Factorization invariants in half-factorial affine semigroups

Let $\mathbb{N} \mathcal{A}$ be the monoid generated by $\mathcal{A} = {\mathbf{a}_1, ..., \mathbf{a}_n} \subseteq \mathbb{Z}^d.$ We introduce the homogeneous catenary degree of $\mathbb{N} \mathcal{A}$ as the smallest $N \in \mathbb N$ with the following property: for each $\mathbf{a} \in \mathbb{N} \mathcal{A}$ and any two factorizations $\mathbf{u}, \mathbf{v}$ of $\mathbf{a}$, there exists factorizations $\mathbf{u} = \mathbf{w}_1, ..., \mathbf{w}_t = \mathbf{v}$ of $\mathbf{a}$ such that, for every $k, \mathrm{d}(\mathbf{w}_k, \mathbf{w}_{k+1}) \leq N,$ where $\mathrm{d}$ is the usual distance between factorizations, and the length of $\mathbf{w}_k, |\mathbf{w}_k|,$ is less than or equal to $\max{|\mathbf{u}|, |\mathbf{v}|}.$ We prove that the homogeneous catenary degree of $\mathbb{N} \mathcal{A}$ improves the monotone catenary degree as upper bound for the ordinary catenary degree, and we show that it can be effectively computed. We also prove that for half-factorial monoids, the tame degree and the $\omega$-primality coincide, and that all possible catenary degrees of the elements of an affine semigroup of this kind occur as the catenary degree of one of its Betti elements.Comment: 8 pages, 1 figur

Prevalence of severe atopic dermatitis in adults in 3 areas of Spain

The study was sponsored by Sanof

Instabilities and turbulence in stellarators from the perspective of global codes

In this work, a comparison of the global gyrokinetic codes EUTERPE and GENE-3D in stellarator configurations of LHD and W7-X is carried out. In linear simulations with adiabatic electrons, excellent agreement is found in the mode numbers, growth rate and frequency, mode structure, and spatial localization of the most unstable mode in LHD. In W7-X, the dependence of the growth rate and frequency with the mode number is well reproduced by both codes. The codes are also compared in linear simulations with kinetic ions and electrons in W7-X using model profiles, and reasonable agreement is found in the wavenumber of the most unstable modes. A stabilization of small-scale modes in kinetic-electron simulations with respect to the adiabatic-electron case is consistently found in both codes. Nonlinear simulations using adiabatic electrons and model profiles are also studied and the heat fluxes are compared. Very good agreement is found in the turbulent ion heat fluxes in both LHD and W7-X. Two problems that cannot be properly accounted for in local flux tube codes are studied: the localization of instabilities and turbulence over the flux surface and the influence of a background long-wavelength electric field. Good agreement between codes is found with respect to the spatial localization of instabilities and turbulence over the flux surface. The localization of saturated turbulence is found in both codes to be much smaller than that of the linear instabilities and smaller than previously reported in full-surface radially-local simulations. The influence of the electric field on the localization is also found to be smaller in the developed turbulent state than in the linear phase, and smaller than in previous works. A stabilizing effect of a constant electric field on the linearly unstable modes is found in both codes. A moderate reduction of turbulent transport by the radial electric field..

Affine convex body semigroups

In this paper we present a new kind of semigroups called convex body semigroups which are generated by convex bodies of R^k. They generalize to arbitrary dimension the concept of proportionally modular numerical semigroup of [7]. Several properties of these semigroups are proven. Affine convex body semigroups obtained from circles and polygons of R^2 are characterized. The algorithms for computing minimal system of generators of these semigroups are given. We provide the implementation of some of them

Evidence of strong antiferromagnetic coupling between localized and itinerant electrons in ferromagnetic Sr2FeMoO6

Magnetic dc susceptibility ($\chi$) and electron spin resonance (ESR) measurements in the paramagnetic regime, are presented. We found a Curie-Weiss (CW) behavior for $\chi$(T) with a ferromagnetic $\Theta = 446(5)$ K and $\mu_{eff} = 4.72(9) \mu_{B}/f.u.$, this being lower than that expected for either $Fe^{3+}(5.9\mu_{B})$ or $Fe^{2+}(4.9\mu_{B})$ ions. The ESR g-factor $g = 2.01(2)$, is associated with $Fe^{3+}$. We obtained an excellent description of the experiments in terms of two interacting sublattices: the localized $Fe^{3+}$ ($3d^{5}$) cores and the delocalized electrons. The coupled equations were solved in a mean-field approximation, assuming for the itinerant electrons a bare susceptibility independent on $T$. We obtained $\chi_{e}^{0} = 3.7$ $10^{-4}$ emu/mol. We show that the reduction of $\mu_{eff}$ for $Fe^{3+}$ arises from the strong antiferromagnetic (AFM) interaction between the two sublattices. At variance with classical ferrimagnets, we found that $\Theta$ is ferromagnetic. Within the same model, we show that the ESR spectrum can be described by Bloch-Hasegawa type equations. Bottleneck is evidenced by the absence of a $g$-shift. Surprisingly, as observed in CMR manganites, no narrowing effects of the ESR linewidth is detected in spite of the presence of the strong magnetic coupling. These results provide evidence that the magnetic order in $Sr_{2}FeMoO_{6}$ does not originates in superexchange interactions, but from a novel mechanism recently proposed for double perovskites

Leibnizian, Galilean and Newtonian structures of spacetime

The following three geometrical structures on a manifold are studied in detail: (1) Leibnizian: a non-vanishing 1-form $\Omega$ plus a Riemannian metric \h on its annhilator vector bundle. In particular, the possible dimensions of the automorphism group of a Leibnizian G-structure are characterized. (2) Galilean: Leibnizian structure endowed with an affine connection $\nabla$ (gauge field) which parallelizes $\Omega$ and \h. Fixed any vector field of observers Z ($\Omega (Z) = 1$), an explicit Koszul--type formula which reconstruct bijectively all the possible $\nabla$'s from the gravitational ${\cal G} = \nabla_Z Z$ and vorticity $\omega = rot Z/2$ fields (plus eventually the torsion) is provided. (3) Newtonian: Galilean structure with \h flat and a field of observers Z which is inertial (its flow preserves the Leibnizian structure and $\omega = 0$). Classical concepts in Newtonian theory are revisited and discussed.Comment: Minor errata corrected, to appear in J. Math. Phys.; 22 pages including a table, Late

IMF - metallicity: a tight local relation revealed by the CALIFA survey

Variations in the stellar initial mass function (IMF) have been invoked to explain the spectroscopic and dynamical properties of early-type galaxies. However, no observations have yet been able to disentangle the physical driver. We analyse here a sample of 24 early-type galaxies drawn from the CALIFA survey, deriving in a homogeneous way their stellar population and kinematic properties. We find that the local IMF is tightly related to the local metallicity, becoming more bottom-heavy towards metal-rich populations. Our result, combined with the galaxy mass-metallicity relation, naturally explains previous claims of a galaxy mass-IMF relation, derived from non-IFU spectra. If we assume that - within the star formation environment of early-type galaxies - metallicity is the main driver of IMF variations, a significant revision of the interpretation of galaxy evolution observables is necessary.Comment: Accepted for publication in ApJL. 6 pages, 4 figure