On Weak∗-Extensible Subspaces of Banach Spaces

Let X be a Banach space and Y⊆X be a closed subspace. We prove that if the quotient X/Y is weakly Lindelöf determined or weak Asplund, then for every w∗-convergent sequence (y∗n)n∈N in Y∗ there exist a subsequence (y∗nk)k∈N and a w∗-convergent sequence (x∗k)k∈N in X∗ such that x∗k|Y=y∗nk for all k∈N. As an application, we obtain that Y is Grothendieck whenever X is Grothendieck and X/Y is reflexive, which answers a question raised by González and Kania.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The research is partially supported by Agencia Estatal de Investigación [MTM2017-86182-P, grant cofunded by ERDF, EU] and Fundación Séneca [20797/PI/18]. The research of G. Martínez-Cervantes was also partially supported by the European Social Fund and the Youth European Initiative under Fundación Séneca [21319/PDGI/19]

Nuevos liderazgos de extrema derecha: Santiago Abascal

El estudio de los liderazgos políticos ha sido una de las producciones científicas más habituales de la Ciencia Política. El trabajo que se presenta a continuación tiene como objetivo analizar el liderazgo de Santiago Abascal en su condición de líder de la formación de derecha radical española VOX en comparación con el resto de líderes de los principales partidos estatales. Para ello, aplicando herramientas propias de la disciplina buscaremos explicar cuales son las diferencias fundamentales entre los liderazgos de los partidos tradicionales del sistema político español y el liderazgo del ya anteriormente mencionado, Santiago Abascal.O estudo dos liderados políticos é unha das producións científicas máis habituais da Ciencia Política. O traballo que se presenta a continuación ten coma obxectivo analizar o liderado de Santiago Abascal na súa condición de líder da formación de dereita radical española VOX en comparación co resto de líderes dos principais partidos estatais. Para elo, apricando ferramentas propias da disciplina tentaremos explicar cales son as diferenzas fundamentais entre os liderados dos partidos tradicionais do sistema político español e o liderado do xa anteriormente mencionado, Santiago Abascal.The study of political leadership has been one of the most common scientific production of Political Science. The work presented bellow aims to analyze the leadership of Santiago Abascal in his condition of leader of the radical right formation VOX compared to the rest of spanish parties. For this, applying tolos of the discipline we will try to explain the fundamental differencesbetween traditional parties leadership and the radical right leader Santiago Abascal

Molecular phylogeny of the genera Palaemon and Palaemonetes (Decapoda, Caridea, Palaemonidae) from a European perspective

A molecular phylogenetic study by Murphy & Austin (2003) showed that Australian representatives of three shrimp genera of the family Palaemonidae (Palaemon, Palaemonetes, and Macrobrachium) do not cluster according to their generic classification. According to their results, the monophyly of these genera is questioned and the generic classification of the subfamily Palaemoninae is at stake. A large number of representatives of Palaemon and Palaemonetes inhabit European waters, including the type species of each genus. To clarify the phylogeny of these species, and thus the position of the generic names Palaemon and Palaemonetes on a phylogenetic tree, we obtained DNA sequences of the same genetic markers (16S mtDNA) as used by Murphy & Austin (2003) and re-addressed the question of taxonomy and phylogeny of these two genera within the subfamily Palaemoninae. Our results confirm the paraphyly of Palaemon and Palaemonetes. In contrast, the resulting monophyletic clades reflect the geographic distribution of the species according to their respective continents: Africa-Europe, Asia, Australia, and America. With the exception of Palaemon elegans the Afro-European species cluster in a way that would support monophyly of the two genera, if representatives from other continents are excluded. Possible taxonomic solutions are discussed.Research was partly funded by the postdoctoral grant from “Ministerio de Educación Cultura y Deporte” (Spain), and a Research contract “Ramón y Cajal” from “Ministerio de Ciencia y Tecnología” (Spain) to J.A.C.Peer Reviewe

Video visualization profile analysis in online courses

In this article, student video visualization profiles are analyzed with two objectives: 1) to identify difficult sections in videos and 2) to predict student performance based on their video visualization profiles. For identifying critical sections in videos two novel indicators are proposed. The first one is designed to measure the complexity of the concept being described. The second proposal, identifies video sections that are more visually complex. For the first indicator, the average number of forward and backward passes are used. The higher the number of backward (forward) passes over a region, the more challenging (easy) the section is. For identifying sections with complex visuals, the number of pauses is recorded. Finally, the student performance prediction is carried out with the purpose of detecting the alignment between videos and their related questions. The results show that video visualization profiles are a good tool to identify video and question alignmen

