On pythagorean real irreducible algebroid curves

In this note we deal with the pythagoras number p of certain 1-dimensional rings, i.e., real irreducible algebroid curves over a real closed ground field k. The problem we are concerned with is to characterize those real irreducible algebroid curves which are pythagorean (i.e., p = 1). We obtain two theorems involving the value-semigroup. Then we apply them to solve the cases of: (a) Gorenstein curves, (b) planar curves, (c) monomial curves, and (d) curves of multiplicity <= 5. Finally, two conjectures are stated

Sobre álgebras de Nash

We obtain some results (a Nullstellensatz, a specialization theorem, `à la E. Artin') for Nash algebras with an algebraic method based on M. Artin's theorem (and easily generalizable to the analytic case) notably simplifying known proof

Aspectos aritméticos y geométricos del problema decimoséptimo de Hilbert para gérmenes analíticos

Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEProQuestunpu

"In vino veritas": factores competitivos en distritos industriales productores de vino

El sector vitivinícola ocupa una destacada posición en el conjunto de la industria agroalimentaria española. La importancia demostrada por esta actividad se traslada también al mercado internacional donde España ostenta una posición de liderazgo tanto en términos de producción, como de ventas al exterior. Buena parte de las empresas elaboradoras de vino de nuestro país se ubican en distritos industriales, o lo que es lo mismo, en entornos geográficos caracterizados por la elevada concentración de pequeñas y medianas empresas cuya organización productiva responde a un esquema basado en la especialización flexible. En anteriores trabajos, se ha podido constatar cómo las empresas elaboradoras de vino ubicadas en este tipo de enclaves industriales presentan una mayor eficiencia respecto de competidores localizados en otro tipo de entornos. El objetivo de este artículo es profundizar en la investigación de los rasgos específicos de los distritos industriales que podrían explicar este plus de eficiencia de sus empresas. Para la identificación y cuantificación de estos factores determinantes de la eficiencia productiva se utiliza una metodología basada en modelos de ajuste paramétrico. Se lleva a cabo una aplicación empírica sobre una muestra de empresas españolas productoras de vino para los años 2000 y 2010, extraída de la base de datos SABI.The wine sector holds a prominent place within the whole Spanish food and agriculture industry. The importance given to this activity has also been transferred to the international market where Spain holds a position of leadership, both in terms of production as in overseas sales. A large number of the wine-producing firms in our country are located in industrial districts, which is to say in geographical areas characterised by a high concentration of small and medium-sized companies whose productive organisation corresponds to a model based on flexible specialisation. In previous papers, it has been possible to verify how wine-producing industries located in industrial areas show greater efficiency in relation to rivals located in other types of environments. The aim of this article is to further research on the specific features of industrial districts which could explain their firms’ increase in efficiency. For the identification and quantification of these determining factors affecting productive efficiency, a methodology based on parametric adjustments models is to be used. An empirical application is to be carried out on a sample of Spanish wine producers for the years 2000 and 2010, extracted from the SABI database

On the pythagoras numbers of real analytic set germs.

We Show that (i) the Pythagoras number of a real analytic set germ is the supremum of the Pythagoras numbers of the curve germs it contains, and (ii) every real analytic curve germ is contained in a real analytic surface germ with the same Pythagoras number (or Pythagoras number 2 if the curve is Pythagorean). This gives new examples and counterexamples concerning sums of squares and positive semidefinite analytic function germs

Sums of squares of linear forms: the quaternions approach

Let A = k[y] be the polynomial ring in one single variable y over a field k. We discuss the number of squares needed to represent sums of squares of linear forms with coefficients in the ring A. We use quaternions to obtain bounds when the Pythagoras number of A is ≤ 4. This provides bounds for the Pythagoras number of algebraic curves and algebroid surfaces over k

Sums of squares of linear forms

Let k be a real field. We show that every non-negative homogeneous quadratic polynomial f (x(1),..., x(n)) with coefficients in the polynomial ring k[t] is a sum of 2n center dot tau(k) squares of linear forms, where tau(k) is the supremum of the levels of the finite non-real field extensions of k. From this result we deduce bounds for the Pythagoras numbers of affine curves over fields, and of excellent two-dimensional local henselian rings

The Artin-Lang property for normal real analytic surfaces

We solve the 17th Hilbert Problem and prove the Artin-Lang property for normal real analytic surfaces. Then we deduce that the absolute (resp. relative) holomorphy ring of such a surface consists of all bounded (resp. locally bounded) meromorphic functions

Sobre compactificaciones de Wallman-Frink de espacios discretos

Dado un espacio T3α (X,T), es posible obtener una compactificación T2 del mismo, mediante ultrafiltros asociados a ciertas bases distinguidas de cerrados de (X,T) (Frink [4]). Se plantea así el problema siguiente: ¿Puede obtenerse toda compactificación T2 de (X,T) por este método? Desde el año 1964 en que Frink lo planteó, este interrogante ha tenido respuestas afirmativas parciales. Sin embargo, la solución definitiva es negativa