On packing measures and a theorem of Besicovitch [PDF]
, 2014 Let Hh be the h-dimensional Hausdorff measure on Rd. Besicovitch showed that if a set E is null for Hh, then it is null for Hg , for some dimension g smaller than h. We prove that this is not true for packing measures.
Garcia, Ignacio Andres, Shmerkin, Pablo
core
Applying Multi-Metric Deformable Image Registration for Dose Accumulation in Combined Cervical Cancer Radiotherapy. [PDF]
J Pers Med, 2023 Fu Q +9 more
europepmc +1 more source
Bulletin of the London Mathematical Society, Volume 58, Issue 6, June 2026.Abstract In this article, we investigate the existence and multiplicity of solutions to the Robin problem −Δu=λf(u)inΩ,∂u∂ν+γu=0on∂Ω,$$\begin{equation*} {\begin{cases} -\Delta u = \lambda f(u) & \text{in } \Omega,\\ \frac{\partial u}{\partial \nu } + \gamma u=0 & \text{on } \partial \Omega, \end{cases}} \end{equation*}$$where Ω⊂RN$\Omega \subset ...
José Carmona Tapia +2 more
wiley +1 more source
Photogrammetry-Based Volume Measurement Framework for the Particle Density Estimation of LECA. [PDF]
Materials (Basel), 2022 Brzeziński K +3 more
europepmc +1 more source
Sharp estimates for the Laplacian torsional rigidity with negative Robin boundary conditions
Bulletin of the London Mathematical Society, Volume 58, Issue 6, June 2026.Abstract Motivated by pioneering works of Bandle and Wagner, given a bounded Lipschitz domain Ω⊂Rd$\Omega \subset \mathbb {R}^d$ with d⩾3$d\geqslant 3$, we consider the Robin–Laplacian torsional rigidity τα(Ω)$\tau _\alpha (\Omega)$ with negative boundary parameter α$\alpha$ and we show that sharp inequalities for τα(Ω)$\tau _\alpha (\Omega)$ hold if ...
Nunzia Gavitone +2 more
wiley +1 more source
Spectral Packing Dimensions through Power-Law Subordinacy
, 2013 We offer a method of classification of spectral measures of discrete one-dimensional Schrodinger operators with respect to packing measures, which can be seen as dual to results for Hausdorff measures in subordinacy theory.
Oliveira, Cesar R. de +1 more
core +1 more source
An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists. [PDF]
Front Artif Intell, 2021 Chazal F, Michel B.
europepmc +1 more source
Stable factorization of the Calderón problem via the Born approximation
Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.Abstract In this article, we prove the existence of the Born approximation in the context of the radial Calderón problem for Schrödinger operators. The Born approximation naturally appears as the linear component of a factorization of the Calderón problem; we show that the nonlinear part, obtaining the potential from the Born approximation, enjoys ...
Thierry Daudé +3 more
wiley +1 more source
Hausdorff and packing dimension of fibers and graphs of prevalent continuous maps
, 2016 The notions of shyness and prevalence generalize the property of being zero and full Haar measure to arbitrary (not necessarily locally compact) Polish groups.
Darji, U. B. +2 more
core +1 more source
A strong quantitative form of the fractional isoperimetric inequality
Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.Abstract We show a strong version of the fractional quantitative isoperimetric inequality, in which the isoperimetric deficit controls not only the Fraenkel asymmetry but also a sort of oscillation of the boundary. This generalizes the local result by Fusco and Julin in [22].
Eleonora Cinti +2 more
wiley +1 more source