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