Results 81 to 90 of about 3,079 (209)

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 ...
openaire   +3 more sources

Influence of Superimposition Strategies and Landmark Distribution on the Full‐Arch Trueness of Orthodontic Digital Models

Journal of Esthetic and Restorative Dentistry, EarlyView.
ABSTRACT Objective To evaluate the influence of superimposition protocols and landmark distribution on deviation outcomes in orthodontic full‐arch models. Materials and Methods Twenty plaster models were scanned using an intraoral and desktop scanner. Ten models were evaluated for landmark suitability and inter‐scanner coordinate agreement.
Ezgi Cansu Firinciogullari, Edanur Dark, Genta Agani Sabah, Aslıhan Mediha Erdinc   +3 more
wiley   +1 more source

Hausdorff dimension of fermions on a random lattice

Nuclear Physics B
Geometric properties of lattice quantum gravity in two dimensions are studied numerically via Monte Carlo on Euclidean Dynamical Triangulations. A new computational method is proposed to simulate gravity coupled with fermions, which allows the study of ...
Mattia Varrone, William E.V. Barker
doaj   +1 more source

Deep learning assisted high‐resolution microscopy image processing for phase segmentation in functional composite materials

Journal of Microscopy, EarlyView.
Abstract In the domain of battery research, the processing of high‐resolution microscopy images is a challenging task, as it involves dealing with complex images and requires a prior understanding of the components involved. The utilisation of deep learning methodologies for image analysis has attracted considerable interest in recent years, with ...
Ganesh Raghavendran, Bing Han, Fortune Adekogbe, Shuang Bai, Bingyu Lu, William Wu, Minghao Zhang, Ying Shirley Meng   +7 more
wiley   +1 more source

Generalized Dimensions of Self-Affine Sets with Overlaps

Fractal and Fractional
Two decades ago, Ngai and Wang introduced a well-known finite type condition (FTC) on the self-similar iterated function system (IFS) with overlaps and used it to calculate the Hausdorff dimension of self-similar sets. In this paper, inspired by Ngai and
Guanzhong Ma, Jun Luo, Xiao Zhou
doaj   +1 more source

On spectra of probability measures generated by GLS-expansions

Modern Stochastics: Theory and Applications, 2016
We study properties of distributions of random variables with independent identically distributed symbols of generalized Lüroth series (GLS) expansions (the family of GLS-expansions contains Lüroth expansion and $Q_{\infty }$- and ${G_{\infty }^{2 ...
Marina Lupain
doaj   +1 more source

Structural determinants of re‐entrant drivers in atrial fibrillation: insights from digital twins derived from 3D micrometre‐resolution imaging of human heart

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, Roshan Sharma, James Kennelly, Ning Li, Jieyun Bai, Bruce H. Smaill, Mark L. Trew, Vadim V. Fedorov, Jichao Zhao   +8 more
wiley   +1 more source

Hausdorff dimension of collision times in one-dimensional log-gases

AIP Advances
We consider systems of multiple Brownian particles in one dimension that repel mutually via a logarithmic potential on the real line, more specifically the Dyson model.
Nicole Hufnagel, Sergio Andraus
doaj   +1 more source

On the Visibility of Homogeneous Cantor Sets

Fractal and Fractional
The problems associated with the visible set have been explored by various scholars. In this paper, we investigate the Hausdorff dimension and the topological properties of the visible set in relation to the products of homogeneous Cantor sets.
Yi Cai, Yufei Chen
doaj   +1 more source

Hausdorff dimension of the Apollonian gasket

Inventiones mathematicae
Abstract 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
openaire   +2 more sources