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 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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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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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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ON THE MUTUAL MULTIFRACTAL ANALYSIS FOR SOME NON-REGULAR MORAN MEASURES
Проблемы анализа, 2023 In this paper, we study the mutual multifractal Hausdorff dimension and the packing dimension of level sets 𝐾(𝛼, 𝛽) for some non-regular Moran measures satisfying the so-called Strong Separation Condition.We obtain sufficient conditions for the valid ...
B. Selmi, N. Yu. Svetova
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Some Dimensional Results of a Class of Homogeneous Moran Sets
Journal of Mathematics, 2021 In this paper, we construct a class of special homogeneous Moran sets: mk-quasi-homogeneous perfect sets, and obtain the Hausdorff dimension of the sets under some conditions.
Jingru Zhang, Yanzhe Li, Manli Lou
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Quasi-Packing Different Spheres with Ratio Conditions in a Spherical Container
Mathematics, 2023 This paper considers the optimized packing of different spheres into a given spherical container under non-standard placement conditions. A sphere is considered placed in the container if at least a certain part of the sphere is in the container. Spheres
Andreas Fischer +4 more
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