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pro vyhledávání: '"Olson, Eric J."'
If $X$ is a set with finite Assouad dimension, it is known that the Assouad dimension of $X-X$ does not necessarily obey any non-trivial bound in terms of the Assouad dimension of $X$. In this paper, we consider self-similar sets on the real line and
Externí odkaz:
http://arxiv.org/abs/1910.01835
An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. We consider a nudging-based approach for data assimilation that constructs an approximate solution based on a feedback con
Externí odkaz:
http://arxiv.org/abs/1809.00106
Publikováno v:
In Journal of Chromatography A 27 September 2021 1654
We study the continuity of pullback and uniform attractors for non-autonomous dynamical systems with respect to perturbations of a parameter. Consider a family of dynamical systems parameterised by a complete metric space $\Lambda$ such that for each
Externí odkaz:
http://arxiv.org/abs/1601.07436
Autor:
Olson, Eric J., Ma, Rui, Sun, Tao, Ebrish, Mona A., Haratipour, Nazila, Min, Kyoungmin, Aluru, Narayana R., Koester, Steven J.
Understanding the interactions of ambient molecules with graphene and adjacent dielectrics is of fundamental importance for a range of graphene-based devices, particularly sensors, where such interactions could influence the operation of the device.
Externí odkaz:
http://arxiv.org/abs/1508.05147
Autor:
McCormick, David S., Olson, Eric J., Robinson, James C., Rodrigo, Jose L., Vidal-Lopez, Alejandro, Zhou, Yi
If $u$ is a smooth solution of the Navier--Stokes equations on ${\mathbb R}^3$ with first blowup time $T$, we prove lower bounds for $u$ in the Sobolev spaces $\dot H^{3/2}$, $\dot H^{5/2}$, and the Besov space $\dot B^{5/2}_{2,1}$, with optimal rate
Externí odkaz:
http://arxiv.org/abs/1503.04323
We show that self-similar sets arising from iterated function systems that satisfy the Moran open-set condition, a canonical class of fractal sets, are `equi-homogeneous'. This is a regularity property that, roughly speaking, means that at each fixed
Externí odkaz:
http://arxiv.org/abs/1409.4659
Publikováno v:
Real Analysis Exchange, 42, (2017), 253-268
A Besicovitch set is a subset of $\R^d$ that contains a unit line segment in every direction and the famous Kakeya conjecture states that Besicovitch sets should have full dimension. We provide a number of results in support of this conjecture in a v
Externí odkaz:
http://arxiv.org/abs/1407.6689
Let $\Lambda$ be a complete metric space, and let $\{S_\lambda(\cdot):\ \lambda\in\Lambda\}$ be a parametrised family of semigroups with global attractors ${\mathscr A}_\lambda$. We assume that there exists a fixed bounded set $D$ such that ${\mathsc
Externí odkaz:
http://arxiv.org/abs/1407.3306
Publikováno v:
Math. Proc. Camb. Phil. Soc. 160 (2015) 51-75
In this paper we consider the relationship between the Assouad and box-counting dimension and how both behave under the operation of taking products. We introduce the notion of `equi-homogeneity' of a set, which requires a uniformity in the size of l
Externí odkaz:
http://arxiv.org/abs/1407.0676