Results 11 to 20 of about 187 (146)

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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The Hausdorff measure and the packing measure on a perturbed Cantor set [PDF]

Real Analysis Exchange, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Packing and Hausdorff Measures of Stable Trees [PDF]

, 2010
In this paper we discuss Hausdorff and packing measures of random continuous trees called stable trees. Stable trees form a specific class of Lévy trees (introduced by Le Gall and Le Jan in 1998) that contains Aldous's continuum random tree (1991) which corresponds to the Brownian case.
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Hausdorff and packing measure for thick solenoids [PDF]

Studia Mathematica, 2004
Summary: For a linear solenoid with two different contraction coefficients and box dimension greater than 2, we give precise formulas for the Hausdorff and packing dimensions. We prove that the packing measure is infinite and give a condition necessary and sufficient for the Hausdorff measure to be positive, finite and equivalent to the SBR measure. We
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The Hausdorff and packing measure of some digital expansions

Acta Arithmetica, 2022
Minor changes.
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Свойство выпуклости взаимных мультифрактальных размерностей [PDF]

Проблемы анализа, 2010
В работе установлено свойство выпуклости взаимной мультифрактальной упаковочной размерности подмножества пересечения носителей вероятностных борелевских мер μ и v.
Светова Н. Ю.
doaj  

A φ-Contractivity and Associated Fractal Dimensions

Fractal and Fractional
In this paper, we extend the concept of dimension of sets to some general frameworks relative to a gauge function φ, where two simultaneous dimensions are introduced.
Nifeen H. Altaweel, Olayan Albalawi, Razan Albalawi   +2 more
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New Insights into the Multifractal Formalism of Branching Random Walks on Galton–Watson Tree

Mathematics
In the present work, we consider three branching random walk SnZ(t),Z∈{X,Y,Φ} on a supercritical random Galton–Watson tree ∂T. We compute the Hausdorff and packing dimensions of the level set Eχ(α,β)=t∈∂T:limn→∞SnX(t)SnY(t)=αandlimn→∞SnY(t)n=β, where ∂T ...
Najmeddine Attia
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Hausdorff and Packing Measures of Balanced Cantor Sets

Real Analysis Exchange, 2015
We estimate the \(h\)-Hausdorff and \(h\)-packing measures of balanced Cantor sets, and characterize the corresponding dimension partitions. This generalizes results known for Cantor sets associated with positive decreasing summable sequences and central Cantor sets.
Hare, Kathryn, Ng, Ka-Shing
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Cell Segmentation Beyond 2D—A Review of the State‐of‐the‐Art

Advanced Intelligent Discovery, EarlyView.
Cell segmentation underpins many biological image analysis tasks, yet most deep learning methods remain limited to 2D despite the inherently 3D nature of cellular processes. This review surveys segmentation approaches beyond 2D, comparing 2.5D and fully 3D methods, analyzing 31 models and 32 volumetric datasets, and introducing a unified reference ...
Fabian Schmeisser, Haseeb Muhammad, Junaid Younas, Gillian Lovell, Bianca Migliori, Andreas Dengel, Sheraz Ahmed   +6 more
wiley   +1 more source