AbstractIn this note, we study the long-time dynamics of passive scalars driven by rotationally symmetric flows. We focus on identifying precise conditions on the velocity field in order to prove enhanced dissipation and Taylor dispersion in three-dimensional infinite pipes. As a byproduct of our analysis, we obtain an enhanced decay for circular flows on a disc of arbitrary radius.
It is consistent with ZF set theory that the Euclidean topology on the real line is not sequential, yet every infinite set of reals contains a countably infinite subset. This answers a question of Gutierres.
El presente artículo es una reflexión desde la perspectiva de la experiencia como doctora en Educación, desde hace diecinueve años. Lo que me permite realizar un análisis crítico de la Educación en América Latina y el estado juicioso de los procesos que de una u otra forma han sucedido, en el escenario de los países. La educación es un fenómeno social de relevante importancia para la formación y el desarrollo del hombre. El destacado pedagogo catalán Octavi Fullat ha expresado: “el ser hombre es tener que educarse”, para significar que no se pueden separar: antropos y educación.
We give a refinement of proof-theoretic analysis of the lpo (lexicographic path order) due to W. Buchholz. This note was written in Feb. 5, 2015 when G. Moser visited Japan.
Assuming the existence of a Mahlo cardinal, we construct a model in which there exists an $ω_2$-Aronszajn tree, the $ω_1$-approachability property fails, and every stationary subset of $ω_2 \cap \mathrm{cof}(ω)$ reflects.
We show that if $λ^{<κ} = λ$ and every normal filter on $P_κλ$ can be extended to a $κ$-complete ultrafilter then so does every $κ$-complete filter on $λ$. This answers a question of Gitik.
We relate the notions of spectral gap for unitary representations and subfactors with definability of certain important sets in the corresponding structures. We give several applications of this relationship.
A complete analysis is given of the computable reductions that hold between $\mathsf{SRT}^2_2$, $\mathsf{SPT}^2_2$, and $\mathsf{SIPT}^2_2$. In particular, while $\mathsf{D}^2_2\le_{\rm sW}\mathsf{SIPT}^2_2\le_{\rm sW}\mathsf{SPT}^2_2\le_{\rm sW}\mathsf{SRT}^2_2$, it is shown that $\mathsf{SRT}^2_2\not\le_{\rm sc}\mathsf{SPT}^2_2\not\le_{\rm sc}\mathsf{SIPT}^2_2\not\le_{\rm sc}\mathsf{D}^2_2$.
We show that a hypersimple unidimensional theory that has a club of reducts, in the partial order of all countable reducts, that are coordinatized in finite rank, is supersimple.
These notes find a canonical representation of the $\aleph_0$-categorical linear orders based on Joseph Rosenstein's description. A unique minimal representation, called the normal form, is obtained.
We extend Baumgartner's result on isomorphisms of aleph_1 dense subsets of the reals R in two ways: First, the function can be made to be absolutely continuous. Second, one can replace R by R^n.
We prove that there is a factor of the Muchnik lattice that captures intuitionistic propositional logic. This complements a now classic result of Skvortsova for the Medvedev lattice.