An isoperimetric-type inequality for electrostatic shell interactions for Dirac operators

In this article we investigate spectral properties of the coupling $H+V_\lambda$, where $H=-i\alpha\cdot\nabla +m\beta$ is the free Dirac operator in $\mathbb R^3$, $m>0$ and $V_\lambda$ is an electrostatic shell potential (which depends on a parameter $\lambda\in\mathbb R$) located on the boundary of a smooth domain in $\mathbb R^3$. Our main result is an isoperimetric-type inequality for the admissible range of $\lambda$'s for which the coupling $H+V_\lambda$ generates pure point spectrum in $(-m,m)$. That the ball is the unique optimizer of this inequality is also shown. Regarding some ingredients of the proof, we make use of the Birman-Schwinger principle adapted to our setting in order to prove some monotonicity property of the admissible $\lambda$'s, and we use this to relate the endpoints of the admissible range of $\lambda$'s to the sharp constant of a quadratic form inequality, from which the isoperimetric-type inequality is derived.Comment: 21 page

The MIT Bag Model as an infinite mass limit

Peer ReviewedPostprint (published version

Distinguished self-adjoint extensions of Dirac operators via Hardy-Dirac inequalities

We prove some Hardy-Dirac inequalities with two different weights including measure valued and Coulombic ones. Those inequalities are used to construct distinguished self-adjoint extensions of Dirac operators for a class of diagonal potentials related to the weights in the above mentioned inequalities.Comment: 16 page

Ekuazio diferentzialak

261 p.Ekuazio diferentzialak funtzioak eta haien deribatuak erlazionatzen dituzten ekuazio matematikoak dira. Ezezagunak aldagai bateko funtzioak badira, ekuazio diferentzialak arruntak direla esaten da; aldiz, ezezagunak aldagai anitzeko funtzioak badira deribatu partzialetako ekuazioak ditugu. Liburu honetan jorratzen diren gaiak Euskal Herriko Unibertsitateko Matematika graduko Ekuazio diferentzialak irakasgaiaren programa jarraituz aukeratu dira, baina testua lagungarria izan daiteke beste zenbait ikasketetan

Ekuazio diferentzialak

261 p.Ekuazio diferentzialak funtzioak eta haien deribatuak erlazionatzen dituzten ekuazio matematikoak dira. Ezezagunak aldagai bateko funtzioak badira, ekuazio diferentzialak arruntak direla esaten da; aldiz, ezezagunak aldagai anitzeko funtzioak badira deribatu partzialetako ekuazioak ditugu. Liburu honetan jorratzen diren gaiak Euskal Herriko Unibertsitateko Matematika graduko Ekuazio diferentzialak irakasgaiaren programa jarraituz aukeratu dira, baina testua lagungarria izan daiteke beste zenbait ikasketetan

Spatial dynamics and mixing of bluefin tuna in the Atlantic Ocean and Mediterranean Sea revealed using next generation sequencing

The Atlantic bluefin tuna is a highly migratory species emblematic of the challenges associated with shared fisheries management. In an effort to resolve the species’ stock dynamics, a genomewide search for spatially informative single nucleotide polymorphisms (SNPs) was undertaken, by way of sequencing reduced representation libraries. An allele frequency approach to SNP discovery was used, combining the data of 555 larvae and young-of-the-year (LYOY) into pools representing major geographical areas and mapping against a newly assembled genomic reference. From a set of 184,895 candidate loci, 384 were selected for validation using 167 LYOY. A highly discriminatory genotyping panel of 95 SNPs was ultimately developed by selecting loci with the most pronounced differences between western Atlantic and Mediterranean Sea LYOY. The panel was evaluated by genotyping a different set of LYOY (n = 326), and from these, 77.8% and 82.1% were correctly assigned to western Atlantic and Mediterranean Sea origins, respectively. The panel revealed temporally persistent differentiation among LYOY from the western Atlantic and Mediterranean Sea (FST = 0.008, p = .034). The composition of six mixed feeding aggregations in the Atlantic Ocean and Mediterranean Sea was characterized using genotypes from medium (n = 184) and large (n = 48) adults, applying population assignment and mixture analyses. The results provide evidence of persistent population structuring across broad geographic areas and extensive mixing in the Atlantic Ocean, particularly in the mid-Atlantic Bight and Gulf of St. Lawrence. The genomic reference and genotyping tools presented here constitute novel resources useful for future research and conservation efforts