Results 31 to 40 of about 3,112 (208)
The Annals of Probability, 2004 We prove that the Hausdorff dimension of the trace of SLE_6 is almost surely 7/4 and give a more direct derivation of the result (due to Lawler-Schramm-Werner) that the dimension of its boundary is 4/3. We also prove that, for all κ<8, the SLE_κ trace has cut-points.
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A. Baker's conjecture and Hausdorff dimension
Publicationes Mathematicae Debrecen, 2000 Let \(M_n(\varepsilon)\) (for \(n\in \mathbb N\) and for \(\varepsilon >0\)) denote the set of \(x\in \mathbb R\) such that the inequality \[ |P(x)|
Beresnevich, V., Bernik, V.
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Advanced Science, EarlyView.DDSurfer reconstructs cortical surfaces directly from diffusion MRI without requiring T1‐weighted scans. By fusing complementary microstructural features and learning diffeomorphic deformations, it efficiently generates accurate white matter and pial surfaces, improving geometric fidelity and morphometric reliability across datasets for robust surface ...
Chengjin Li +10 more
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On sets containing a unit distance in every direction
Discrete Analysis, 2021 On sets containing a unit distance in every direction, Discrete Analysis 2021:5, 13 pp. A _Kakeya set_ in $\mathbb R^d$ is a subset $A\subset\mathbb R^d$ that contains a line in every direction. Besicovitch famously proved that a Kakeya set in $\mathbb
Pablo Shmerkin, Han Yu
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Cell Segmentation Beyond 2D—A Review of the State‐of‐the‐Art
Advanced Intelligent Discovery, EarlyView.Cell segmentation underpins many biological image analysis tasks, yet most deep learning methods remain limited to 2D despite the inherently 3D nature of cellular processes. This review surveys segmentation approaches beyond 2D, comparing 2.5D and fully 3D methods, analyzing 31 models and 32 volumetric datasets, and introducing a unified reference ...
Fabian Schmeisser +6 more
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Kolmogorov complexity and Hausdorff dimension
Information and Computation, 1989 This interesting note develops several formal relationships between program-size complexity of infinite strings and various measures of information content. The idea is to bound the complexity of a maximally complex string in a prescribed set of strings by the Hausdorff dimension as well as the entropy of that set.
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Errata to ‘Hausdorff dimension for horseshoes’ [PDF]
Ergodic Theory and Dynamical Systems, 1985 In our paper ‘Hausdorff dimension for horseshoes’ (H. McCluskey and A. Manning, Ergod. Th. & Dynam. Sys. (1983) 3, 251–260), § 3 entitled ‘Continuity across a bifurcation’ should be deleted since the proof of theorem 3 there is wrong.The mistake is that does not in fact imply that δs → 1.
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Front Propagation Through a Perforated Wall
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We consider a bistable reaction– diffusion equation ut=Δu+f(u)$u_t=\Delta u +f(u)$ on RN${\mathbb {R}}^N$ in the presence of an obstacle K$K$, which is a wall of infinite span with many holes. More precisely, K$K$ is a closed subset of RN${\mathbb {R}}^N$ with smooth boundary such that its projection onto the x1$x_1$‐axis is bounded and that ...
Henri Berestycki +2 more
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The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping
International Journal of Mathematics and Mathematical Sciences, 2002 We weaken the open set condition and define a finite intersection property in the construction of the random recursive sets. We prove that this larger class of random sets are fractals in the sense of Taylor, and give conditions when these sets have ...
Hongwen Guo, Dihe Hu
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A Geometric Characterization of Steady Laminar Flow
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We study the steady states of the Euler equations on the periodic channel or annulus. We show that if these flows are laminar (layered by closed non‐contractible streamlines which foliate the domain), then they must be either parallel or circular flows.
Theodore D. Drivas, Marc Nualart
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