Información del autor
Autor Ruiz Sancho, Jesús María |
Documentos disponibles escritos por este autor (73)
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A set which can be defined by systems of polynomial inequalities is called semialgebraic. When such a scription is possible locally around every point, by means of analytic inequalities varying with the point, the set; is called semianalytic. If[...]texto impreso
A semialgebraic set is called basic if it can be described by a single system of strict polynomial inequalities. A semianalytic set is called basic if it can be described by a system of strict real analytic inequalities in a neighborhood of each[...]texto impreso
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Let ??Rn be a compact Nash manifold; A,B the rings of Nash, analytic global functions on ?. The main result of this paper is the following: Theorem 1. Let ?,?? be a pair of Nash submanifolds of some Rn ,Rq and let us suppose ? is compact. Let F1[...]texto impreso
Baro González, Elías ; Fernando Galván, José Francisco ; Ruiz Sancho, Jesús María | Elsevier | 2014-09This paper is devoted to the approximation of differentiable semialgebraic functions by Nash functions. Approximation by Nash functions is known for semialgebraic functions defined on an affine Nash manifold M, and here we extend it to functions[...]texto impreso
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We give an expository account of the basic features of analytic and semianalytic germs. The main results treated here are Risler's Nullstellensatz, the curve selection lemma and the finiteness theorem for semianalytic germs. The method of proof [...]texto impreso
Abánades, Miguel A. ; Joglar-Prieto, Nuria ; Ruiz Sancho, Jesús María | Elsevier Science B.V. (North-Holland) | 1999-10-01We show that the ring of bounded meromorphic functions on an irreducible compact real analytic set of dimension d is a Prüfer domain of dimension d. Consequently, every finitely generated ideal in this ring can be generated by d + 1 elements, an[...]texto impreso
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The paper deals with orderings in the field K(X0) of meromorphic function germs on an irreducible analytic germ X0?Rn0 of dimension d. It is inspired by the theory of central points of real algebraic varieties (the set of central points is the c[...]texto impreso
Hilbert's 17th Problem asked the following. Let f(x1,?,xn) be a real polynomial which for all real values ?1,?,?n satisfies f(?1,?,?n)?0. Is it true that f=?(gi/hi)2 for polynomials gi,hi?R[x1,?,xn]? (It was known that f=?(gi)2, gi?R[x1,?,xn], i[...]texto impreso
Let A be a local ring; let  denote the completion of A and Spec r A,Spec R  the real spectra of A and Â,respectively. The author studies the fibers of the canonical morphism Spec r  ? Spec r A, for an excellent ring A, and computes its images[...]texto impreso
In this note, the author proves, in the context of excellent rings, two results on chains of specializations in the real spectrum and some corollaries about real dimension. The first result (Theorem I) is the following: let ?0 be a point of Spec[...]texto impreso
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En este trabajo obtemos algunos resultados básicos sobre determinación finita y clasificación de singularidades para series con coeficientes en un cuerpo de características cero. Estos resultados son clásicos para coeficientes complejos, y reale[...]texto impreso
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The paper contains a technical but useful theorem about stratification of semianalytic setstexto impreso
Este texto está dedicado a la geometría analítica elemental del plano y del espacio, insistiendo en la distinción natural entre las nociones vectoriales, las afines y las euclídes. Tras recordar brevemente las operaciones básicas de escalares y [...]texto impreso
Rodríguez Sanjurjo, José Manuel ; Ruiz Sancho, Jesús María | Addison-Wesley Iberoamericana España | 1998Este libro presenta, de modo directo y accesible, las nociones y los resultados básicos de la geometría proyectiva: variedades y aplicaciones proyectivas, razón doble, homografías y cuádricas. La exposición teórica se completa con notas históric[...]texto impreso
This is a survey on the history of and the solutions to the basic global problems on Nash functions, which have been only recently solved, namely: separation, extension, global equations, Artin-Mazur description and idempotency, also noetheriann[...]texto impreso
In this note, the author gives a proof of the following going-down theorem: If ?:A?B is a regular map between Noetherian rings with A excellent, any chain of specialization in Spec r A comes from a chain of the same length in Spec r B with corr[...]texto impreso
Let X be a real affine algebraic set and S a semialgebraic set. Many important results are known about the basicness of S: mainly, if S is basic open, S can be defined by s strict inequalities, where s is bounded by the dimension of X. It is als[...]texto impreso
The literature devoted to degree theory and its applications is abundant, but the richness of the topics is such that it is not surprising to see regularly the publication of new books in this area. The emphasis of the present one is on Brouwer[...]texto impreso
