1.

Record Nr.

UNISALENTO991001840649707536

Autore

Georgia International Topology Conference <2009 : University of Georgia>

Titolo

Low-dimensional and symplectic topology / Michael Usher, editor

Pubbl/distr/stampa

Providence, R. I. : American Mathematical Society, c2011

ISBN

9780821852354

Descrizione fisica

ix, 228 p. : ill. ; 26 cm

Collana

Proceedings of symposia in pure mathematics, 0082-0717 ; 82

Classificazione

AMS 57-06

AMS 20F36

AMS 53D12

LC QA612.14.G46

Altri autori (Persone)

Usher, Michaelauthor

Disciplina

514.22

Soggetti

Low-dimensional topology - Congreses

Symplectic and contact topology - Congresses

Manifolds (Mathematics) - Congresses

Simplexes (Mathematics) - Congresses

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Papers presented at the 2009 Georgia International Topology Conference, held at the University of Georgia, Athens, Georgia, May 18-29, 2009

Nota di bibliografia

Includes bibliographical references



2.

Record Nr.

UNINA9910806857203321

Autore

Lombardi Henri

Titolo

An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem / / Henri Lombardi, Daniel Perrucci, Marie-Françoise Roy

Pubbl/distr/stampa

Providence, Rhode Island : , : American Mathematical Society, , 2020

ISBN

1-4704-5662-1

Descrizione fisica

1 online resource (138 pages)

Collana

Memoirs of the American Mathematical Society ; ; Volume 263

Classificazione

12D1514P9913J30

Disciplina

512.9422

Soggetti

Polynomials

Algebraic fields

Recursive functions

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

Weak inference and weak existence -- Intermediate value theorem -- Fundamental theorem of algebra -- Hermite's theory -- Elimination of one variable -- Proof of the main theorems -- Annex.

Sommario/riassunto

"We prove an elementary recursive bound on the degrees for Hilbert's 17th problem. More precisely we express a nonnegative polynomial as a sum of squares of rational functions, and we obtain as degree estimates for the numerators and denominators the following tower of five exponentials 222d4k where d is the degree and k is the number of variables of the input polynomial. Our method is based on the proof of an elementary recursive bound on the degrees for Stengle's Positivstellensatz. More precisely we give an algebraic certificate of the emptyness of the realization of a system of sign conditions and we obtain as degree bounds for this certificate a tower of five exponentials, namely 2²(2max{2,d}4k+s2kmax{2,d}16kbit(d)) where d is a bound on the degrees, s is the number of polynomials and k is the number of variables of the input polynomials--