Zobrazeno 1 - 10
of 387
pro vyhledávání: '"Richter, P. K."'
Originating in harmonic analysis, interpolation sets were first studied in dynamics by Glasner and Weiss in the 1980s. A set $S \subset \mathbb{N}$ is an interpolation set for a class of topological dynamical systems $\mathcal{C}$ if any bounded sequ
Externí odkaz:
http://arxiv.org/abs/2401.15339
In contrast to finite arithmetic configurations, relatively little is known about which infinite patterns can be found in every set of natural numbers with positive density. Building on recent advances showing infinite sumsets can be found, we explor
Externí odkaz:
http://arxiv.org/abs/2311.06197
Let $(G/\Gamma,R_a)$ be an ergodic $k$-step nilsystem for $k\geq 2$. We adapt an argument of Parry to show that $L^2(G/\Gamma)$ decomposes as a sum of a subspace with discrete spectrum and a subspace of Lebesgue spectrum with infinite multiplicity. I
Externí odkaz:
http://arxiv.org/abs/2307.07213
Publikováno v:
Phys. Rev. E 106, 054609 (2022)
Thin fluid or elastic films and membranes are found in nature and technology, for instance, as confinements of living cells or in loudspeakers. When applying a net force, resulting flows in an unbounded two-dimensional incompressible low-Reynolds-num
Externí odkaz:
http://arxiv.org/abs/2211.14660
We show that every set $A$ of natural numbers with positive upper density can be shifted to contain the restricted sumset $\{b_1 + b_2 : b_1, b_2\in B \text{ and } b_1 \neq b_2 \}$ for some infinite set $B \subset A$.
Comment: 14 pages. Changes
Comment: 14 pages. Changes
Externí odkaz:
http://arxiv.org/abs/2206.12377
Motivated by questions asked by Erdos, we prove that any set $A\subset{\mathbb N}$ with positive upper density contains, for any $k\in{\mathbb N}$, a sumset $B_1+\cdots+B_k$, where $B_1,\dots,B_k\subset{\mathbb N}$ are infinite. Our proof uses ergodi
Externí odkaz:
http://arxiv.org/abs/2206.01786
Autor:
Richter, Sonja K., Menzel, Andreas M.
Publikováno v:
Phys. Rev. E 105, 014609 (2022)
Interactions between rigid inclusions in continuous three-dimensional linearly elastic solids and low-Reynolds-number viscous fluids have largely been quantified during the past. Prime example systems are given by functionalized elastic composite mat
Externí odkaz:
http://arxiv.org/abs/2111.05047
Publikováno v:
EPL (Europhys. Lett.) 134, 68002 (2021)
Using analytical calculations, we characterize the rotational behavior of a rigid spherical particle when subject to a net external torque in a continuous viscoelastic environment. On long time scales, the embedding medium can either feature a net te
Externí odkaz:
http://arxiv.org/abs/2108.12270
Publikováno v:
Combinatorica 43 2023, no 2, 299-328
We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if $\log r / \log s$ is irrational and $X$ and $Y$ are $\times r$- and $\times s$-invariant subsets of $[0,1]$, respectively, then $\dim_
Externí odkaz:
http://arxiv.org/abs/2107.10605
Publikováno v:
Bull. Amer. Math. Soc., Volume 59 (2022), Number 4, pages 569-606
Katznelson's Question is a long-standing open question concerning recurrence in topological dynamics with strong historical and mathematical ties to open problems in combinatorics and harmonic analysis. In this article, we give a positive answer to K
Externí odkaz:
http://arxiv.org/abs/2106.11393