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Castrillón López, Marco ; Martín Peinador, Elena ; Rodríguez Sanjurjo, José Manuel ; Ruiz Sancho, Jesús María | Departamento de Geometría y Topología | 2015-09This volume contains the contributions presented by several colleagues as a tribute to the mathematical and human qualities of José María Montesinos Amilibia on the occasion of his seventieth birthday. The editors would like to express their tha[...]texto impreso
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The author proves the following theorem: Let A0 be a closed 1-dimensional semianalytic germ at the origin 0?Rn. Let Z be a semianalytic set in Rn whose germ Z0 at 0 is closed and A0?Z0={0}. Then there exists a polynomial h?R[x1,?,xn] such that h[...]texto impreso
Let M superset-of R be a compact Nash manifold, and N (M) [resp. O(M)] its ring of global Nash (resp. analytic) functions. A global Nash (resp. analytic) set is the zero set of finitely many global Nash (resp. analytic) functions, and we have th[...]texto impreso
The author proves a Nullstellensatz for the ring of real analytic functions on a compact analytic manifold. The main results are the following. Theorem 1: Let X be a compact irreducible analytic set of a real analytic manifold M and f:X?R a nonn[...]texto impreso
The main application of the results of this paper is to prove the existence of real valuation rings of the quotient field K of an excellent domain A having prescribed centers, ranks, rational ranks and residue dimensions. The major part of the p[...]texto impreso
Gamboa, J. M. ; Alonso García, María Emilia ; Ruiz Sancho, Jesús María | Elsevier Science B.V. (North-Holland) | 1985It is well-known that if C is an algebraic curve over the real closed field R and is a total ordering of the function field R(C) of C then there is a semi-algebraic embedding w : (0, 1) ! C such that f 2 R(C) is positive with respect to if and[...]texto impreso
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 cu[...]texto impreso
The authors study some properties of the ring of abstract semialgebraic functions over a constructible subset of the real spectrum of an excellent ring. To be more precise, let X be a constructible subset of the real spectrum of a ring A. The r[...]texto impreso
It is known that a compact space can fail to be sequentially compact. In this paper we consider the following problem: when does a space admit a sequentially compact T2 compactification? In the first section we develop a method to produce such c[...]texto impreso
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Let M be a real analytic manifold and O(M) its ring of global analytic functions. A global semianalytic subset of M is any set Z of the form Z=? i=0 r {x?M:fi1(x)> 0,?,fis(x)> 0,gi(x)=0}, (1.1), where fij,gi?O(M). This imitates the definitions [...]texto impreso
Acquistapace, Francesca ; Broglia, Fabrizio ; Fernando Galván, José Francisco ; Ruiz Sancho, Jesús María | French Mathematical Society | 2010We consider the 17(th) Hilbert Problem for global real analytic functions in a modified form that involves infinite sums of squares. Then we prove a local-global principle for a real global analytic function to be a sum of squares of global real[...]texto impreso
Acquistapace, Francesca ; Broglia, Fabrizio ; Fernando Galván, José Francisco ; Ruiz Sancho, Jesús María | 2004-01-26We consider Hilbert’s 17 problem for global analytic functions in a modified form that involves infinite sums of squares. This reveals an essential connection between the solution of the problem and the computation of Pythagoras numbers of merom[...]texto impreso
In this paper the authors study irregular metacyclic branched covering spaces. These arise as follows: Suppose G is a Z/m extension of Z/n. Then G contains a cyclic subgroup of order m, Cm, which we suppose is not normal. Suppose G acts on a PL [...]texto impreso
We show that the Pythagoras number of a real analytic curve is the supremum of the Pythagoras numbers of its singularities, or that supremum plus 1. This includes cases when the Pythagoras number is infinite.texto impreso
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 Pytha[...]texto impreso
Acquistapace, Francesca ; Broglia, Fabrizio ; Fernando Galván, José Francisco ; Ruiz Sancho, Jesús María | Société Mathématique de France | 2005We show that (i) every positive semidefinite meromorphic function germ on a surface is a sum of 4 squares of meromorphic function germs, and that (ii) every positive semidefinite global meromorphic function on a normal surface is a sum of 5 squa[...]texto impreso
We present here some applications of the theory of real spectra of excellent rings to the ring of global analytic functions on a compact real analytic manifold. Section 1 contains the facts of the theory that shall be used in the sequel. Section[...]texto impreso
Let M be a real analytic manifold and O(M) its ring of global analytic functions. Let Z be a global semianalytic set of M (that is, a subset of M of the form Z=?r i=0{x?M:fi1 (x)> 0,?,fis (x)> 0, gi (x)=0}, where fij,gi?O(M)). In this paper, the[...]texto impreso
After describing explicitly all total orderings in the ring R[[x,y]], we prove that each ordering in the quotient field of the ring of germs of real analytic functions at an irreducible point O of a real analytic surface X is defined by a half-b[...]texto impreso
We show that any positive semidefinite analytic function germ on the cone z(2) = x(2) + y(2) is a sum of two squares of analytic function germs.