Trees, homology, and automorphism groups of RAAGs

We study the homology of an explicit finite-index subgroup of the automorphism group of a partially commutative group, in the case when its defining graph is a tree. More concretely, we give a lower bound on the first Betti number of this subgroup, based on the number and degree of a certain type of vertices, which we call deep. We then use combinatorial methods to analyze the average value of this Betti number, in terms of the size of the defining tree

Heat and Poisson semigroups for Fourier-Neumann expansions

Given $\alpha > -1$, consider the second order differential operator in $(0,\infty)$, $$L_\alpha f \equiv (x^2 \frac{d^2}{dx^2} + (2\alpha+3)x \frac{d}{dx} + x^2 + (\alpha+1)^2)(f),$$ which appears in the theory of Bessel functions. The purpose of this paper is to develop the corresponding harmonic analysis taking $L_\alpha$ as the analogue to the classical Laplacian. Namely we study the boundedness properties of the heat and Poisson semigroups. These boundedness properties allow us to obtain some convergence results that can be used to solve the Cauchy problem for the corresponding heat and Poisson equations.Comment: 16 page

The role of the Public University of Navarre in achieving the 1st SDG for the end of poverty

The end of poverty is the first of the 17 sustainable development goals of the United Nations. Universities are strategic spaces for promoting the SDGs, from training, research, and outreach capacity to implementing sustainable actions, helping to reduce inequalities and, significantly, promoting sustainable cities and communities. This article aims to answer how the Public University of Navarre contributes to promoting the 1st SDG, what mechanisms for the end of poverty endorses in its territory, and what can we learn from these experiences. To this end, a case study has been carried out based on qualitative techniques. This work analyzes the strategies implemented, such as incorporating social clauses for responsible recruiting, the development of applied research and teaching or network participation. From this example, some engaging lessons will be extracted to address this issue in other contexts, promoting their consolidation and identifying the obstacles that may hinder their spread

Identidad contra identidades : el destino contra Babelia

El impulso de los nacionalismos y la constatación de la crisis ecológica global, son fenómenos paradójicos y contradictorios. En base a las contribuciones desde la sociología de Eisenstadt y Geisen, y desde el derecho y la teoría política de Wendt y Falk, nosotros argumentamos que el concepto de identidad planetaria, al tiempo que se opone conceptualmente al babelismo nacionalista dominante en ciertos sectores intelectuales, puede cimentar las bases para un entendimiento racional del devenir en este fin de siglo.Nationalism and environmental global conscience are contradictory ideas. We argue in this paper, using as a source from the sociological point of view the work of Eisenstadt and Giesen and from the point of view of legal theory the work of Wendt and Falk, that the concept of planetarian identity is rationally sound. We defend that planetarian collective identity may work against the shortcomings of this return to Babelia represented by nationalism, and it may also set a valid framework of reference to understand developments at the end of the twentieth century

A catalog of planetary nebula candidates in the Sculptor spiral galaxy NGC 300

[OIII]5007 on-band off-band images, obtained with the VLT and FORS2 spectrograph in two zones (center and outskirts) of the spiral galaxy NGC300, are analyzed searching for emission line objects. In particular we search for planetary nebula (PN) candidates to analyze their distribution and luminosity properties, to perform follow-up spectroscopy, and to study the planetary nebula luminosity function, PNLF. In the continuum-subtracted images, a large number of emission line objects were detected. From this sample we selected as PN candidates those objects with stellar appearance and no detectable central star. [OIII]5007 instrumental magnitudes were measured and calibrated by using spectrophotometric data from the follow-up spectroscopy. We identified more than a hundred PN candidates and a number of compact HII regions. The PN sample is the largest one reported for this galaxy so far. For all the objects we present coordinates, instrumental [OIII]5007 magnitudes and apparent nebular [OIII]5007 fluxes and magnitudes. The [OIII]5007 observed luminosity function for PNe (PNLF) was calculated for the whole sample and for the central and outskirts samples. The three PNLF are similar within uncertainties. We fit the empirical PNLF to the observed PNLF for all the samples. From our best fit for the whole sample we derived a maximum value for the apparent magnitudes of m*(5007)=22.019\pm0.022 and we obtained a tentative estimate of the distance modulus m(5007)-M(5007)= 26.29 {+0.12} {-0.22} mag, which agrees well with the recent value derived from Cepheid stars.Comment: 8 pages, 3 figures, one long table. Accepted by A&

Rectification of electronic heat current by a hybrid thermal diode

We report the realization of an ultra-efficient low-temperature hybrid heat current rectifier, thermal counterpart of the well-known electric diode. Our design is based on a tunnel junction between two different elements: a normal metal and a superconducting island. Electronic heat current asymmetry in the structure arises from large mismatch between the thermal properties of these two. We demonstrate experimentally temperature differences exceeding $60$ mK between the forward and reverse thermal bias configurations. Our device offers a remarkably large heat rectification ratio up to $\sim 140$ and allows its prompt implementation in true solid-state thermal nanocircuits and general-purpose electronic applications requiring energy harvesting or thermal management and isolation at the nanoscale.Comment: 8 pages, 6 color figure