http://hdl.handle.net/10498/6793 2026-05-09T04:37:18Z http://hdl.handle.net/10498/39385 Unit neighborhoods of zero in topological ordered rings García Pacheco, Francisco Javier A closed unit neighborhood of zero in a topological ring is an additively symmetric and multiplicatively idempotent regular closed neighborhood of zero containing the unity whose interior is multiplicatively idempotent as well. The search for nontrivial closed unit neighborhoods of zero in topological rings is an ongoing quest. A unital ordered ring is a ring endowed with a partial ordering compatible with the addition and multiplication by positive elements for which zero and the unity are comparable. A topological ordered ring is a unital ordered ring for which the order topology is a ring topology. Recently, it was posed the question whether the set of elements lying in between −1 and 1 is a closed unit neighborhood of 0 in a topological ordered ring. This question has been partially solved on topological totally ordered division rings with no holes. Here, we provide a full answer in topological ordered rings (not relying on total orderings nor on division rings). 2025-01-01T00:00:00Z http://hdl.handle.net/10498/39355 Mobile mutual-visibility sets in graphs Dettlaff, Magda; Lemanska, Magdalena; Rodríguez Velázquez, Juan A.; González Yero, Ismael Given a connected graph G, the mutual-visibility number of G is the cardinality of a largest set S such that for every pair of vertices x, y ∈ S there exists a shortest x, y-path whose interior vertices are not contained in S. Assume that a robot is assigned to each vertex of the set S. At each stage, one robot can move to a neighbouring vertex. Then S is a mobile mutual-visibility set of G if there exists a sequence of moves of the robots such that all the vertices of G are visited while maintaining the mutual-visibility property at all times. The mobile mutual-visibility number of G, denoted Mobµ(G), is the cardinality of a largest mobile mutual-visibility set of G. In this paper we introduce the concept of the mobile mutual-visibility number of a graph. We begin with some basic properties of the mobile mutual-visibility number of G and its relationship with the mutual-visibility number of G. We give exact values of Mobµ(G) for particular classes of graphs, i.e. cycles, wheels, complete bipartite graphs, and block graphs (in particular trees). Moreover, we present bounds for the lexicographic product of two graphs and show characterizations of the graphs achieving the limit values of some of these bounds. As a consequence of this study, we deduce that the decision problem concerning finding the mobile mutual-visibility number is NP-hard. Finally, we focus our attention on the mobile mutual-visibility number of line graphs of complete graphs, prism graphs and strong grids of two paths. 2025-01-01T00:00:00Z http://hdl.handle.net/10498/39345 GNSS-Based Models of Displacement, Stress, and Strain in the SHETPENANT Region: Impact of Geodynamic Activity from the ORCA Submarine Volcano Rosado Moscoso, Belén; Jiménez, Vanessa; Pérez Peña, Alejandro; Martín, Rosa; de Gil, Amos; Carmona Medeiro, Enrique; Gárate, Jorge; Berrocoso Domínguez, Manuel The South Shetland Islands and Antarctic Peninsula (SHETPENANT region) constitute a geodynamically active area shaped by the interaction of major tectonic plates and active magmatic systems. This study analyzes GNSS time series spanning from 2017 to 2024 to investigate surface deformation associated with the 2020–2021 seismic swarm near the Orca submarine volcano. Horizontal and vertical displacement velocities were estimated for the preseismic, coseismic, and postseismic phases using the CATS method. Results reveal significant coseismic displacements exceeding 20 mm in the horizontal components near Orca, associated with rapid magmatic pressure release and dike intrusion. Postseismic velocities indicate continued, though slower, deformation attributed to crustal relaxation. Stations located near the Orca exhibit nonlinear, transient behavior, whereas more distant stations display stable, linear trends, highlighting the spatial heterogeneity of crustal deformation. Stress and strain fields derived from the velocity models identify zones of extensional dilatation in the central Bransfield Basin and localized compression near magmatic intrusions. Maximum strain rates during the coseismic phase exceeded 200 νstrain/year, supporting a scenario of crustal thinning and fault reactivation. These patterns align with the known structural framework of the region. The integration of GNSS-based displacement and strain modeling proves essential for resolving active volcano-tectonic interactions. The findings enhance our understanding of back-arc deformation processes in polar regions and support the development of more effective geohazard monitoring strategies. 2025-01-01T00:00:00Z http://hdl.handle.net/10498/39343 Comprehensive Optoelectronic Study of Copper Nitride: Dielectric Function and Bandgap Energies Ballester, Manuel; Marquez, Almudena P.; Blanco Ollero, Eduardo; Mánuel, José M.; Rodriguez-Tapiador, Maria I.; Fernandez, Susana M.; Willomitzer, Florian; Katsaggelos, Aggelos K.; Márquez Navarro, Emilio José Copper nitride (Cu3N) is gaining attention as an eco-friendly thin-film semiconductor in a myriad of applications, including storage devices, microelectronic components, photodetectors, and photovoltaic cells. This work presents a detailed optoelectronic study of Cu3N thin films grown by reactive RF-magnetron sputtering under pure N2. An overview of the state-of-the-art literature on this material and its potential applications is also provided. The studied films consist of Cu3N polycrystals with a cubic anti-ReO3 type structure exhibiting a preferential (100) orientation. Their optical properties across the UV-Vis-NIR spectral range were investigated using a combination of multi-angle spectroscopic ellipsometry, broadband transmission, and reflection measurements. Our model employs a stratified geometrical approach, primarily to capture the depth-dependent compositional variations of the Cu3N film while also accounting for surface roughness and the underlying glass substrate. The complex dielectric function of the film material is precisely determined through an advanced dispersion model that combines multiple oscillators. By integrating the Tauc–Lorentz, Gaussian, and Drude models, this approach captures the distinct electronic transitions of this polycrystal. This customized optical model allowed us to accurate extract both the indirect (1.83–1.85 eV) and direct (2.38–2.39 eV) bandgaps. Our multifaceted characterization provides one of the most extensive studies of Cu3N thin films to date, paving the way for optimized device applications and broader utilization of this promising binary semiconductor, and showing its particular potential for photovoltaic given its adequate bandgap energies for solar applications. 2025-01-01T00:00:00Z