Factorizations and minimality of the Calkin Algebra norm for C(K)$C(K)$‐spaces
Journal of the London Mathematical Society, Volume 112, Issue 4, October 2025.Abstract For a scattered, locally compact Hausdorff space K$K$, we prove that the essential norm on the Calkin algebra B(C0(K))/K(C0(K))$\mathcal {B}(C_0(K))/\mathcal {K}(C_0(K))$ is a minimal algebra norm. The proof relies on establishing a quantitative factorization for the identity operator on c0$c_0$ through noncompact operators T:C0(K)→X$T: C_0(K)
Antonio Acuaviva
wiley +1 more source
On Cantor sets with arbitrary Hausdorff and packing measures
For every couple of Hausdorff functions $ψ, φ$ verifying some mild assumptions, we construct a compact subset $ K $ of the Baire space such that the $φ$-Hausdorff measure and the $ψ$-packing measure on $ K $ are both finite and positive. We then embed such examples in any infinite-dimensional Banach space to answer positively to a question of Fan on ...
openaire +2 more sources
New fiber and graph combinations of convex bodies
Mathematika, Volume 71, Issue 4, October 2025.Abstract Three new combinations of convex bodies are introduced and studied: the Lp$L_p$ fiber, Lp$L_p$ chord, and graph combinations. These combinations are defined in terms of the fibers and graphs of pairs of convex bodies, and each operation generalizes the classical Steiner symmetral, albeit in different ways.
Steven Hoehner, Sudan Xing
wiley +1 more source
A multiscale generative model to understand disorder in domain boundaries. [PDF]
Sci Adv, 2023 Dan J +6 more
europepmc +1 more source
Geometric inequalities, stability results and Kendall's problem in spherical space
Mathematika, Volume 71, Issue 4, October 2025.Abstract In Euclidean space, the asymptotic shape of large cells in various types of Poisson‐driven random tessellations has been the subject of a famous conjecture due to David Kendall. Since shape is a geometric concept and large cells are identified by means of geometric size functionals, the resolution of the conjecture is inevitably connected with
Daniel Hug, Andreas Reichenbacher
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Neural network-assisted automated image registration for MRI-guided adaptive brachytherapy in cervical cancer. [PDF]
Z Med Phys, 2022 Ecker S +8 more
europepmc +1 more source
Tightening inequalities on volume‐extremal k$k$‐ellipsoids using asymmetry measures
Mathematika, Volume 71, Issue 4, October 2025.Abstract We consider two well‐known problems: upper bounding the volume of lower dimensional ellipsoids contained in convex bodies given their John ellipsoid, and lower bounding the volume of ellipsoids containing projections of convex bodies given their Loewner ellipsoid.
René Brandenberg, Florian Grundbacher
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A Comprehensive Survey with Quantitative Comparison of Image Analysis Methods for Microorganism Biovolume Measurements. [PDF]
Arch Comput Methods Eng, 2023 Zhang J +8 more
europepmc +1 more source
Mathematika, Volume 71, Issue 4, October 2025.Abstract Let μ$\mu$ be a probability measure on R$\mathbb {R}$. We give conditions on the Fourier transform of its density for functionals of the form H(a)=∫Rnh(⟨a,x⟩)μn(dx)$H(a)=\int _{\mathbb {R}^n}h(\langle a,x\rangle)\mu ^n(dx)$ to be Schur monotone. As applications, we put certain known and new results under the same umbrella, given by a condition
Andreas Malliaris
wiley +1 more source
Frontiers of Cranial Base Surgery: Integrating Technique, Technology, and Teamwork for the Future of Neurosurgery. [PDF]
Brain Sci, 2023 Toader C +8 more
europepmc +1 more source