Results 21 to 30 of about 338 (182)
Numerical Values of the Hausdorff and Packing Measures for Limit Sets of Iterated Function Systems [PDF]
, 2017 In the context of fractal geometry, the natural extension of volume in Euclidean space is given by Hausdorff and packing measures. These measures arise naturally in the context of iterated function systems (IFS).
Reid, James Edward
core +1 more source
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
Dimension and measure for generic continuous images
, 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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A φ-Contractivity and Associated Fractal Dimensions
Fractal and FractionalIn 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 +2 more
doaj +1 more source
New Insights into the Multifractal Formalism of Branching Random Walks on Galton–Watson Tree
MathematicsIn 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
openaire +2 more sources
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 +6 more
wiley +1 more source
Exact dimensionality and projections of random self-similar measures and sets
, 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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Multifractal Structure of Irregular Sets via Weighted Random Sequences
Fractal and FractionalWe study the multifractal structure of irregular sets arising from Fibonacci-weighted sums of sequences of random variables. Focusing on Cantor-type subsets Kε of the unit interval, we construct sequences of free and forced blocks, where the free blocks ...
Najmeddine Attia, Taoufik Moulahi
doaj +1 more source
Front Propagation Through a Perforated Wall
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We consider a bistable reaction– diffusion equation ut=Δu+f(u)$u_t=\Delta u +f(u)$ on RN${\mathbb {R}}^N$ in the presence of an obstacle K$K$, which is a wall of infinite span with many holes. More precisely, K$K$ is a closed subset of RN${\mathbb {R}}^N$ with smooth boundary such that its projection onto the x1$x_1$‐axis is bounded and that ...
Henri Berestycki +2 more
wiley +1 more source