: Edited to
Kusner, Wöden
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The sphere packing problem in dimension 24 [PDF]
Annals of Mathematics, 2017 Building on Viazovska's recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing.
Cohn, H. +4 more
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Randomness extraction and asymptotic Hamming distance [PDF]
Logical Methods in Computer Science, 2013 We obtain a non-implication result in the Medvedev degrees by studying sequences that are close to Martin-L\"of random in asymptotic Hamming distance. Our result is that the class of stochastically bi-immune sets is not Medvedev reducible to the class of
Cameron E. Freer, Bjoern Kjos-Hanssen
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On distance sets, box-counting and Ahlfors-regular sets [PDF]
Discrete Analysis, 2017 On distance sets, box-counting and Ahlfors-regular sets, Discrete Analysis 2017:9, 22 pp. A well-known problem of Falconer, a sort of continuous analogue of the Erdős distinct-distance problem, asks how large the Hausdorff dimension of a Borel subset of
Pablo Shmerkin
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The Second Generalization of the Hausdorff Dimension Theorem for Random Fractals
Mathematics, 2022 In this paper, we present a second partial solution for the problem of cardinality calculation of the set of fractals for its subcategory of the random virtual ones.
Mohsen Soltanifar
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Packing dimensions of basins generated by distributions on a finite alphabet
Журнал Белорусского государственного университета: Математика, информатика, 2021 We consider a space of infinite signals composed of letters from a finite alphabet. Each signal generates a sequence of empirical measures on the alphabet and the limit set corresponding to this sequence.
Victor I. Bakhtin, Bruno Sadok
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Optimizing e-commerce warehousing through open dimension management in a three-dimensional bin packing system [PDF]
PeerJ Computer Science, 2023 In the field of e-commerce warehousing, maximizing the utilization of packing bins is a fundamental goal for all major logistics enterprises. However, determining the appropriate size of packing bins poses a practical challenge for many logistics ...
Jianglong Yang +6 more
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Multifractal phenomena and packing dimension [PDF]
Revista Matemática Iberoamericana, 2019 We undertake a general study of multifractal phenomena for functions or measures. We show that the existence of several kinds of multifractal functions or measures can be easily deduced from an abstract statement, leading to new results. This general approach does not work for Fourier or Dirichlet series.
Bayart, Frédéric, Heurteaux, Yanick
openaire +4 more sources
On the Fractal Measures and Dimensions of Image Measures on a Class of Moran Sets
Mathematics, 2023 In this work, we focus on the centered Hausdorff measure, the packing measure, and the Hewitt–Stromberg measure that determines the modified lower box dimension Moran fractal sets. The equivalence of these measures for a class of Moran is shown by having
Najmeddine Attia, Bilel Selmi
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