Results 11 to 20 of about 9,371 (281)
Hausdorff measure on o-minimal structures [PDF]
The Journal of Symbolic Logic, 2012 AbstractWe introduce the Hausdorff measure for definable sets in an o-minimal structure, and prove the Cauchy–Crofton and co-area formulae for the o-minimal Hausdorff measure. We also prove that every definable set can be partitioned into “basic rectifiable sets”, and that the Whitney arc property holds for basic rectifiable sets.
Fornasiero, A., Vasquez Rifo, E.
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ON THE HAUSDORFF MEASURE OF CERTAIN PLANE SET PROJECTIONS [PDF]
Pesquimat, 2014 A characterization of plane sets whose projection have zero Hausdorff measure is given. This is obtained through the study of an angular density introduced first by Marstrand [2].
Carlos Arnoldo Morales Rojas
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On the Hausdorff Measure of Shrinking Target Sets on Self-Conformal Sets [PDF]
, 2021 In this article, we study the Hausdorff measure of shrinking target sets on self-conformal sets. The Hausdorff dimension of the sets we are interested in here was established by Hill and Velani in 1995.
Allen, Demi +2 more
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THE CENTERED HAUSDORFF MEASURE OF THE SIERPIŃSKI GASKET [PDF]
, 2023 We show that the centered Hausdorff measure, Cs(S), with s=log3log2, of the Sierpiński gasket S, is C-computable (continuous-computable), in the sense that its value is the solution of the minimization problem of a continuous function on a compact ...
MARTA LLORENTE +5 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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GAN‐LSTM‐3D: An efficient method for lung tumour 3D reconstruction enhanced by attention‐based LSTM
CAAI Transactions on Intelligence Technology, EarlyView., 2023 Abstract Three‐dimensional (3D) image reconstruction of tumours can visualise their structures with precision and high resolution. In this article, GAN‐LSTM‐3D method is proposed for 3D reconstruction of lung cancer tumours from 2D CT images. Our method consists of three phases: lung segmentation, tumour segmentation, and tumour 3D reconstruction. Lung
Lu Hong +12 more
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Translating Hausdorff is hard: fine-grained lower bounds for Hausdorff distance under translation
Journal of Computational Geometry, 2022 Computing the similarity of two point sets is a ubiquitous task in medical imaging, geometric shape comparison, trajectory analysis, and many more settings.
Karl Bringmann, André Nusser
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Something About h - Measures of Sets in Plane
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 In this article we estimate the Hausdorff h-measures of the graphs of some functions, for different measure functions.
Bărbulescu Alina
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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 +7 more
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Haar Measure for non-Hausdorff Locally Compact Groups [PDF]
Advances in Group Theory and ApplicationsThe paper describes two possible ways of extending the definition of Haar measure to non-Hausdorff locally compact groups. The first one forces compact sets to be measurable: with this construction, a counterexample to the existence of the Haar measure ...
Lisa Valentini
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