Results 21 to 30 of about 2,931,499 (197)
Multiscale Analysis of 1-rectifiable Measures II: Characterizations
Analysis and Geometry in Metric Spaces, 2017 A measure is 1-rectifiable if there is a countable union of finite length curves whose complement has zero measure. We characterize 1-rectifiable Radon measures μ in n-dimensional Euclidean space for all n ≥ 2 in terms of positivity of the lower density ...
Badger Matthew, Schul Raanan
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Mathematics, 2021 In this paper, a tripled fractional differential system is introduced as three associated impulsive equations. The existence investigation of the solution is based on contraction principle and measures of noncompactness in terms of tripled fixed point ...
Sina Etemad +3 more
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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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Dimension and measure for generic continuous images [PDF]
, 2013 This work is supported by EPSRC Doctoral Training GrantsWe consider the Banach space consisting of continuous functions from an arbitrary uncountable compact metric space, X, into R-n.
James T. Hyde +9 more
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On optimal polyline simplification using the Hausdorff and Fréchet distance
Journal of Computational Geometry, 2020 We revisit the classical polygonal line simplification problem and study it using the Hausdorff distance and Fréchet distance. Interestingly, no previous authors studied line simplification under these measures in its pure form, namely: for a given ε ...
Marc van Kreveld +2 more
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Polyline simplification has cubic complexity
Journal of Computational Geometry, 2021 $\DeclareMathOperator{\poly}{poly}$In the classic polyline simplification problem, given a polygonal curve~$P$ consisting of $n$ vertices and an error threshold $\delta \geq 0$, we want to replace $P$ by a subsequence~$Q$ of minimal size such that the ...
Karl Bringmann, Bhaskar Ray Chaudhury
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Exact dimensionality and projections of random self-similar measures and sets [PDF]
, 2014 We study the geometric properties of random multiplicative cascade measures defined on self-similar sets. We show that such measures and their projections and sections are almost surely exact dimensional, generalizing a result of Feng and Hu's for self ...
Jin, Xiong +4 more
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Discrete Dynamics in Nature and Society, 2021 In this study, considering the traditional geometric operation laws and Pythagorean fuzzy information, we propose a variety of new distance measures of Pythagorean fuzzy sets such as generalized Pythagorean fuzzy geometric distance (GPFGD) measures and ...
Lingyan Meng, Xiaoyan Wei
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Hausdorff h-measures and p-modules
Journal of Numerical Analysis and Approximation Theory, 1978 Not available.
Petru Caraman
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Carleson Measure and Tent Spaces on the Siegel Upper Half Space
Abstract and Applied Analysis, 2012 The Hausdorff capacity on the Heisenberg group is introduced. The Choquet integrals with respect to the Hausdorff capacity on the Heisenberg group are defined. Then the fractional Carleson measures on the Siegel upper half space are discussed.
Kai Zhao
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