Results 31 to 40 of about 144,663 (264)
On the packing dimension of Furstenberg sets
Journal d'Analyse Mathématique, 2022 We prove that if $α\in (0,1/2]$, then the packing dimension of a set $E\subset\mathbb{R}^2$ for which there exists a set of lines of dimension $1$ intersecting $E$ in dimension $\ge α$ is at least $1/2+α+c(α)$ for some $c(α)>0$. In particular, this holds for $α$-Furstenberg sets, that is, sets having intersection of Hausdorff dimension $\geα$ with ...
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The packing spectrum for Birkhoff averages on a self-affine repeller [PDF]
, 2010 We consider the multifractal analysis for Birkhoff averages of continuous potentials on a self-affine Sierpi\'{n}ski sponge. In particular, we give a variational principal for the packing dimension of the level sets.
Reeve, Henry WJ
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Some typical properties of dimensions of sets and measures
Abstract and Applied Analysis, 2005 This paper contains a review of recent results concerning typical properties of dimensions of sets and dimensions of measures. In particular, we are interested in the Hausdorff dimension, box dimension, and packing dimension of sets and in the Hausdorff ...
Józef Myjak
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On the Mass Fractal Character of Si-Based Structural Networks in Amorphous Polymer Derived Ceramics
Nanomaterials, 2015 The intermediate-range packing of SiNxC4−x (0 ≤ x ≤ 4) tetrahedra in polysilycarbodiimide and polysilazane-derived amorphous SiCN ceramics is investigated using 29Si spin-lattice relaxation nuclear magnetic resonance (SLR NMR) spectroscopy.
Sabyasachi Sen, Scarlett Widgeon
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Optimized packing multidimensional hyperspheres: a unified approach
Mathematical Biosciences and Engineering, 2020 In this paper an optimized multidimensional hyperspheres packing problem (HPP) is considered for a bounded container. Additional constraints, such as prohibited zones in the container or minimal allowable distances between spheres can also be taken into ...
Yuriy Stoyan +5 more
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Random packing in three dimensions
, 2023 Abstract Unraveling the complexities of random packing in three dimensions has long puzzled physicists. While both experiments and simulations consistently show a maximum density of 64 percent for tightly packed random spheres, we still lack an unambiguous and universally accepted definition of random packing.
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Assouad dimension influences the box and packing dimensions of orthogonal projections [PDF]
Journal of Fractal Geometry, Mathematics of Fractals and Related Topics, 2021 We present several applications of the Assouad dimension, and the related quasi-Assouad dimension and Assouad spectrum, to the box and packing dimensions of orthogonal projections of sets. For example, we show that if the (quasi-)Assouad dimension of F \subseteq\mathbb{R}^n is no ...
Falconer, Kenneth John +2 more
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Experimental and Numerical Studies on Water Cooling Tower Performance [PDF]
Engineering and Technology Journal, 2007 Theoretical and experimental studies were conducted on forced draftwater cooling tower. In such towers, the heat and mass transfer take placefrom the hot water to the bulk air, which passes through the tower.
Waheed Mohammad, Jalal Jalil
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Packing measures and dimensions on cartesian products [PDF]
Publicacions Matemàtiques, 2013 Packing measures and Hewitt-Stromberg measures on products of metric spaces are investigated. New product inequalities for packing and lower packing dimensions are esatblished and used to solve a problem of Hu and Taylor regarding packing dimension.
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The sphere packing problem in dimension $8$ [PDF]
Annals of Mathematics, 2017 22 pages, 2 ...
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