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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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 [...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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The paper contains a technical but useful theorem about stratification of semianalytic sets![]()
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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 [...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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 [...]![]()
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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[...]![]()
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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[...]![]()
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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 [...]![]()
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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.![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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.![]()
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This is a research survey on results dealing with the following question: Let M be a compact smooth manifold and A a family of geometric objects related to M such that there exists some natural equivalence of the pairs (M,A). Does every equivale[...]![]()
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Este trabajo es una revisión de la historia y las soluciones de los problemas básicos globales de las funciones de Nash que se han resuelto recientemente: separación, extensión, ecuaciones globales, representación de Artin-Mazur e idempotencia![]()
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Let k be a real closed field. A real curve germ over k is a real one-dimensional Noetherian local integral domain with residual field k. A Noetherian local ring A with maximal ideal m and completion  is an AP-ring if for every system of polynom[...]![]()
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Let K be a formally real field and ? its order space. The automorphisms group of K acts on ?, and K is called D.O.P. when all the orbits are dense in ?. In this note the following is shown: The field of meromorphic function germs of a real irred[...]![]()
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In this talk I shall discuss the notion and some basic features of semialgebraic and semianalytic sets, which are one main concern of Real Geometry![]()
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Gascón, Francisco G. ; Peralta Salas, Daniel ; Ruiz Sancho, Jesús María | American Institute of Physics | 2000-05It is shown that when a dynamical system X0 with a proper set of global first integrals is perturbed, the phase space region accessible to the orbits of the perturbed vector field X0+Xp is bounded (we are assuming here that the time variable run[...]![]()
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Nash functions are those real analytic functions which are algebraic over the polynomials. Let M?Rn be a Nash manifold, N(M) the ring of Nash functions on M and O(M) the ring of analytic functions on M. The following problems have been open for [...]![]()
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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 proofs![]()
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Alonso García, María Emilia ; Etayo Gordejuela, J. Javier ; Gamboa, J. M. ; Ruiz Sancho, Jesús María | Real Sociedad Matemática Española;Consejo Superior de Investigaciones Científicas. Instituto "Jorge Juan" de Matemáticas | 1980Dado un espacio T3? (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 compactif[...]![]()
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Let k be a real closed field. A real AP-curve (over k) is a 1-dimensional, excellent Henselian local real domain with residue field k. A 1-dimensional Noetherian local ring is Arf, if emb dim(B)=mult(B) for every local ring B infinitely near to [...]![]()
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Fernando Galván, José Francisco ; Ruiz Sancho, Jesús María ; Scheiderer, Claus | American Mathematical Society | 2004Let A be an excellent ring. We show that if the real dimension of A is at least three then A has in finite Pythagoras number, and there exists a positive semidefinite element in A which is not a sum of squares in A.![]()
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Fernando Galván, José Francisco ; Ruiz Sancho, Jesús María ; Scheiderer, Claus | International Press | 2006Let 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 th[...]![]()
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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 Pytha[...]![]()
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We study analytic singularities for which every positive semidefinite analytic function is a sum of two squares of analytic functions. This is a basic useful property of the plane, but difficult to check in other cases; in particular, what about[...]![]()
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Andradas Heranz, Carlos ; Díaz-Cano Ocaña, Antonio ; Ruiz Sancho, Jesús María | WALTER DE GRUYTER | 2003We 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) meromorphi[...]![]()
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The book is an introduction to analytic geometry and commutative algebra, from the point of view of formal and convergent power series; it stands at the postgraduate level and gives a clear presentation of all the basic results of local analytic[...]![]()
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Outerelo Dominguez, Enrique ; Ruiz Sancho, Jesús María | Addison-Wesley Iberoamericana España | 1998This book provides an introduction to differential topology, mainly to the approximation and transversality theories, and shows how these techniques can be applied to obtain several classical results, such as Brouwer's fixed point theorem, the J[...]![]()
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Lojasiewicz pointed out in 1965 that the semialgebraic set {x![]()
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We show that the complexity of semialgebraic sets and mappings can be used to parametrize Nash sets and mappings by Nash families. From this we deduce uniform bounds on the complexity of Nash functions that lead to first-order descriptions of ma[...]