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of 4 633
pro vyhledávání: '"Barany A"'
Assume two finite families $\mathcal A$ and $\mathcal B$ of convex sets in $\mathbb{R}^3$ have the property that $A\cap B\ne \emptyset$ for every $A \in \mathcal A$ and $B\in \mathcal B$. Is there a constant $\gamma >0$ (independent of $\mathcal A$ a
Externí odkaz:
http://arxiv.org/abs/2409.06472
This paper is partly an exposition, and partly an extension of our work [1] to the multiparameter case. We consider certain classes of parametrized dynamically defined measures. These are push-forwards, under the natural projection, of ergodic measur
Externí odkaz:
http://arxiv.org/abs/2405.06466
Autor:
Katranidis, Vasileios, Barany, Gabor
The demand for accurate and efficient verification of information in texts generated by large language models (LMs) is at an all-time high, but remains unresolved. Recent efforts have focused on extracting and verifying atomic facts from these texts
Externí odkaz:
http://arxiv.org/abs/2403.03888
In this paper, we consider a fractal model motivated by the abrasion of convex polyhedra, where the abrasion is realised by chipping small neighbourhoods of vertices. After providing a formal description of the successive chippings, we show that the
Externí odkaz:
http://arxiv.org/abs/2402.17765
We study the level sets of prevalent H\"older functions. For a prevalent $\alpha$-H\"older function on the unit interval, we show that the upper Minkowski dimension of every level set is bounded from above by $1-\alpha$ and Lebesgue positively many l
Externí odkaz:
http://arxiv.org/abs/2402.08520
Autor:
Barany, Amanda, Scarola, Andi Danielle, Acquah, Alex, Reza, Sayed Mohsin, Johnson, Michael A., Walker, Justice
Publikováno v:
Information and Learning Sciences, 2024, Vol. 125, Issue 10, pp. 794-812.
Externí odkaz:
http://www.emeraldinsight.com/doi/10.1108/ILS-12-2023-0211
Autor:
Bárány, Imre, Domokos, Gábor
Given a polytope $P\subset R^3$ and a non-zero vector $z \in R^3$, the plane $\{x\in R^3:zx=t\}$ intersects $P$ in convex polygon $P(z,t)$ for $t \in [t^-,t^+]$ where $t^-=\min \{zx: x \in P\}$ and $t^+=\max \{zx: x\in P\}$, $zx$ is the scalar produc
Externí odkaz:
http://arxiv.org/abs/2310.18960
We show that any self-conformal measure $\mu$ on $\mathbb{R}$ is uniformly scaling and generates an ergodic fractal distribution. This generalizes existing results by removing the need for any separation condition. We also obtain applications to the
Externí odkaz:
http://arxiv.org/abs/2308.11399
Autor:
Barany, Imre
We give a new proof Tverberg's famous theorem: For every set $X \subset \R^d$ with $|X|=(r-1)(d+1)+1$, there is a partition of $X$ into $r$ sets $X_1,\ldots,X_r$ such that $\bigcap_{p=1}^r \conv X_p\ne \emptyset$. The new proof uses linear algebra, s
Externí odkaz:
http://arxiv.org/abs/2308.10105
Autor:
Barany, Imre
Assume that $k \le d$ is a positive integer and $\C$ is a finite collection of convex bodies in $\R^d$. We prove a Helly type theorem: If for every subfamily $\C^*\subset \C$ of size at most $\max \{d+1,2(d-k+1)\}$ the set $\bigcap \C^*$ contains a $
Externí odkaz:
http://arxiv.org/abs/2308.10106