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MULTIFRACTAL PHENOMENA AND PACKING DIMENSION [PDF]
Revista Matemática Iberoamericana, 2016 We undertake a general study of multifractal phenomena for functions. We show that the existence of several kinds of multifractal functions can be easily deduced from an abstract statement, leading to new results.
Bayart, Frédéric, Heurteaux, Yanick
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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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Packing-Dimension Profiles and Fractional Brownian Motion [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2007 In order to compute the packing dimension of orthogonal projections Falconer and Howroyd (1997) introduced a family of packing dimension profiles ${\rm Dim}_s$ that are parametrized by real numbers $s>0$.
DAVAR KHOSHNEVISAN +4 more
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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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The fractal characteristics of cement-based materials with grinding aid via BSE image analysis [PDF]
Scientific ReportsEnergy conservation and emission reduction are crucial for the cement industry to meet “carbon peak” and “carbon neutrality” targets, with a particular emphasis on grinding aids.
Chunfu Wang, Yuling Wang, Yunfeng Pan
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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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Orthogonal Packings in Two Dimensions [PDF]
SIAM Journal on Computing, 1980 We consider problems of packing an arbitrary collection of rectangular pieces into an open-ended, rectangular bin so as to minimize the height achieved by any piece. This problem has numerous applications in operations research and studies of computer operation.
Baker, Brenda S. +2 more
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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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