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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[...]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[...]