Results 71 to 80 of about 20,938 (205)
Three Cubes Packing for All Dimensions
AlgorithmsLet Vn(d) denote the least number such that every collection of nd-cubes with total volume 1 in d-dimensional (Euclidean) space can be packed parallelly into some d-box of volume Vn(d). We show that V3(d)=r1−dd if d≥11 and V3(d)=1r+1rd+1r−rd+1 if 2≤d≤10, where r is the only solution of the equation 2(d−1)kd+dkd−1=1 on 22,1 and (k+1)d(1−k)d−1dk2+d+k−1 ...
openaire +2 more sources
Packing-dimension profiles and fractional Brownian motion
, 2008 In order to compute the packing dimension of orthogonal projections Falconer and Howroyd (1997) have introduced a family of packing dimension profiles Dims that are parametrized by real numbers s> 0. Subsequently, Howroyd (2001) introduced alternate s-
Yimin Xiao, Davar Khoshnevisan
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Defence TechnologyTwo-dimensional energetic materials (2DEMs), characterized by their exceptional interlayer sliding properties, are recognized as exemplar of low-sensitivity energetic materials.
Xiaokai He +6 more
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Dagstuhl Reports : Volume 1, Issue 2, February 2011
, 2011 Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs ...
Schloss Dagstuhl, Leibniz-Zentrum für Informatik
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Directed graph iterated function systems
, 2011 This thesis concerns an active research area within fractal geometry. In the first part, in Chapters 2 and 3, for directed graph iterated function systems (IFSs) defined on ℝ, we prove that a class of 2-vertex directed graph IFSs have attractors that ...
Boore, Graeme C.
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Bowen's equations for upper metric mean dimension with potential
, 2022 Firstly, we introduce a new notion called induced upper metric mean dimension with potential, which naturally generalizes the definition of upper metric mean dimension with potential given by Tsukamoto to more general cases, then we establish variational
Yang, Rui, Zhou, Xiaoyao, Chen, Ercai
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On distance sets, box-counting and Ahlfors-regular sets
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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Effective packing dimension of Π 0 1-classes
, 2007 We construct a Π0 1-class X that has classical packing dimension 0 and effective packing dimension 1. This implies that, unlike in the case of effective Hausdorff dimension, there is no natural correspondence principle (as defined by Lutz) for effective ...
Chris J. Conidis
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The complexity of combinatorial optimization problems on d‐dimensional boxes [PDF]
, 2007 The Maximum Independent Set problem in d-box graphs, i.e., in intersection graphs of axis-parallel rectangles in R-d, is known to be NP-hard for any fixed d >= 2.
Chlebikova, Janka +5 more
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Hardness and Approximability of Dimension Reduction on the Probability Simplex
AlgorithmsDimension reduction is a technique used to transform data from a high-dimensional space into a lower-dimensional space, aiming to retain as much of the original information as possible.
Roberto Bruno
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