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Let T : X -> Y be a bounded linear operator between Banach spaces X, Y. A vector x(0) is an element of S-X in the unit sphere S-X of X is called a supporting vector of T provided that parallel to T(x(0))parallel to = sup{parallel to T(x)parallel to : parallel to x parallel to = 1} = parallel to T parallel to. Since matrices induce linear operators between finite-dimensional Hilbert spaces, we can consider their supporting vectors. In this manuscript, we unveil the relationship between the principal components of a matrix and its supporting vectors. Applications of our results to real-life problems are provided., Spanish Government FEDER-UCA18-105867, ERDF Operational Programme, University of the Regional Government of Andalusia PGC-101514-B-I00

A supporting vector of a matrix A for a certain norm $$\Vert \cdot \Vert $$ on $$\mathbb {R}^n$$ is a vector x such that $$\Vert x\Vert =1$$ and $$\Vert Ax\Vert =\Vert A\Vert =\displaystyle \max _{\Vert y\Vert =1}\Vert Ay\Vert $$ . In this manuscript, we characterize the existence of supporting vectors in the infinite-dimensional case for both the $$\ell _1$$ -norm and the $$\ell _{\infty }$$ -norm. Besides this characterization, our theorems provide a description of the set of supporting vectors for operators on $$\ell _{\infty }$$ and $$\ell _1$$ . As an application of our results in the finite-dimensional case for both the $$\ell _1$$ -norm and the $$\ell _{\infty }$$ -norm, we study meteorological data from stations located on the province of Cadiz (Spain). For it, we consider a matrix database with the highest temperature deviations of these stations.

SE Iberia Tectonics is presently dominated by the NNW-SSE convergence between the Eurasian and Nubian plates. Farther east, the eastern Spanish coast and the Valencia Trough are dominated by ENE-WSW extension related to thermal subsidence. This extension has been interpreted as the final stage of abort rift responsible for the ENE motion of the Balearic promontory. Our data from 11 CGNSS stations permit us to discuss the deformation partitioning in SE Iberia related to the two abovementioned processes.We identify three kinematic domains: a relatively stable domain, a domain moving towards NNW and undergoing NNW-SSE shortening, and a third domain relatively moving towards ENE and experiencing ENE-WSW extension. Our results indicate that plate convergence-related NNW-SSE shortening is mainly absorbed by the Eastern Betic Shear Zone (EBSZ), in agreement with previous studies, but also show that a significant fraction of this shortening is accommodated south of the EBSZ.We also identify and quantify for the first time ENE-WSW extension northeast of the EBSZ. We propose that this extension could be absorbed by basement normal faults whose surface expression is obscured due to decoupling of deformation between the basement and the cover. Our results shed light on the tectonic puzzle of SE Spain.

We here discuss the results of a local GNSS episodic network from the Baza sub-Basin (S Spain). This network including six sites, was established in 2008 and has been measured seven times since then. Our data permit us to present the first short-term slip rates for the two active faults in this area. The main active structure is the normal Baza Fault. We estimate slip rates for this fault ranging between 0.3±0.3 mm/yr and 1.3±0.4 mm/yr. For the strike-slip Galera Fault, we quantify the slip rate as 0.5±0.3 mm/yr. These values are higher than previously reported long-term slip rates. We postulate that the discrepancy for the Baza Fault between short-term and long-term slip rates could indicate that the fault is presently in a period with a displacement rate higher than the mean of the magnitude 6 seismic cycle. Moreover, the velocity vectors that we obtained also show the regional tectonic significance of the Baza Fault, as this structure accommodates one-third of the regional extension of the Central Betic Cordillera.Our results also show that the Baza and Galera Faults are kinematically coherent and they divide the Baza sub-Basin into two tectonic blocks. This points to a likely physical link between the Baza and Galera Faults; hence, a potential complex rupture involving both faults should be considered in future seismic hazard assessment studies.

