Multivariate Orthogonal Polynomials and Modified Moment Functionals

Multivariate orthogonal polynomials can be introduced by using a moment functional defined on the linear space of polynomials in several variables with real coefficients. We study the so-called Uvarov and Christoffel modifications obtained by adding to the moment functional a finite set of mass points, or by multiplying it times a polynomial of total degree 2, respectively. Orthogonal polynomials associated with modified moment functionals will be studied, as well as the impact of the modification in useful properties of the orthogonal polynomials. Finally, some illustrative examples will be given

The spatially resolved star formation history of CALIFA galaxies: Cosmic time scales

This paper presents the mass assembly time scales of nearby galaxies observed by CALIFA at the 3.5m telescope in Calar Alto. We apply the fossil record method of the stellar populations to the complete sample of the 3rd CALIFA data release, with a total of 661 galaxies, covering stellar masses from 10$^{8.4}$ to 10$^{12}$ M$_{\odot}$ and a wide range of Hubble types. We apply spectral synthesis techniques to the datacubes and process the results to produce the mass growth time scales and mass weighted ages, from which we obtain temporal and spatially resolved information in seven bins of galaxy morphology and six bins of stellar mass (M$_{\star}$) and stellar mass surface density ($\Sigma_{\star}$). We use three different tracers of the spatially resolved star formation history (mass assembly curves, ratio of half mass to half light radii, and mass-weighted age gradients) to test if galaxies grow inside-out, and its dependence with galaxy stellar mass, $\Sigma_{\star}$, and morphology. Our main results are as follows: (a) The innermost regions of galaxies assemble their mass at an earlier time than regions located in the outer parts; this happens at any given M$_{\star}$, $\Sigma_{\star}$, or Hubble type, including the lowest mass systems. (b) Galaxies present a significant diversity in their characteristic formation epochs for lower-mass systems. This diversity shows a strong dependence of the mass assembly time scales on $\Sigma_{\star}$ and Hubble type in the lower-mass range (10$^{8.4}$ to 10$^{10.4}$), but a very mild dependence in higher-mass bins. (c) All galaxies show negative $\langle$log age$\rangle_{M}$ gradients in the inner 1 HLR. The profile flattens with increasing values of $\Sigma_{\star}$. There is no significant dependence on M$_{\star}$ within a particular $\Sigma_{\star}$ bin, except for the lowest bin, where the gradients becomes steeper.Comment: 15 pages, 13 figures, 3 tables, accepted for publication in Astronomy & Astrophysics. *Abridged abstract

Origen, migraciones y relaciones filogenéticas de las razas ganaderas de Andalucía Oriental

Nuestra región a lo largo de la historia se ha visto invadida, conquistada o visitada por una gran variedad de culturas, que provenientes de Africa, el Mediterráneo, o resto de Europa se instalaron en nuestra tierra. Estos pobladores, desde los antiguos Íberos, pasando por los Fenicios, Tartesos y Romanos hasta llegar a los Árabes y los Castellanos, trajeron consigo unas poblaciones de animales que contribuyeron a la formación de la gran variedad actual de razas autóctonas en Andalucía. En este trabajo realizaremos una descripción del origen de las razas autóctonas ovinas, caprinas, bovinas y porcinas de Andalucía Oriental teniendo en cuenta sus vías de acceso y distribución a lo largo de los distintos periodos históricos y sus relaciones filogenéticas, haciendo un análisis de la influencia de estas razas en el mantenimiento del equilibrio ecológico y poblacional de los espacios donde tradicionalmente se han venido explotando

Regeneration niche of the Canarian juniper : the role of adults, shrubs and environmental conditions

Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch

On the Banach lattice structure of L-w(1) of a vector measure on a delta-ring

We study some Banach lattice properties of the space L-w(1)(v) of weakly integrable functions with respect to a vector measure v defined on a delta-ring. Namely, we analyze order continuity, order density and Fatou type properties. We will see that the behavior of L-w(1)(v) differs from the case in which is defined on a sigma-algebra whenever does not satisfy certain local sigma-finiteness property.J. M. Calabuig and M. A. Juan were supported by the Ministerio de Economia y Competitividad (project MTM2008-04594). O. Delgado was supported by the Ministerio de Economia y Competitividad (project MTM2009-12740-C03-02). E. A. Sanchez Perez was supported by the Ministerio de Economia y Competitividad (project MTM2009-14483-C02-02).Calabuig Rodriguez, JM.; Delgado Garrido, O.; Juan Blanco, MA.; Sánchez Pérez, EA. (2014). On the Banach lattice structure of L-w(1) of a vector measure on a delta-ring. Collectanea Mathematica. 65(1):67-85. doi:10.1007/s13348-013-0081-8S6785651Brooks, J.K., Dinculeanu, N.: Strong additivity, absolute continuity and compactness in spaces of measures. J. Math. Anal. Appl. 45, 156–175 (1974)Calabuig, J.M., Delgado, O., Sánchez Pérez, E.A.: Factorizing operators on Banach function spaces through spaces of multiplication operators. J. Math. Anal. Appl. 364, 88–103 (2010)Calabuig, J.M., Juan, M.A., Sánchez Pérez, E.A.: Spaces of $$p$$ -integrable functions with respect to a vector measure defined on a $$\delta$$ -ring. Oper. Matrices 6, 241–262 (2012)Curbera, G.P.: El espacio de funciones integrables respecto de una medida vectorial. Ph. D. thesis, University of Sevilla, Sevilla (1992)Curbera, G.P.: Operators into $$L^1$$ of a vector measure and applications to Banach lattices. Math. Ann. 293, 317–330 (1992)Curbera, G.P., Ricker, W.J.: Banach lattices with the Fatou property and optimal domains of kernel operators. Indag. Math. (N.S.) 17, 187–204 (2006)G. P. Curbera and W. J. Ricker, Vector measures, integration and applications. In: Positivity (in Trends Math.), Birkhäuser, Basel, pp. 127–160 (2007)Curbera, G.P., Ricker, W.J.: The Fatou property in $$p$$ -convex Banach lattices. J. Math. Anal. Appl. 328, 287–294 (2007)Delgado, O.: $$L^1$$ -spaces of vector measures defined on $$\delta$$ -rings. Arch. Math. 84, 432–443 (2005)Delgado, O.: Optimal domains for kernel operators on $$[0,\infty )\times [0,\infty )$$ . Studia Math. 174, 131–145 (2006)Delgado, O., Soria, J.: Optimal domain for the Hardy operator. J. Funct. Anal. 244, 119–133 (2007)Delgado, O., Juan, M.A.: Representation of Banach lattices as $$L_w^1$$ spaces of a vector measure defined on a $$\delta$$ -ring. Bull. Belg. Math. Soc. Simon Stevin 19(2), 239–256 (2012)Diestel, J., Uhl, J.J.: Vector measures (Am. Math. Soc. surveys 15). American Mathematical Society, Providence (1997)Dinculeanu, N.: Vector measures, Hochschulbcher fr Mathematik, vol. 64. VEB Deutscher Verlag der Wissenschaften, Berlin (1966)Fernández, A., Mayoral, F., Naranjo, F., Sáez, C., Sánchez Pérez, E.A.: Spaces of $$p$$ -integrable functions with respect to a vector measure. Positivity 10, 1–16 (2006)Fremlin, D.H.: Measure theory, broad foundations, vol. 2. Torres Fremlin, Colchester (2001)Jiménez Fernández, E., Juan, M.A., Sánchez Pérez, E.A.: A Komlós theorem for abstract Banach lattices of measurable functions. J. Math. Anal. Appl. 383, 130–136 (2011)Lewis, D.R.: On integrability and summability in vector spaces. Ill. J. Math. 16, 294–307 (1972)Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces II. Springer, Berlin (1979)Luxemburg, W.A.J., Zaanen, A.C.: Riesz spaces I. North-Holland, Amsterdam (1971)Masani, P.R., Niemi, H.: The integration theory of Banach space valued measures and the Tonelli-Fubini theorems. I. Scalar-valued measures on $$\delta$$ -rings. Adv. Math. 73, 204–241 (1989)Masani, P.R., Niemi, H.: The integration theory of Banach space valued measures and the Tonelli-Fubini theorems. II. Pettis integration. Adv. Math. 75, 121–167 (1989)Thomas, E.G.F.: Vector integration (unpublished) (2013)Turpin, Ph.: Intégration par rapport à une mesure à valeurs dans un espace vectoriel topologique non supposé localement convexe, Intègration vectorielle et multivoque, (Colloq., University Caen, Caen, 1975), experiment no. 8, Dèp. Math., UER Sci., University Caen, Caen (1975)Okada, S., Ricker, W.J., Sánchez Pérez, E.A.: Optimal domain and integral extension of operators acting in function spaces (Oper. Theory Adv. Appl.), vol. 180. Birkhäuser, Basel (2008)Zaanen, A.C.: Riesz spaces II. North-Holland, Amsterdam (1983

The cosmic evolution of the spatially-resolved star formation rate and stellar mass of the CALIFA survey

We investigate the cosmic evolution of the absolute and specific star formation rate (SFR, sSFR) of galaxies as derived from a spatially-resolved study of the stellar populations in a set of 366 nearby galaxies from the CALIFA survey. The analysis combines GALEX and SDSS images with the 4000 break, H_beta, and [MgFe] indices measured from the datacubes, to constrain parametric models for the SFH, which are then used to study the cosmic evolution of the star formation rate density (SFRD), the sSFR, the main sequence of star formation (MSSF), and the stellar mass density (SMD). A delayed-tau model, provides the best results, in good agreement with those obtained from cosmological surveys. Our main results from this model are: a) The time since the onset of the star formation is larger in the inner regions than in the outer ones, while tau is similar or smaller in the inner than in the outer regions. b) The sSFR declines rapidly as the Universe evolves, and faster for early than for late type galaxies, and for the inner than for the outer regions of galaxies. c) SFRD and SMD agree well with results from cosmological surveys. At z< 0.5, most star formation takes place in the outer regions of late spiral galaxies, while at z>2 the inner regions of the progenitors of the current E and S0 are the major contributors to SFRD. d) The inner regions of galaxies are the major contributor to SMD at z> 0.5, growing their mass faster than the outer regions, with a lookback time at 50% SMD of 9 and 6 Gyr for the inner and outer regions. e) The MSSF follows a power-law at high redshift, with the slope evolving with time, but always being sub-linear. f) In agreement with galaxy surveys at different redshifts, the average SFH of CALIFA galaxies indicates that galaxies grow their mass mainly in a mode that is well represented by a delayed-tau model, with the peak at z~2 and an e-folding time of 3.9 Gyr.Comment: 23 pages, 16 figures, 6 tables, accepted for publication in Astronomy & Astrophysics. *Abridged abstract