Results 21 to 30 of about 2,785 (188)

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
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

Fractal Anatomy of Human Organs: A Narrative Review of Structure, Function, and Clinical Perspectives

Clinical Anatomy, EarlyView.
ABSTRACT Fractal geometry describes complex, self‐similar patterns that repeat across spatial scales and is increasingly recognized as relevant in anatomical research. Indeed, the fractal organization is consistently observed in respiratory, cardiovascular, gastrointestinal, nervous, renal, hepatic, and dermatological systems.
Immacolata Belviso, Jacopo Junio Valerio Branca, Giulia Guarnieri, Annamaria Morelli, Alessandra Pacini, Daniele Della Posta, Domenico Ribatti, Ferdinando Paternostro   +7 more
wiley   +1 more source

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
doaj   +1 more source

Packing-Dimension Profiles and Fractional Brownian Motion [PDF]

, 2007
In order to compute the packing dimension of orthogonal projections Falconer and Howroyd (1997) introduced a family of packing dimension profiles ${\rm Dim}_s$ that are parametrized by real numbers $s>0$.
DAVAR KHOSHNEVISAN, Falconer, Järvenpää, Kahane, YIMIN XIAO   +4 more
core   +2 more sources

Isoperimetric inequalities on slabs with applications to cubes and Gaussian slabs

Communications on Pure and Applied Mathematics, EarlyView.
Abstract We study isoperimetric inequalities on “slabs”, namely weighted Riemannian manifolds obtained as the product of the uniform measure on a finite length interval with a codimension‐one base. As our two main applications, we consider the case when the base is the flat torus R2/2Z2$\mathbb {R}^2 / 2 \mathbb {Z}^2$ and the standard Gaussian measure
Emanuel Milman
wiley   +1 more source

Degree theory for 4‐dimensional asymptotically conical gradient expanding solitons

Communications on Pure and Applied Mathematics, EarlyView.
Abstract We develop a new degree theory for 4‐dimensional, asymptotically conical gradient expanding solitons. Our theory implies the existence of gradient expanding solitons that are asymptotic to any given cone over S3$S^3$ with non‐negative scalar curvature. We also obtain a similar existence result for cones whose link is diffeomorphic to S3/Γ$S^3/\
Richard H. Bamler, Eric Chen
wiley   +1 more source

Multifractal Structure of Irregular Sets via Weighted Random Sequences

Fractal and Fractional
We 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

Fractal properties of the random string processes

, 2006
Let $\{u_t(x),t\ge 0, x\in {\mathbb{R}}\}$ be a random string taking values in ${\mathbb{R}}^d$, specified by the following stochastic partial differential equation [Funaki (1983)]: \[\frac{\partial u_t(x)}{\partial t}=\frac{{\partial}^2u_t(x)}{\partial ...
Wu, Dongsheng, Xiao, Yimin
core   +3 more sources

Comparison of Auto‐Contouring Tools for Delineation of Normal Organs at Risk in Paediatric Patients Undergoing Radiotherapy

Journal of Medical Radiation Sciences, EarlyView.
Contouring organs at risk (OARs) manually in paediatric patients undergoing cranial‐spinal radiation therapy (CSI) is a time‐consuming, labour‐intensive task. This study aims to assess the accuracy and clinical acceptability of auto‐contours produced by the Siemens DirectORGANS auto‐contouring software on paediatric patients receiving CSI treatment ...
Isabel Cant, Jonathan Sykes, Yolanda Surjan, Rachael Beldham‐Collins, Laura Murphy, John Fernandez, Alison Salkeld   +6 more
wiley   +1 more source