Good air quality is essential for both human beings and the environment in general. The three most harmful air pollutants are nitrogen dioxide (NO2), ozone (O-3) and particulate matter. Due to the high cost of monitoring stations, few examples of this type of infrastructure exist, and the use of low-cost sensors could help in air quality monitoring. The cost of metal-oxide sensors (MOS) is usually below EUR 10 and they maintain small dimensions, but their use in air quality monitoring is only valid through an exhaustive calibration process and subsequent precision analysis. We present an on-field calibration technique, based on the least squares method, to fit regression models for low-cost MOS sensors, one that has two main advantages: it can be easily applied by non-expert operators, and it can be used even with only a small amount of calibration data. In addition, the proposed method is adaptive, and the calibration can be refined as more data becomes available. We apply and evaluate the technique with a real dataset from a particular area in the south of Spain (Granada city). The evaluation results show that, despite the simplicity of the technique and the low quantity of data, the accuracy obtained with the low-cost MOS sensors is high enough to be used for air quality monitoring., The researchers would like to thank the University of Cadiz for the grant obtained through its "Programa de Fomento e Impulso de la actividad de Investigacion y Transferencia". The authors would also like to thank to the Environmental Technology researching group and Acoustic Engineering Laboratory researching group, TEP-181 and TEP-195, respectively, for the access to the devices and data of the EcoBici Project (number G-GI3002/IDIC). Alfonso J. Bello acknowledges the support received from the 2014-2020 ERDF Operational Program and by the Department of Economy, Knowledge, and Business and the University of the Regional Government of Andalusia, Spain, under grant: FEDER-UCA18-107519.

This research analyses the impact of COVID-19 on the Spanish university system during the period of home lockdown put in place by the government of Spain between 15 March and 21 June 2020. This period did not involve a change to online teaching. Instead, it involved emergency remote teaching, wherein the content of face-to-face teaching was taught through non-classroom training using media, devices and tools available at that time. The main objective of the paper is related to the perceptions of students and teachers on emergency remote teaching regarding the face-to-face model. We applied statistical techniques of descriptive and inferential analysis over a sample of 2778 students and 221 teaching staff from the University of Cádiz. We also analysed the methodologies used, as well as the acquisition of skills, competencies and knowledge by the students in this situation, in order to detect whether this type of action can achieve sustainable education. This term refers to education that is capable of maintaining the continuous quality of the training of each student, who should acquire the required knowledge and competences regardless of unforeseen events. However, according to the results of this research, the sudden transition to e-learning, based on available technological and computer-based methods, did not guarantee sustainable education or its quality. This study establishes different possibilities for improving non-face-to-face teaching in this kind of situation. The results show greatly concerning levels of training and evaluation, as well as worse acquisition of skills. Both teachers and students declared a preference for face-to-face teaching. This perception should prompt the educational authorities to solve the existing problems in e-learning education, improving the transition and guaranteeing the sustainability of non-face-to-face education. This research highlights the areas for improvement in e-learning education in the ongoing situation, the general uncertainty in the transition, the lack of communication and the completion of a fair evaluation system. The results show that the methods used in this period must be improved to achieve sustainable teaching and learning during a pandemic. The results also emphasize the uncertainty in the educational community about the entire process. This study will help the educational authorities to improve the change of paradigm in higher education in the future.