Lattice embeddings in free Banach lattices over lattices

In this article we deal with the free Banach lattice generated by a lattice and its behavior with respect to subspaces. In general, any lattice embedding i:L⟶M between two lattices L⊆M induces a Banach lattice homomorphism ı^:FBL⟨L⟩⟶FBL⟨M⟩ between the corresponding free Banach lattices. We show that this mapping ı^ might not be an isometric embedding neither an isomorphic embedding. In order to provide sufficient conditions for ı^ to be an isometric embedding we define the notion of locally complemented lattices and prove that, if L is locally complemented in M, then ı^ yields an isometric lattice embedding from FBL⟨L⟩ into FBL⟨M⟩. We provide a wide number of examples of locally complemented sublattices and, as an application, we obtain that every free Banach lattice generated by a lattice is lattice isomorphic to an AM-space or, equivalently, to a sublattice of a C(K)-space. Furthermore, we prove that ı^ is an isomorphic embedding if and only if it is injective, which in turn is equivalent to the fact that every lattice homomorphism x∗:L⟶[−1,1] extends to a lattice homomorphism x^∗:M⟶[−1,1]. Using this characterization we provide an example of lattices L⊆M for which ı^ is an isomorphic not isometric embedding.Research partially supported by Fundación Séneca [20797/PI/18] and by project MTM2017-86182-P (Government of Spain, AEI/FEDER, EU). The research of G. Martínez-Cervantes was co-financed by the European Social Fund and the Youth European Initiative under Fundación Séneca [21319/PDGI/19]. J. D. Rodríguez Abellán was also supported by project 20262/FPI/17, Fundación Séneca, Región de Murcia (Spain). The research of A. Rueda Zoca was also supported by Juan de la Cierva-Formación fellowship FJC2019-039973, by MICINN (Spain) Grant PGC2018-093794-B-I00 (MCIU, AEI, FEDER, UE), by Junta de Andalucía Grant A-FQM-484-UGR18 and by Junta de Andalucía Grant FQM-0185

Topological properties in tensor products of Banach spaces

Given two Banach spaces X and Y , we analyze when the projective tensor product X⊗πY has Corson’s property (C) or is weakly Lindelöf determined (WLD), subspace of a weakly compactly generated (WCG) space or subspace of a Hilbert generated space. For instance, we show that: (i) X⊗πY is WLD if and only if both X and Y are WLD and all operators from X to Y ∗ and from Y to X∗ have separable range; (ii) X ⊗πY is subspace of a WCG space if the same holds for both X and Y under the assumption that every operator from X to Y ∗ is compact; (iii) p(Γ)⊗πq(Γ) is subspace of a Hilbert generated space for any 1 < p,q < ∞ such that 1/p + 1/q < 1 and for any infinite set Γ. We also pay attention to the injective tensor product X⊗εY . In this case, the stability of property (C) and the property of being WLD turn out to be closely related to the condition that all regular Borel probability measures on the dual ball have countable Maharam type. Along this way, we generalize a result of Plebanek and Sobota that if K is a compact space such that C(K × K) has property (C), then all regular Borel probability measures on K have countable Maharam type. This generalization provides a consistent negative answer to a question of Ruess and Werner about the preservation of the w∗-angelicity of the dual unit ball under injective tensor products.The research is partially supported by grants MTM2017-86182-P (funded by MCIN/AEI/10.13039/501100011033 and “ERDF A way of making Europe”) and 20797/PI/18 (funded by Fundación Séneca - ACyT Región de Murcia). A. Rueda Zoca was also partially supported by: grant PGC2018-093794-B-I00 (funded by MCIN/AEI/10.13039/501100011033 and “ERDF A way of making Europe”), grant FJC2019-039973 (funded by MCIN/AEI/10.13039/501100011033) and grants A-FQM-484-UGR18 and FQM-0185 (funded by Junta de Andalucía)

LCG Service Challenge 3 at the Spanish Tier-1 and Tier-2 sites

This note describes the participation of the Spanish centres PIC and CIEMAT in the LCG Service Challenge 3 as Tier-1 and Tier-2 sites respectively. Data transfer, job submission and data throughput from mass storage to the data processing jobs have been successfully exercised at the desired level. Very valuable experience has been gained running the complex computing system under realistic conditions at a signi cant scale