Polinomis positius i desigualtats polinomials

La caracterització dels polinomis positius sobre tot l'espai afí Rn fou l'objecte del problema 17 de Hilbert, resolt per Artin el 1929. Arran d'aquest mateix, s'han plantejat nombrosos problemes colaterals relatius a propietats dels conjunts de l'espai afí definits per desigualtats polinomials (anomenats semialgebraics) i la caracterització dels polinomis positius sobre ells. En aquest article s'ofereix una exposició dels principals resultats sobre aquest tema.The characterization of positive polynomials over the whole affine space R^n was the goal of Hilbert’s 17th problem, solved by Artin in 1929. Then came a host of related colateral problems, concerning properties of the subsets of affine space defined by polynomial inequalities (called semialgebraic sets) and the characterization of the positive polynomials over them. In this paper we offer an exposition of the main results on this topic

Interaction and cooperative effort among scientific societies. Twelve years of COSCE

The evolution of knowledge and technology in recent decades has brought profound changes in science policy, not only in the countries but also in the supranational organizations. It has been necessary, therefore, to adapt the scientific institutions to new models in order to achieve a greater and better communication between them and the political counterparts responsible for defining the general framework of relations between science and society. The Federationon of Scientific Societies of Spain (COSCE, Confederación de Sociedades Científicas de España) was founded in October 2003 to respond to the urgent need to interact with the political institutions and foster a better orientation in the process of making decisions about the science policy. Currently COSCE consists of over 70 Spanish scientific societies and more than 40,000 scientists. During its twelve years of active life, COSCE has developed an intense work of awareness of the real situation of science in Spain by launching several initiatives (some of which have joined other organizations) or by joining initiatives proposed from other groups related to science both at the Spanish level and at the European and non-European scenarios

Selección de profesores y carrera universitaria

Con el fin de asegurar la competencia y excelencia de la plantilla docente se han arbitrado diferentes mecanismos de selección y de acreditación. Según el rector de la Universidad Complutense, el actual sistema no es del todo adecuado y propone en la siguiente reflexión algunas medidas para mejorarl

Selección de profesores y carrera universitaria

Uno de los pilares en los que se asienta la calidad de la enseñanza universitaria es el profesorado. Con el fin de asegurar la competencia y excelencia de la plantilla docente se han arbitrado diferentes mecanismos de selección y de acreditación. Según el rector de la Universidad Complutense, el actual sistema no es del todo adecuado y propone en la siguiente reflexión algunas medidas para mejorarlo.Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu

Valoraciones reales en cuerpos reales de funciones

Tesis Univ. Compl. de Madrid. Dpto. de Geometría y Topología. Dir por Tomás Recio Muñiz, leída en Madrid, el 27 de septiembre de 1982.Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEProQuestpu

Valoraciones reales en cuerpos reales de funciones

Tesis Univ. Compl. de Madrid. Dpto. de Geometría y Topología. Dir por Tomás Recio Muñiz, leída en Madrid, el 27 de septiembre de 1982.Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEProQuestpu

On Marshall’s p-invariant for semianalytic set germs

The invariant p(V ) has been introduced by M. Marshall as a measure of the complexity of semialgebraic sets of a real algebraic variety V . This invariant is defined as the least integer such that every semialgebraic set S ⊂ V has a separating family with p(V ) polynomials. In this paper we provide estimates for the invariant p in the case of analytic set germs. One of the tools we use is a realization theorem which is interesting by itself

A note on projections of real algebraic varieties.

We prove that any regularly closed semialgebraic set of R", where R is any real closed field and regularly closed means that it is the closure of its interior, is the projection under a finite map of an irreducible algebraic variety in some Rn + k. We apply this result to show that any clopen subset of the space of orders of the field of rational functions K= R(X1,...iXn) is the image of the space of orders of a finite extension of K

On projections of real algebraic varieties.

In this paper we generalize an earlier result of the authors, showing that any closed semialgebraic set whose Zariski-closure is irreducible, is the projection under a finite map of an irreducible real algebraic set (see Theorem 3.2 below)