One of the most significant parameters for seismic hazard assessment analyses is the fault slip rate. The combination of both geological (long-term) and geodetic (short-term) data offers a more complete characterization of the seismic potential of active faults. Moreover, geodetic data are also a helpful tool for the analysis of geodynamic processes. In this work, we present the results of a local GPS network from the Baza sub-Basin (SE Spain). This network, which includes six sites, was established in 2008 and has been observed for seven years. For the first time, we obtain short-term slip rates for the two active faults in this area. For the normal Baza Fault, we estimate slip rates ranging between 0.3 ± 0.3 mm/yr and 1.3 ± 0.4 mm/yr. For the strike-slip Galera Fault, we quantify the slip rate as 0.5 ± 0.3 mm/yr. Our GPS study shows a discrepancy for the Baza Fault between the short-term slip rates and previously reported long-term rates. This discrepancy indicates that the fault could be presently in a period with a displacement rate higher than the mean of the magnitude 6 seismic cycle. Moreover, the velocity vectors that we obtained also show the regional tectonic significance of the Baza Fault, as this structure accommodates one-third of the regional extension of the Central Betic Cordillera. Our GPS-related slip rates form the basis for future seismic hazard analysis in this area. Our results have further implications, as they indicate that the Baza and Galera Faults are kinematically coherent and they divide the Baza sub-Basin into two tectonic blocks. This points to a likely physical link between the Baza and Galera Faults; hence, a potential complex rupture involving both faults should be considered in future seismic hazard assessment studies., We acknowledge the comments of Editor Prof. Irina M. Artemieva and two anonymous reviewers, which significantly improved the quality of this paper. This research was funded by the Spanish Ministry of Science, Innovation and University (Research Projects: RTI2018-100737-BI00 and CGL2016-80687-R), the University of Alicante (Research Project: VIGROB053), the University of Jaén (PAIUJA 2019-2020 and Programa Operativo FEDER Andalucía 2014-2020 - call made by UJA 2018), the University of Granada (B-RNM-301-UGR18) and the Junta de Andalucía regional government (RNM148, RNM282, and RNM370 and P18-RT-3275 research groups). We thank all observers who collected the data of survey-mode GPS measurements.

There are typically several perturbation methods for approaching the solution of weakly nonlinear vibrations (where the nonlinear terms are “small” compared to the linear ones): the Method of Strained Parameters, the Naive Singular Perturbation Method, the Method of Multiple Scales, the Method of Harmonic Balance and the Method of Averaging. The Straightforward Expansion Perturbation Method (SEPM) applied to weakly nonlinear vibrations does not usually yield to correct solutions. In this manuscript, we provide mathematical proof of the inaccuracy of the SEPM in general cases. Nevertheless, we also provide a sufficient condition for the SEPM to be successfully applied to weakly nonlinear vibrations. This mathematical formalism is written in the syntax of the first-order formal language of Set Theory under the methodology framework provided by the Category Theory.

The Betic Cordillera (S Spain), located in the convergent plate boundary between Eurasia and Nubia, is an area of moderate seismicity. These plates converge at a rate of approximately 4 to 6 mm/yr in the NW-SE direction (see review by Nocquet, 2012). Between 2.7 to 3.9 mm/yr of present-day plate convergence is accommodated in N Africa. Active shortening must occur at rates ranging from 1.6 to 2.7±0.6 mm/year across the Algero-Balearic Basin and the SE Iberian Peninsula (Serpelloni et al., 2007; Pérez-Peña et al., 2010; Echeverría et al., 2013). In the Betic Cordillera, most of the deformation is concentrated in the Betic Internal Zones, while the Betic External zones are considered as a slow-strain area.In SE of Spain onshore active deformation and seismicity are mainly located along the Eastern Betic Shear Zone (EBSZ), a major strike-slip tectonic corridor belonging to the Betic Internal Zones. Regional and local geodetic studies indicate that the EBSZ is absorbing between 0.2 and 1.3 mm/yr (Serpelloni et al., 2007; Pérez-Peña et al., 2010; Echeverría et al., 2013; Borque et al., 2019), i.e. only a portion of regional deformation. We postulate that part of this deformation not absorbed by the EBSZ is accommodated in the eastern Betic External Zones, located to the north of the EBSZ, where several major historical earthquakes occurred (e.g., the 1748 Estubeny, 1396 Tavernes, and 2017 Caudete earthquakes). These major events have been attributed to the Jumilla Fault, the only major active structure described in this area (Giner-Robles et al. 2014; García-Mayordomo, J. and Jiménez-Díaz, A., 2015).We present new CGPS data analysis that corroborate that the eastern Betic External Zones accommodate a significant part of the present convergence. Furthermore, our preliminary data quantify deformation in this area for the first time, as we obtain a shortening rate in the N-S direction of 1.43±0.06 mm/yr in the western sector of the Jumilla Fault (Murcia sector) and of 1.69±0.07 mm/yr in the eastern sector of the fault (Valencia sector). We propose that this deformation is likely related to the Jumilla Fault. Our study place constraints on the seismic potential of the highly populated eastern Betic External Zones, as the preliminary values that we obtained are significantly higher than those previously stated. Consequently, we propose that a re-assesment of seismic hazard is necessary for this highly populated region. Moreover, we also propose a regional geodynamic model that provide insights into mechanisms controlling earthquakes in the eastern Betic External Zones. ReferencesBorque et al. (2019). Tectonics, 38, 5, 1824-1839Echeverria et al. (2013). Tectonophysics, 608, 600-612.Giner-Robles et al. (2014). Resúmenes de la 2ª Reunión Ibérica sobre Fallas Activas y Paleosismología, Lorca, España, 155-158.García-Mayordomo, J. and Jiménez-Díaz, A. (2015). In: Quaternary Faults Database of Iberia v.3.0 - November 2015 (García-Mayordomo et al., eds.), IGME, Madrid.Nocquet, J.M. (2012). Tectonophysics, 579, 220-242.Pérez-Peña et al. (2010). Geomorphology, 119, 74-87Serpelloni et al. (2007). Geophysical Journal Internationl, 169(3), 1180-1200.

