192 research outputs found
On periodic homeomorphisms of spheres
The purpose of this paper is to study how small orbits of periodic
homemorphisms of spheres can be.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-22.abs.htm
Self-dual Maps III: projective links
In this paper, we present necessary and sufficient combinatorial conditions
for a link to be projective, that is, a link in . This characterization
is closely related to the notions of antipodally self-dual and antipodally
symmetric maps. We also discuss the notion of symmetric cycle, an interesting
issue arising in projective links leading us to an easy condition to prevent a
projective link to be alternating.Comment: arXiv admin note: substantial text overlap with arXiv:2106.0537
Acknowledgement of priority - A fractional Helly theorem for boxes
In our recent paper [1] we prove a fractional Helly type theorem for boxes in Rd. This short note is to acknowledge
priority: in 1980 Meir Katchalski [4] proved exactly the same result and in 1988 Jürgen Eckhoff [2] proved the same result
in much more generality. In fact, Eckhoff established an upper bound theorem for the f -vectors of finite families of boxes
in Rd from which his result is derived. Besides apologies for our ignorance we would like to mention that Eckhoff extended
his results further in a more recent paper [3]
Recommended from our members
University Scholars Day
This paper explores the experience of 30 university students in their final year of the teacher education program
Topological transversals to a family of convex sets
Let be a family of compact convex sets in . We say
that has a \emph{topological -transversal of index }
(, ) if there are, homologically, as many transversal
-planes to as -planes containing a fixed -plane in
.
Clearly, if has a -transversal plane, then
has a topological -transversal of index for and . The converse is not true in general.
We prove that for a family of compact convex sets in
a topological -transversal of index implies an
ordinary -transversal. We use this result, together with the
multiplication formulas for Schubert cocycles, the Lusternik-Schnirelmann
category of the Grassmannian, and different versions of the colorful Helly
theorem by B\'ar\'any and Lov\'asz, to obtain some geometric consequences
Surface Reconstruction and Decahedral Structure of Bimetallic Nanoparticles
We report on energetic surface reconstruction phenomena observed on bimetallic nanoparticle systems of AuPd and AuCu, similar to a resolidification effect observed during the cooling process in lead clusters. These binary alloy nanoparticles show the fivefold edges truncated, resulting in { 100 } facets on decahedral structures, an effect largely envisioned and reported theoretically, with no experimental evidence so far. We demonstrate experimentally as well as by computational simulations that this new eutectic structure is favored in such nanoalloy systems.Fil: Rodríguez López J. L.. Instituto Potosino de Investigación Científica y Tecnológica ; MéxicoFil: Montejano Carrizales, J. M.. Universidad Autónoma de San Luis Potosí; MéxicoFil: Pal, U.. Universidad Auto´noma de Puebla; MéxicoFil: Sánchez Ramírez, J. F.. Universidad Auto´noma de Puebla; MéxicoFil: Troiani, Horacio Esteban. Comision Nacional de Energía Atómica. Gerencia de Área Investigaciones y Aplicaciones no Nucleares. Gerencia de Física (Centro Atómico Bariloche). División Física de Metales; ArgentinaFil: García, D.. The University of Texas; Estados UnidosFil: Miki Yoshida, M.. The University of Texas; Estados UnidosFil: José Yacamán, Miguel. The University of Texas; Estados Unido
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