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