A palladium-hinged organometallic square with a perfect-sized cavity for the encapsulation of three heteroguests

This is a pre-print of an article published in Chemical Communications. The final authenticated version is available online at: https://doi.org/10.1039/C9CC08595E.A nanometer-sized tetrapalladium metallosquare with a pyrene-bisimidazolylidene ligand was found to display a perfect-sized cavity for the encapsulation of three heteroguests, enabling the formation of quintuple D–A–D–A–D stacks. The encapsulating properties of the metallosquare are clearly determined by the presence of the pyrene panels, which endow the metallosquare with a three-dimensional shape, and also behave as effective antennae for π-stacking interactions

Coarse geometry of the fire retaining property and group splittings

Given a non-decreasing function $f \colon \mathbb{N} \to \mathbb{N}$ we define a single player game on (infinite) connected graphs that we call fire retaining. If a graph $G$ admits a winning strategy for any initial configuration (initial fire) then we say that $G$ has the $f$-retaining property; in this case if $f$ is a polynomial of degree $d$, we say that $G$ has the polynomial retaining property of degree $d$. We prove that having the polynomial retaining property of degree $d$ is a quasi-isometry invariant in the class of uniformly locally finite connected graphs. Henceforth, the retaining property defines a quasi-isometric invariant of finitely generated groups. We prove that if a finitely generated group $G$ splits over a quasi-isometrically embedded subgroup of polynomial growth of degree $d$, then $G$ has polynomial retaining property of degree $d-1$. Some connections to other work on quasi-isometry invariants of finitely generated groups are discussed and some questions are raised.Comment: 16 pages, 1 figur

Relative Quasiconvexity using Fine Hyperbolic Graphs

We provide a new and elegant approach to relative quasiconvexity for relatively hyperbolic groups in the context of Bowditch's approach to relative hyperbolicity using cocompact actions on fine hyperbolic graphs. Our approach to quasiconvexity generalizes the other definitions in the literature that apply only for countable relatively hyperbolic groups. We also provide an elementary and self-contained proof that relatively quasiconvex subgroups are relatively hyperbolic.Comment: 21 pages, 6 figures. New section on fine graphs. Version to appear in AG

Bot para practicar inglés

En este proyecto se ha desarrollado un bot para la aplicación Telegram cuyo objetivo es ofrecer al usuario la posibilidad de practicar inglés. Para ello, el bot presentará sus opciones en castellano, para que el usuario las tenga que traducir al inglés. Para conseguirlo, hemos utilizado diferentes tecnologías: Los servicios “Cognitive Services” de Microsoft y “speech to text” de Google, que los utilizamos para procesar el audio, y así el usuario pueda practicar su pronunciación del idioma, y los servicios de “google translate api” para comparar las respuestas. Asimismo, se utilizan diferentes herramientas: “twitterscraper” y “twitter API” con las que obtenemos las frases a traducir y una base de datos “MySQL” para almacenar las frases recogidas de Twitter (las traducciones posibles) y las interacciones del usuario con el bot

Simple permutations with order 4n+24n + 2. Part I

The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Hum\'anez & Bernhardt (power of two). It is well known that Sharkovskii's theorem shows the relationship between the cardinal of the set of periodic points of a continuous map, but simple permutations will show the behavior of those periodic points. This paper studies the structure of permutations of mixed order $4n+2$, its properties and a way to describe its genealogy by using Pasting and Reversing.Comment: 17 page