Results 91 to 100 of about 3,079 (209)

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
wiley   +1 more source

Calculation of Hausdorff dimensions of basins of ergodic measures in encoding spaces

Журнал Белорусского государственного университета: Математика, информатика, 2018
In the article we consider spaces XN of sequences of elements of finite alphabet X (encoding spaces) and ergodic measures on them, basins of ergodic measures and Hausdorff dimensions of such basins with respect to ultrametrics defined by a product of ...
Pavel N. Varabei
doaj  

On the Hausdorff dimension of circular Furstenberg sets

Discrete Analysis
On the Hausdorff dimension of circular Furstenberg sets, Discrete Analysis 2024:18, 83 pp. In the late 1990s, Wolff proved the following result. Suppose that the set $E\subset \mathbb R^2$ contains circles centered at all points of a Borel set with ...
Katrin Fässler, Jiayin Liu, Tuomas Orponen   +2 more
doaj   +1 more source

Projections of measures with small supports

Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2021
In this paper, we use a characterization of the mutual multifractal Hausdorff dimension in terms of auxiliary measures to investigate the projections of measures with small supports.
Bilel Selmi
doaj  

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, Eleftherios Kastis, Derek Kitson, William Sims   +3 more
wiley   +1 more source

Finite (Hausdorff) dimension of plants and roots as indicator of ontogeny

Revista de la Facultad de Ciencias Agrarias, 2019
The architecture of plants responds to endogenous processes and to the influence of environmental factors. The allometric study of architecture has been a challenge for biology. We define a new finite (Hausdorff) dimension of plants, that considers both
Juan M. Alonso, Juan Agustín Alvarez, Cecilia Vega Riveros, Villagra Pablo   +3 more
doaj  

Heisenberg Hausdorff Dimensionof Besicovitch Sets

Analysis and Geometry in Metric Spaces, 2014
We consider (bounded) Besicovitch sets in the Heisenberg group and prove that Lp estimates forthe Kakeya maximal function imply lower bounds for their Heisenberg Hausdorff dimension.
Venieri Laura
doaj   +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, Stephen Lindsay, Jen Pearson, Tom Crick, Alma Rahat   +4 more
wiley   +1 more source

Some lacunarity properties of partial quotients of real numbers

Comptes Rendus. Mathématique
We consider lacunarity properties of sequence of partial quotients for real numbers in their continued fraction expansions. Hausdorff dimension of the sets of points with different lacunarity conditions on their partial quotients are calculated.
Zhao, Xuan, Zhang, Zhenliang
doaj   +1 more source

Dimension estimates of the attractor for the dissipative quantum Zakharov equations

Journal of Inequalities and Applications, 2019
The finite dimension estimates of Hausdorff dimension and fractal dimension of the attractor of the dissipative quantum Zakharov equations are mainly studied by using the estimates of the Lyapunov exponents. The main results on the attractor are obtained
Donglong Li, Yanfeng Guo
doaj   +1 more source