The Padul Fault is located in the Central Betic Cordillera, formed in the framework of the NW-SE Eurasian-African plate convergence. In the Internal Zone, large E-W to NE-SW folds of western Sierra Nevada accommodated the greatest NW-SE shortening and uplift of the cordillera. However, GPS networks reveal a present-day dominant E-W to NE-SW extensional setting at surface. The Padul Fault is the most relevant and best exposed active normal fault that accommodates most of the NE-SW extension of the Central Betics. This WSW-wards dipping fault, formed by several segments of up to 7 km maximum length, favored the uplift of the Sierra Nevada footwall away from the Padul graben hanging wall. A non-permanent GPS network installed in 1999 constrains an average horizontal extensional rate of 0.5 mm/yr in N66°E direction. The fault length suggests that a (maximum) 6 magnitude earthquake may be expected, but the absence of instrumental or historical seismic events would indicate that fault activity occurs at least partially by creep. Striae on fault surfaces evidence normal-sinistral kinematics, suggesting that the Padul Fault may have been a main transfer fault of the westernmost end of the Sierra Nevada antiform. Nevertheless, GPS results evidence: (1) shortening in the Sierra Nevada antiform is in its latest stages, and (2) the present-day fault shows normal with minor oblique dextral displacements. The recent change in Padul fault kinematics will be related to the present-day dominance of the ENE-WSW regional extension versus ~ NNW-SSE shortening that produced the uplift and northwestwards displacement of Sierra Nevada antiform. This region illustrates the importance of heterogeneous brittle extensional tectonics in the latest uplift stages of compressional orogens, as well as the interaction of folding during the development of faults at shallow crustal levels. This research was funded by PAIUJA 2017/2018, UJA2016/00086/001 project, CGL2016-80687-R AEI/FEDER, UE project and RNM148 and RNM282 research groups of Junta de Andalucía.

We present a P-wave scattering image of the volcanic structures under Tenerife Island using the autocorrelation functions of P-wave vertical velocity fluctuations. We have applied a cluster analysis to total quality factor attenuation ( $$ {Q}_t^{-1} $$ ) and scattering quality factor attenuation ( $$ {Q}_{PSc}^{-1} $$ ) images to interpret the structures in terms of intrinsic and scattering attenuation variations on a 2D plane, corresponding to a depth of 2000 m, and check the robustness of the scattering imaging. The results show that scattering patterns are similar to total attenuation patterns in the south of the island. There are two main areas where patterns differ: at Canadas-Teide-Pico Viejo Complex, high total attenuation and average-to-low scattering values are observed. We interpret the difference as induced by intrinsic attenuation. In the Santiago Ridge Zone (SRZ) region, high scattering values correspond to average total attenuation. In our interpretation, the anomaly is induced by an extended scatterer, geometrically related to the surficial traces of Garachico and El Chinyero historical eruptions and the area of highest seismic activity during the 2004–2008 seismic crises.

