Results 101 to 110 of about 3,112 (208)
Hausdorff dimension of the Apollonian gasket
Inventiones mathematicaeAbstract The Apollonian gasket is a well-studied circle packing. Important properties of the packing, including the distribution of the circle radii, are governed by its Hausdorff dimension. No closed form is currently known for the Hausdorff dimension, and its computation is a special case of a more general and hard problem: effective ...
Polina Vytnova, Caroline Wormell
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Journal of Geophysical Research: Atmospheres, Volume 131, Issue 15, 16 August 2026.Abstract Atmospheric Rivers (ARs) are narrow regions of extratropical water vapor transport, situated in the lower troposphere. They are responsible for a large proportion of poleward vapor transport from the tropics to the midlatitudes. Although ARs are known to cause devastating floods when encountering topography, they are a crucial source of water ...
A. K. Sneddon +2 more
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International Journal for Numerical Methods in Engineering, Volume 127, Issue 15, 15 August 2026.ABSTRACT Fluid‐filled phase‐field fracture simulations require robust, scalable solvers that can handle strongly nonlinear, non‐smooth mechanics and tightly coupled flow on locally refined meshes. In this work, we develop an adaptive finite element framework for quasi‐static, fluid‐filled phase‐field fractures that combines semi‐smooth Newton methods ...
Leon M. Kolditz +3 more
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Journal of Applied Clinical Medical Physics, Volume 27, Issue 8, August 2026.Abstract Background Synthetic CTs (sCT) were developed to provide electron density information for MR‐only treatment planning. Some AI‐based sCT generators have received FDA‐clearance and better capture tissue heterogeneity through voxel‐wise mappings to improve image guidance and dose calculation.
Morgan Aire +7 more
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Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic
Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1973-2102, August 2026.ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
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Edge‐Length Preserving Embeddings of Graphs Between Normed Spaces
Journal of Graph Theory, Volume 112, Issue 4, Page 491-506, August 2026.ABSTRACT The concept of graph embeddability, initially formalized by Belk and Connelly and later expanded by Sitharam and Willoughby, extends the question of embedding finite metric spaces into a given normed space. A finite simple graph G = ( V , E ) is said to be ( X , Y )‐embeddable if any set of induced edge lengths from an embedding of G into a ...
Sean Dewar +3 more
wiley +1 more source
Complex continued fractions with restricted entries
Electronic Journal of Differential Equations, 1998 We study special infinite iterated function systems derived from complex continued fraction expansions with restricted entries. We focus our attention on the corresponding limit set whose Hausdorff dimension will be denoted by $h$. Our primary goal is to
Pawel Hanus, Mariusz Urbanski
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The International Journal of Medical Robotics and Computer Assisted Surgery, Volume 22, Issue 4, August 2026.ABSTRACT Background This single‐centre study aimed to implement and internally validate a deep learning pipeline based on a 3D SegResNet architecture for automatic segmentation of renal vascular structures from contrast‐enhanced CT images, enabling accurate three‐dimensional reconstructions to support surgical planning in robot‐assisted partial ...
Davide Brusa +9 more
wiley +1 more source
Rendering transparency to ranking in educational assessment via Bayesian comparative judgement
Review of Education, Volume 14, Issue 2, August 2026.Abstract Transparency in educational assessment has become an increasingly pressing concern, particularly in the aftermath of the pandemic, as institutions seek more equitable, robust and defensible methods of evaluating student work. Comparative judgement (CJ) has gained traction as a promising alternative to traditional rubric‐based marking. However,
Andy Gray +4 more
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