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Autor Ruiz Sancho, Jesús María |
Documentos disponibles escritos por este autor (73)
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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[...]