Entire functions uniformly bounded on balls of a Banach space

Let X be an in�finite-dimensional complex Banach space. Very recently, several results on the existence of entire functions on X bounded on a given ball B1 � X and unbounded on another given ball B2 � X have been obtained. In this paper we consider the problem of �finding entire functions which are uniformly bounded on a collection of balls and unbounded on the balls of some other collection. RESUMEN. Sea X un espacio de Banach complejo de dimensión infinita. En este trabajo, los autores estudian el problema de encontrar una función entera en X que esté uniformemente acotada en una colección de de bolas en X y que no esté acotada en las bolas de otra colección.

Vector spaces of entire functions of unbounded type

Let E be an infinite dimensional complex Banach space. We prove the existence of an infinitely generated algebra, an infinite dimensional closed subspace and a dense subspace of entire functions on E whose non-zero elements are functions of unbounded type. We also show that the τδ topology on the space of all holomorphic functions cannot be obtained as a countable inductive limit of Fr´echet spaces. RESUMEN. Sea E un espacio de Banach complejo de dimensión infinita y sea H(E) el espacio de funciones holomorfas definidas en E. En el artículo se demuestra la existencia de un álgebra infinitamente generada en H(E), un subespacio vectorial en H(E) cerrado de dimensión infinita y un subespacio denso en H(E) cuyos elementos no nulos son funciones de tipo no acotado. También se demuestra que el espacio de funciones holomorfas con la topología ? no es un límite inductivo numberable de espacios de Fréchet.

Lineability of the set of holomorphic mappings with dense range

Let U be an open subset of a separable Banach space. Let F be the collection of all holomorphic mappings f from the open unit disc D � C into U such that f(D) is dense in U. We prove the lineability and density of F in appropriate spaces for diferent choices of U. RESUMEN. Sea U un subconjunto abierto de un espacio de Banach separable. Sea F el conjunto de funciones holomorfas f definidas en el disco unidad D del plano complejo con valores en U tales que f(D) es denso en U. En el artículo se demuestra la lineabilidad y densidad del conjunto F para diferentes elecciones de U.

On real analytic functions of unbounded type

In this paper we prove several results on the existence of analytic functions on an infinite dimensional real Banach space which are bounded on some given collection of open sets and unbounded on others. In addition, we also obtain results on the density of some subsets of the space of all analytic functions for natural locally convex topologies on this space. RESUMEN. Los autores demuestran varios resultados de existencia de funciones analíticas en espacios de Banach reales de dimensión infinita que están acotadas en un colección de subconjuntos abiertos y no acotadas en los conjuntos de otra colección. Además, se demuestra la densidad de ciertos subconjuntos de funciones analíticas para varias topologías localmente convexas.

Descriptive study of production factors affecting performance traits in growing-finishing pgis in Spain.

The objective of this study was to build up a data set including productive performance and production factors data of growing-finishing (GF) pigs in Spain in order to perform a representative and reliable description of the traits of Spanish growing-finishing pig industry. Data from 764 batches from 452 farms belonging to nine companies (1,157,212 pigs) were collected between 2008 and 2010 through a survey including five parts: general, facilities, feeding, health status and performance. Most studied farms had only GF pigs on their facilities (94.7%), produced ‘industrial’ pigs (86.7%), had entire male and female (59.5%) and Pietrain-sired pigs (70.0%), housed between 13-20 pigs per pen (87.2%), had  50% of slatted floor (70%), single-space dry feeder (54.0%), nipple drinker (88.7%) and automatic ventilation systems (71.2%). A 75.0% of the farms used three feeding phases using mainly pelleted diets (91.0%), 61.3% performed three or more antibiotic treatments and 36.5% obtained water from the public supply. Continuous variables studied had the following average values: number of pigs placed per batch, 1,515 pigs; initial and final body weight, 19.0 and 108 kg; length of GF period, 136 days; culling rate, 1.4%; barn occupation, 99.7%; feed intake per pig and fattening cycle, 244 kg; daily gain, 0.657 kg; feed conversion ratio, 2.77 kg kg-1 and mortality rate, 4.3%. Data reflecting the practical situation of the Spanish growing and finishing pig production and it may contribute to develop new strategies in order to improve the productive and economic efficiency of GF pig units.