Results 91 to 100 of about 66,461 (287)
Hausdorff Dimension and Gaussian Fields
The Annals of Probability, 1977 Let $X(t)$ be a Gaussian process taking values in $R^d$ and with its parameter in $R^N$. Then if $X_j$ has stationary increments and the function $\sigma^2(t) = E\{|X_j(s + t) - X_j(s)|^2\}$ behaves like $|t|^{2\alpha}$ as $|t| \downarrow 0, 0 < \alpha < 1$, the graph of $X$ has Hausdorff dimension $\min \{N/\alpha, N + d(1 - \alpha)\}$ with ...
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Hausdorff Dimension in Stochastic Dispersion
Journal of Statistical Physics, 2002 26 ...
Dolgopyat, D., Kaloshin, V., Koralov, L.
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Changes in corticospinal excitability in response to mediolateral gait instability
Experimental Physiology, EarlyView.Abstract Unpredictable gait disturbances, particularly in the mediolateral direction, pose a significant challenge to stability and are a common contributor to falls. Although the corticospinal tract is critical for gait and postural control, its response to such instabilities remains unclear.
Raven O. Huiberts +2 more
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The Journal of Physiology, EarlyView.Abstract figure legend Digital heart models of human donor atria with cardiac co‐morbidities revealed that regions with AWT variation, aligned myofibres adjacent to disorganised zones and fibrotic borders promoted the localisation and stability of RDs. AWT had a global influence, whereas fibre orientation and fibrosis exerted chamber‐specific regional ...
Anuradha Kulathilaka +8 more
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Singular dimension of spaces of real functions
Le Matematiche, 2007 Let X be a space of measurable real functions defined on a fixed open set Ω ⊆ R^N . It is natural to define the singular dimension of X as the supremum of Hausdorff dimension of singular sets of all functions in X.We say that f ∈ X is a maximally ...
Darko Žubrinić
doaj
The Hausdorff dimension of the visible sets of connected compact sets
, 2003 For a compact subset K of the plane and a point x, we define the visible part of K from x to be the set K_x={u\in K : [x,u]\cap K={u}}. (Here [x,u] denotes the closed line segment joining x to u.) In this paper, we use energies to show that if K is a ...
O'Neil, Toby C
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Hausdorff Dimension of Caloric Measure
American Journal of Mathematicsabstract: We examine caloric measures $\omega$ on general domains in $\RR^{n+1}=\RR^n\times\RR$ (space $\times$ time) from the perspective of geometric measure theory. On one hand, we give a direct proof of a consequence of a theorem of Taylor and Watson (1985) that the lower parabolic Hausdorff dimension of $\omega$ is at least $n$ and $\omega\ll ...
Badger, Matthew, Genschaw, Alyssa
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Semiclassical inequalities for Dirichlet and Neumann Laplacians on convex domains
Communications on Pure and Applied Mathematics, Volume 79, Issue 3, Page 762-822, March 2026.Abstract We are interested in inequalities that bound the Riesz means of the eigenvalues of the Dirichlet and Neumann Laplacians in terms of their semiclassical counterpart. We show that the classical inequalities of Berezin–Li–Yau and Kröger, valid for Riesz exponents γ≥1$\gamma \ge 1$, extend to certain values γ<1$\gamma <1$, provided the underlying ...
Rupert L. Frank, Simon Larson
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Magnetic Resonance in Medicine, Volume 95, Issue 3, Page 1762-1777, March 2026.ABSTRACT Purpose This study aims to develop an automated framework for operator‐independent assessment of cardiac ventricular function from highly accelerated images. Methods We introduce a deep learning framework that generates reliable ventricular volumetric parameters and strain measures from fully sampled and retrospectively accelerated MR images ...
Aya Ghoul +7 more
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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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