New examples of constant mean curvature surfaces in S2×R\mathbb{S}^2\times\mathbb{R} and H2×R\mathbb{H}^2\times \mathbb{R}

We construct non-zero constant mean curvature H surfaces in the product spaces $\mathbb{S}^2 \times \mathbb{R}$ and $\mathbb{H}^2\times \mathbb{R}$ by using suitable conjugate Plateau constructions. The resulting surfaces are complete, have bounded height and are invariant under a discrete group of horizontal translations. In $\mathbb{S}^2\times\mathbb{R}$ (for any $H > 0$) or $\mathbb{H}^2\times\mathbb{R}$ (for $H > 1/2$), a 1-parameter family of unduloid-type surfaces is obtained, some of which are shown to be compact in $\mathbb{S}^2\times\mathbb{R}$. Finally, in the case of $H = 1/2$ in $\mathbb{H}^2 \times \mathbb{R}$, the constructed examples have the symmetries of a tessellation of $\mathbb{H}^2$ by regular polygons.Comment: 22 pages, 5 figure

Parallel mean curvature surfaces in four-dimensional homogeneous spaces

We survey different classification results for surfaces with parallel mean curvature immersed into some Riemannian homogeneous four-manifolds, including real and complex space forms, and product spaces. We provide a common framework for this problem, with special attention to the existence of holomorphic quadratic differentials on such surfaces. The case of spheres with parallel mean curvature is also explained in detail, as well as the state-of-the-art advances in the general problem.Comment: 19 pages, 1 table. Minor mistakes have been corrected, and some references have been added in the second and third version

On the Use of Second Order Neighbors to Escape from Local Optima

Designing efficient local search based algorithms requires to consider the specific properties of the problems. We introduce a simple and effi- cient strategy, the Extended Reach, that escapes from local optima ob- tained from a best improvement local search and apply it to the linear ordering problem (LOP), the traveling salesperson problem (TSP) and the quadratic assignment problem (QAP). This strategy is based on two landscape properties observed in the literature. First, it considers that a local optimum is usually located in the frontier of its own attraction basin, and thus, it is enough to inspect the second order neighbors to reach a (better) solution inside an attraction basin of a better local optimum. Second, taking into account that for the LOP and specific neighborhoods it is possible to discard solutions without the need of being evaluated, we extend this result to the TSP with the 2-opt neighborhood to avoid the unnecessary evaluation of solutions. Efficient ways of evaluating the second order neighbors are also presented, based on the cost differences, reducing significantly the computation cost. Experimental results on ran- dom and benchmark instances show that our strategy, indeed, escapes from local optima despite its simplicity.PID2019-104966GB-I00 AXA Research Fun

Research in Mathematics Education in Spain: SEIEM Symposia

Spain produces a large amount of research in mathematics education and its results are presented in the symposia of the Spanish Society for Research in Mathematics Education (SEIEM). This paper presents a study of the proceedings of these symposia. Its aim is to identify some bibliometric indicators and networks of institutional collaboration and co-authorship. The analysis was performed with 268 SEIEM documents. We found a low level of scientific collaboration between researchers in the field. Similar results are obtained for international cooperationEn España se realizan un gran número de investigaciones en Educación Matemática y se presentan avances de sus resultados en los simposios de la Sociedad Española de Investigación en Educación Matemática (SEIEM). En este artículo se presenta un estudio de las actas de dichos simposios. El objetivo de este trabajo es identificar algunos indicadores bibliométricos así como las redes de colaboración institucional y de coautoría. El análisis se realizó con 268 documentos de las actas SEIEM, observándose un bajo porcentaje de colaboración científica entre los investigadores del área. También se obtienen similares resultados en la cooperación internaciona

Sistemes socioeconòmics i financers

Els mercats fi nancers, entre molts altres contextos socials i econòmics, amaguen diverses relacions amb la �� sica estadís�� ca. Sense anar més lluny, el model matemà�� c de les co�� tzacions fi nanceres és el mateix u�� litzat per a la teoria de gasos o per les par�� cules en suspensió en un líquid. En aquest ar�� cle recorrem la trajectòria de l'anomenada econo�� sica des de 1900 i presentem algunes de les contribucions a la matèria feta per membres de Complexitat.CAT

Análisis cienciométrico de las tesis doctorales españolas en Educación Matemática (1976-1998)

Este estudio realiza una revisión cienciométrica usando indicadores de productividad y citación en una muestra de tesis españolas sobre Educación Matemática defendidas en la Universidad española desde 1976 hasta 1998. En concreto, se han analizado 135 tesis recuperadas usando un instrumento de recogida de datos ad hoc. Se infieren patrones cienciométricos contundentes que podrían ayudar a posicionar la Educación Matemática española sobre un estatus científico más firme.This study accomplishes a scientometric review relative to productivity and citation indicators over a sample of doctoral dissertations about Mathematics Education, defended in the Spanish university during the period 1976-1998. We have analysed 135 retrieved thesis using an ad hoc instrument for data collection. Strong scientometric patterns are inferred which could help the Spanish Mathematics Education stand on a sounder scientific status

Magnetic-film atom chip with 10 μ\mum period lattices of microtraps for quantum information science with Rydberg atoms

We describe the fabrication and construction of a setup for creating lattices of magnetic microtraps for ultracold atoms on an atom chip. The lattice is defined by lithographic patterning of a permanent magnetic film. Patterned magnetic-film atom chips enable a large variety of trapping geometries over a wide range of length scales. We demonstrate an atom chip with a lattice constant of 10 $\mu$m, suitable for experiments in quantum information science employing the interaction between atoms in highly-excited Rydberg energy levels. The active trapping region contains lattice regions with square and hexagonal symmetry, with the two regions joined at an interface. A structure of macroscopic wires, cut out of a silver foil, was mounted under the atom chip in order to load ultracold $^{87}$Rb atoms into the microtraps. We demonstrate loading of atoms into the square and hexagonal lattice sections simultaneously and show resolved imaging of individual lattice sites. Magnetic-film lattices on atom chips provide a versatile platform for experiments with ultracold atoms, in particular for quantum information science and quantum simulation.Comment: 7 pages, 7 figure

Research in Mathematics Education through Spanish scholarly publications

Se presenta un estudio bibliométrico y de análisis de las redes de colaboración en los artículos de investigación en Educación Matemática publicados en una muestra de revistas españolas en el período 1999-2008. Para ello se han analizado los 774 artículos publicados en un conjunto de ocho revistas españolas representativas verificándose el cumplimiento de las leyes o patrones propios de la Cienciometría y comprobándose un bajo grado de colaboración científica entre los investigadores del área y también entre las institucionesWe present a bibliometric study of research articles on mathematics education, as well as an analysis of networks of collaboration in the same, based on a sample of Spanish journals published during the period 1999-2008. For this purpose we analyzed 774 articles published in the eight most representative Spanish journals in the fi eld. The results show compliance with scientometric laws and patterns, as well as verifying the low level of scientifi c collaboration among researchers in the area, as well as among institution