Results 31 to 40 of about 2,719 (189)
, 2016 In this paper we obtain the rates of convergence of the algorithms given in [13] and [14] for an automatic computation of the centered Hausdorff and packing measures of a totally disconnected self-similar set.
Llorente, Marta +2 more
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Exact Hausdorff and packing measures for random self-similar code-trees with necks [PDF]
Studia Mathematica, 2021 Random code-trees with necks were introduced recently to generalise the notion of $V$-variable and random homogeneous sets. While it is known that the Hausdorff and packing dimensions coincide irrespective of overlaps, their exact Hausdorff and packing measure has so far been largely ignored.
openaire +4 more sources
Sharp commutator estimates of all order for Coulomb and Riesz modulated energies
Communications on Pure and Applied Mathematics, EarlyView.Abstract We prove functional inequalities in any dimension controlling the iterated derivatives along a transport of the Coulomb or super‐Coulomb Riesz modulated energy in terms of the modulated energy itself. This modulated energy was introduced by the second author and collaborators in the study of mean‐field limits and statistical mechanics of ...
Matthew Rosenzweig, Sylvia Serfaty
wiley +1 more source
Convergence properties of dynamic mode decomposition for analytic interval maps
Communications on Pure and Applied Mathematics, EarlyView.Abstract Extended dynamic mode decomposition (EDMD) is a data‐driven algorithm for approximating spectral data of the Koopman operator associated to a dynamical system, combining a Galerkin method with N$N$ functions and a quadrature method with M$M$ quadrature nodes.
Elliz Akindji +3 more
wiley +1 more source
A note on the generalized Hausdorff and packing measures of product sets in metric space
Mathematical Inequalities & Applications, 2022 Let $μ$ and $ν$ be two Borel probability measures on two separable metric spaces $\X$ and $\Y$ respectively. For $h, g$ be two Hausdorff functions and $q\in \R$, we introduce and investigate the generalized pseudo-packing measure ${\RRR}_μ^{q, h}$ and the weighted generalized packing measure ${\QQQ}_μ^{q, h}$ to give some product inequalities ...
Guedri, Rihab, Attia, Najmeddine
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Semiclassical inequalities for Dirichlet and Neumann Laplacians on convex domains
Communications on Pure and Applied Mathematics, EarlyView.Abstract We are interested in inequalities that bound the Riesz means of the eigenvalues of the Dirichlet and Neumann Laplacians in terms of their semiclassical counterpart. We show that the classical inequalities of Berezin–Li–Yau and Kröger, valid for Riesz exponents γ≥1$\gamma \ge 1$, extend to certain values γ<1$\gamma <1$, provided the underlying ...
Rupert L. Frank, Simon Larson
wiley +1 more source
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 +6 more
wiley +1 more source
The Laryngoscope, EarlyView.The purpose of this study was to validate and provide an open‐source segmentation algorithm of paranasal sinus CT scans for the otolaryngology research community. This can be used for further AI‐based analysis and radiomic analysis in future research. ABSTRACT Objective Artificial Intelligence (AI) research needs to be clinician led; however, expertise
Rhea Darbari Kaul +12 more
wiley +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
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The domination theorem for operator classes generated by Orlicz spaces
Mathematische Nachrichten, EarlyView.Abstract We study lattice summing operators between Banach spaces focusing on two classes, ℓφ$\ell _\varphi$‐summing and strongly φ$\varphi$‐summing operators, which are generated by Orlicz sequence lattices ℓφ$\ell _\varphi$. For the class of strongly φ$\varphi$‐summing operators, we prove the domination theorem, which complements Pietsch's ...
D. L. Fernandez +3 more
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