Assouad type dimensions and homogeneity of fractals [PDF]
, 2013 We investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural `dimension pair'. In particular, we compute these dimensions for certain classes of self-affine sets and quasi-self-similar sets and study ...
Fraser, Jonathan M.
core +3 more sources
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
Apollonian circle packings: Dynamics and Number theory [PDF]
, 2014 We give an overview of various counting problems for Apollonian circle packings, which turn out to be related to problems in dynamics and number theory for thin groups.
Oh, Hee
core +1 more source
Hausdorff measures and packing measures of limit sets of CIFSs of generalized complex continued fractions [PDF]
Journal of Difference Equations and Applications, 2020 arXiv admin note: text overlap with arXiv:1810 ...
Kanji Inui, Hiroki Sumi
openaire +3 more sources
A note on the 1-prevalence of continuous images with full Hausdorff dimension [PDF]
, 2014 We consider the Banach space consisting of real-valued continuous functions on an arbitrary compact metric space. It is known that for a prevalent (in the sense of Hunt, Sauer and Yorke) set of functions the Hausdorff dimension of the image is as large ...
Fraser, Jonathan M., Hyde, James T.
core +2 more sources
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
On the Hausdorff and packing measures of slices of dynamically defined sets [PDF]
Journal of Fractal Geometry, Mathematics of Fractals and Related Topics, 2016 Let 1 \le m < n be integers, and let K \subset \mathbb{R}^{n} be a self-similar set satisfying the strong separation condition, and with dim K = s > m .
openaire +3 more sources
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
doaj +1 more source
Hausdorff and packing dimensions of the images of random fields
, 2010 Let $X=\{X(t),t\in\mathbb{R}^N\}$ be a random field with values in $\mathbb{R}^d$. For any finite Borel measure $\mu$ and analytic set $E\subset\mathbb{R}^N$, the Hausdorff and packing dimensions of the image measure $\mu_X$ and image set $X(E)$ are ...
Shieh, Narn-Rueih, Xiao, Yimin
core +1 more source
Mainstream Artificial Intelligence Technologies in Contemporary Ophthalmology
Advanced Intelligent Systems, EarlyView.This review explores the latest artificial intelligence (AI) technologies in ophthalmology, focusing on four key data types: medical imaging, electronic health records, robotic‐assisted surgery, and genomics. It examines the structural features, use cases, clinical goals, and evaluation metrics of various AI algorithms, while also introducing emerging ...
Shiqi Yin +9 more
wiley +1 more source