The numerical index of 22-dimensional Lipschitz-free spaces

We provide the explicit formula for the numerical index of any $2$-dimensional Lipschitz-free space, also giving the construction of operators attaining this value as its numerical radius. As a consequence, the numerical index of $2$-dimensional Lipschitz-free spaces can take any value of the interval $[\frac{1}{2},1]$, and this whole range of numerical indices can be attained by taking $2$-dimensional subspaces of any Lipschitz-free space of the form $\mathcal{F}(A)$, where $A\subset {\mathbb{R}}^n$ with $n\geq 2$ is any set with non-empty interior

On the preserved extremal structure of Lipschitz-free spaces

[EN] We characterize preserved extreme points of the unit ball of Lipschitz-free spaces F(X) in terms of simple geometric conditions on the underlying metric space (X,d). Namely, the preserved extreme points are the elementary molecules corresponding to pairs of points p,q in X such that the triangle inequality d(p,q)<=d(p,r)+d(q,r) is uniformly strict for r away from p,q. For compact X, this condition reduces to the triangle inequality being strict. As a consequence, we give an affirmative answer to a conjecture of N. Weaver that compact spaces are concave if and only if they have no triple of metrically aligned points, and we show that all extreme points are preserved for several classes of compact metric spaces X, including Hölder and countable compacta.The research of the second author was partially supported by MINECO grant MTM2014-57838-C2-1-P and Fundacion Seneca, Region de Murcia grant 19368/PI/14.Aliaga, RJ.; Guirao Sánchez, AJ. (2019). On the preserved extremal structure of Lipschitz-free spaces. Studia Mathematica. 245(1):1-14. https://doi.org/10.4064/sm170529-30-11S114245

Quantum cavitation in liquid helium

Using a functional-integral approach, we have determined the temperature below which cavitation in liquid helium is driven by thermally assisted quantum tunneling. For both helium isotopes, we have obtained the crossover temperature in the whole range of allowed negative p essures. Our results are compatible with recent experimental results on 4He.Comment: Typeset using Revtex, 10 pages and 2 figures, Phys. Rev B (1996

Gene body DNA methylation in seagrasses: inter- and intraspecific differences and interaction with transcriptome plasticity under heat stress

The role of DNA methylation and its interaction with gene expression and transcriptome plasticity is poorly understood, and current insight comes mainly from studies in very few model plant species. Here, we study gene body DNA methylation (gbM) and gene expression patterns in ecotypes from contrasting thermal environments of two marine plants with contrasting life history strategies in order to explore the potential role epigenetic mechanisms could play in gene plasticity and responsiveness to heat stress. In silico transcriptome analysis of CpG(O/E) ratios suggested that the bulk of Posidonia oceanica and Cymodocea nodosa genes possess high levels of intragenic methylation. We also observed a correlation between gbM and gene expression flexibility: genes with low DNA methylation tend to show flexible gene expression and plasticity under changing conditions. Furthermore, the empirical determination of global DNA methylation (5-mC) showed patterns of intra and inter-specific divergence that suggests a link between methylation level and the plants' latitude of origin and life history. Although we cannot discern whether gbM regulates gene expression or vice versa, or if other molecular mechanisms play a role in facilitating transcriptome responsiveness, our findings point to the existence of a relationship between gene responsiveness and gbM patterns in marine plants