Results 81 to 90 of about 69,690 (223)
Green’s formula, linear continuity, and Hausdorff measure [PDF]
, 1965 Robert M. Fesq
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Journal of Applied Clinical Medical Physics, Volume 26, Issue 9, September 2025.Abstract Background Deep learning (DL)‐based organ segmentation is increasingly used in radiotherapy. While methods exist to generate voxel‐wise uncertainty maps from DL‐based auto‐segmentation models, these maps are rarely presented to clinicians. Purpose This study aimed to evaluate the impact of DL‐generated uncertainty maps on experienced radiation
Viktor Rogowski +14 more
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On Decomposable Measures Induced by Metrics
Journal of Applied Mathematics, 2012 We prove that for a given normalized compact metric space it can induce a σ-max-superdecomposable measure, by constructing a Hausdorff pseudometric on its power set.
Dong Qiu, Weiquan Zhang
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Journal of Applied Clinical Medical Physics, Volume 26, Issue 9, September 2025.Abstract Background The poor soft tissue resolution of four‐dimensional computed tomography (4D‐CT) limits its utility in delineating liver cancer target volumes. Purpose To compare the consistency between four‐dimensional magnetic resonance imaging (4D‐MRI) using T1‐weighted (T1w) radial stack‐of‐stars (SOS) gradient echo (GRE) sequences and 4D‐CT in ...
Shuoyan Chen +11 more
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On planar self-similar sets with a dense set of rotations
, 2006 We prove that if $E$ is a planar self-similar set with similarity dimension $d$ whose defining maps generate a dense set of rotations, then the $d$-dimensional Hausdorff measure of the orthogonal projection of $E$ onto any line is zero.
Eroglu, Kemal Ilgar
core
First passage times and sojourn times for Brownian motion in space and the exact Hausdorff measure of the sample path [PDF]
, 1962 Z. Ciesielski, S. J. Taylor
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First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet
Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1523-1608, September 2025.Abstract For any p∈(1,∞)$p \in (1,\infty)$, we construct p$p$‐energies and the corresponding p$p$‐energy measures on the Sierpiński carpet. A salient feature of our Sobolev space is the self‐similarity of energy. An important motivation for the construction of self‐similar energy and energy measures is to determine whether or not the Ahlfors regular ...
Mathav Murugan, Ryosuke Shimizu
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Hausdorff measure of noncompactness of matrix operators on some new difference sequence spaces
Journal of Inequalities and Applications, 2016 The new sequence spaces X ( r , s , t ; Δ ) $X(r,s,t;\Delta)$ for X ∈ { l ∞ , c , c 0 } $X\in\{l_{\infty}, c, c_{0}\}$ have been defined by using generalized means and difference operator.
Elahe Abyar, Mohammad Bagher Ghaemi
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Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1656-1702, September 2025.Abstract Let (Mn,g)$(M^n,g)$ be a complete Riemannian manifold which is not isometric to Rn$\mathbb {R}^n$, has nonnegative Ricci curvature, Euclidean volume growth, and quadratic Riemann curvature decay. We prove that there exists a set G⊂(0,∞)$\mathcal {G}\subset (0,\infty)$ with density 1 at infinity such that for every V∈G$V\in \mathcal {G}$ there ...
Gioacchino Antonelli +2 more
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