In this manuscript we provide an exact solution to the maxmin problem max ∥ A x ∥ subject to ∥ B x ∥ &le, 1 , where A and B are real matrices. This problem comes from a remodeling of max ∥ A x ∥ subject to min ∥ B x ∥ , because the latter problem has no solution. Our mathematical method comes from the Abstract Operator Theory, whose strong machinery allows us to reduce the first problem to max ∥ C x ∥ subject to ∥ x ∥ &le, 1 , which can be solved exactly by relying on supporting vectors. Finally, as appendices, we provide two applications of our solution: first, we construct a truly optimal minimum stored-energy Transcranian Magnetic Stimulation (TMS) coil, and second, we find an optimal geolocation involving statistical variables.

CSIC Servicio de enlaces(opens in a new window)|Library catalogue(opens in a new window)|View at Publisher| Export | Download | Add to List | More... Journal of Volcanology and Geothermal Research January 21, 2016 Subsidence and current strain patterns on Tenerife Island (Canary Archipelago, Spain) derived from continuous GNSS time series (2008-2015) ( Articles not published yet, but available online Article in press About articles in press (opens in a new window) ) Sánchez-Alzola, A.a , Martí, J.b, García-Yeguas, A.c, Gil, A.J.d a Departamento de Estadística e Investigación Operativa, Universidad de Cádiz, Spain b Instituto de Ciencias de la Tierra Jaume Almera CSIC, Barcelona, Spain c Departamento de Física Aplicada, Universidad de Cádiz, Spain View additional affiliations Abstract In this paper we present the current crustal deformation model of Tenerife Island derived from daily CGPS time series processing (2008-2015). Our results include the position time series, a global velocity estimation and the current crustal deformation on the island in terms of strain tensors. We detect a measurable subsidence of 1.5-2. mm/yr. in the proximities of the Cañadas-Teide-Pico Viejo (CTPV) complex. These values are higher in the central part of the complex and could be explained by a lateral spreading of the elastic lithosphere combined with the effect of the drastic descent of the water table in the island experienced during recent decades. The results show that the Anaga massif is stable in both its horizontal and vertical components. The strain tensor analysis shows a 70. nstrain/yr. E-W compression in the central complex, perpendicular to the 2004 sismo-volcanic area, and 50. nstrain/yr. SW-NE extension towards the Northeast ridge. The residual velocity and strain patterns coincide with a decline in volcanic activity since the 2004 unrest. © 2016 Elsevier B.V.

In this paper, we present a first estimation, using the GIPSY-OASIS software, of the crustal velocity and strain rate fields in the Balearic Islands (Spain), based on continuous GPS observations from the XGAIB network spanning the period 2010-2013. The XGAIB network consists of nine permanent, widely distributed stations that have operated continuously since 2010. In this paper, we describe the XGAIB network and the CGPS data processing and present our principle results in terms of the position time series and velocities of all of the sites, which were observed for more than three and a half years. In addition, strain tensors were estimated from the velocity field to obtain the first realistic crustal deformation model of the archipelago. The strains exhibit gradual variation across the Balearic Islands, from WNW-ESE extension in the southwest (Ibiza and Formentera) to NW-SE compression in the northeast (Menorca). These results constitute an advance in our knowledge of the tectonics of the western Mediterranean region. This research was partly funded by the Spanish Ministry of Science and Innovation through the AYA2010-15501, CGL2011-30153-C02-02 and CSD2006-0041 projects (European Regional Development Fund-ERDF).

Since 1987, Spain has been continuously developing several scientific projects, mainly based on Earth Sciences, in Geodesy, Geochemistry, Geology or Volcanology. The need of a geodetic reference frame when doing hydrographic and topographic mapping meant the organization of the earlier campaigns with the main goals of updating the existing cartography and of making new maps of the area. During this period of time, new techniques arose in Space Geodesy improving the classical methodology and making possible its applications to other different fields such as tectonic or volcanism. Spanish Antarctic Geodetic activities from the 1987–1988 to 2006–2007 campaigns are described as well as a geodetic and a levelling network are presented. The first network, RGAE, was designed and established to define a reference frame in the region formed by the South Shetlands Islands, the Bransfield Sea and the Antarctic Peninsula whereas the second one, REGID, was planned to control the volcanic activity in Deception Island. Finally, the horizontal and vertical deformation models are described too, as well as the strategy which has been followed when computing an experimental geoid.