As dificultades de incorporación das mulleres matemáticas á universidade

[RESUMO] Votamos una ollada as primeiras mulleres matemáticas no eido universitario en Europa dende finais do século XIX, analizamos tamén a situación actual en datos porcentuais facendo especial fincapé nas mulleres españolas e nas galegas. Destacamos as singularidades dalgunhas mulleres que nun ámbito desfavorable sobresaíron polos seus logros académicos e/ou científicos

Resolving Sets Tolerant to Failures in Three-Dimensional Grids

[Abstract] An ordered set S of vertices of a graph G is a resolving set for G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set. In this paper we study resolving sets tolerant to several failures in three-dimensional grids. Concretely, we seek for minimum cardinality sets that are resolving after removing any k vertices from the set. This is equivalent to finding (k+1)-resolving sets, a generalization of resolving sets, where, for every pair of vertices, the vector of distances to the vertices of the set differs in at least k+1 coordinates. This problem is also related with the study of the (k+1)-metric dimension of a graph, defined as the minimum cardinality of a (k+1)-resolving set. In this work, we first prove that the metric dimension of a three-dimensional grid is 3 and establish some properties involving resolving sets in these graphs. Secondly, we determine the values of k≥1 for which there exists a (k+1)-resolving set and construct such a resolving set of minimum cardinality in almost all cases.This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No 734922. M. Mora is supported by projects H2020-MSCA-RISE-2016-734922 CONNECT, PID2019-104129GB-I00/MCIN/AEI/10.13039/501100011033 of the Spanish Ministry of Science and Innovation and Gen.Cat. DGR2017SGR1336; M. J. Souto-Salorio is supported by project PID2020-113230RB-C21 of the Spanish Ministry of Science and Innovation. Open Access funding provided thanks to the CRUECSIC agreement with Springer NatureGeneralitat de Catalunya; DGR2017SGR133

Resolving Sets Tolerant to Failures in Three-Dimensional Grids

[Abstract] An ordered set S of vertices of a graph G is a resolving set for G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set. In this paper we study resolving sets tolerant to several failures in three-dimensional grids. Concretely, we seek for minimum cardinality sets that are resolving after removing any k vertices from the set. This is equivalent to finding (k+1)-resolving sets, a generalization of resolving sets, where, for every pair of vertices, the vector of distances to the vertices of the set differs in at least k+1 coordinates. This problem is also related with the study of the (k+1)-metric dimension of a graph, defined as the minimum cardinality of a (k+1)-resolving set. In this work, we first prove that the metric dimension of a three-dimensional grid is 3 and establish some properties involving resolving sets in these graphs. Secondly, we determine the values of k≥1 for which there exists a (k+1)-resolving set and construct such a resolving set of minimum cardinality in almost all cases.This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No 734922. M. Mora is supported by projects H2020-MSCA-RISE-2016-734922 CONNECT, PID2019-104129GB-I00/MCIN/AEI/10.13039/501100011033 of the Spanish Ministry of Science and Innovation and Gen.Cat. DGR2017SGR1336; M. J. Souto-Salorio is supported by project PID2020-113230RB-C21 of the Spanish Ministry of Science and Innovation. Open Access funding provided thanks to the CRUECSIC agreement with Springer NatureGeneralitat de Catalunya; DGR2017SGR133

Algorithms for determining relative position between spheroids and hyperboloids with one sheet

©2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https:// creativecommons.org/licenses/by-nc-nd/4.0/. This version of the article: Castro, P. M., Dapena, A., Souto- Salorio, M. J., & Tarrío-Tobar, A. D. (2019). 'Algorithms for determining relative position between spheroids and hyperboloids with one sheet', has been accepted for publication in Mathematics and Computers in Simulation, 160, 168–179.The Version of Record is available online at https://doi.org/10.1016/j.matcom.2018.12.006.[Abstract]: In this work we present a new method for determining relative positions between one moving object, modelled by a bounding spheroid, and surrounding static objects, modelled by circular hyperboloids of one sheet. The proposed strategy is based on the real-time calculation of the coefficients of degree three polynomial. We propose several algorithms for two real applications of this geometric problem: the first one, oriented to the design of video games, and the second one, devoted to surveillance tasks of a quadcopter in industrial or commercial environments.This work has been funded by the Xunta de Galicia, Spain (ED431C 2016-045, ED341D R2016/012, ED431G/01), the Agencia Estatal de Investigación of Spain (TEC2013-47141-C4-1-R, TEC2015-69648-REDC, TEC2016-75067-C4-1-R) and ERDF funds of the EU (AEI/FEDER, UE). The authors wish to thank José Sanmartín for his helpful work in the graphic design of the pictures included in this paper.Xunta de Galicia; ED431C 2016-045Xunta de Galicia; ED341D R2016/012Xunta de Galicia; ED431G/0

Classification of the relative positions between a small ellipsoid and an elliptic paraboloid

©2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/. This version of the article Brozos-Vázquez, M., Pereira-Sáez, M. J., Souto-Salorio, M. J., & Tarrío-Tobar, A. D. (2019). “Classification of the relative positions between a small ellipsoid and an elliptic paraboloid” has been accepted for publication in Computer Aided Geometric Design, 72, 34–48. The Version of Record is available online at https://doi.org/10.1016/j.cagd.2019.05.002.[Abstract]: We classify all the relative positions between an ellipsoid and an elliptic paraboloid when the ellipsoid is small in comparison with the paraboloid (small meaning that the two surfaces cannot be tangent at two points simultaneously when one is moved with respect to the other). This provides an easy way to detect contact between the two surfaces by a direct analysis of the coefficients of a fourth degree polynomial.The authors wish to thank the referees for extremely valuable comments and suggestions, which were essential to improve the final version of the paper. Supported by Projects ED431F 2017/03, TIN2017-85160-C2-1-R, MTM2016-75897-P and MTM2016-78647-P (AEI/FEDER, UE).Xunta de Galicia; ED431F 2017/0

Contact detection between a small ellipsoid and another quadric

[Abstract] We analyze the characteristic polynomial associated to an ellipsoid and another quadric in the context of the contact detection problem. We obtain a necessary and sufficient condition for an efficient method to detect contact. This condition, named smallness condition, is a feature on the size and the shape of the quadrics and can be checked directly from their parameters. Under this hypothesis, contact can be noticed by means of the expressions in a discriminant system of the characteristic polynomial. Furthermore, relative positions can be classified through the sign of the coefficients of this polynomial. As an application of these results, a method to detect contact between a small ellipsoid and a combination of quadrics is given