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1. |
Record Nr. |
UNISA996466561803316 |
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Autore |
Powers Victoria |
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Titolo |
Certificates of positivity for real polynomials : theory, practice, and applications / / Victoria Powers |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2021] |
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©2021 |
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ISBN |
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9783030855475 |
9783030855468 |
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Descrizione fisica |
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1 online resource (161 pages) : illustrations |
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Collana |
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Developments in mathematics ; ; Volume 69 |
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Disciplina |
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Soggetti |
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Polinomis |
Polynomials |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Intro -- Preface -- Contents -- 0 Introduction -- 1 Preliminaries -- 1.1 Basic Notation -- 1.2 The Real Numbers -- 1.3 Polynomials -- 1.4 Polynomials Versus Forms -- 1.5 Matrices and Quadratic Forms -- 1.6 Convex Sets and Cones -- Reference -- 2 Sums of Squares and Positive Polynomials -- 2.1 SOS and PSD Polynomials -- 2.2 Hilbert's 17th Problem -- 2.2.1 Uniform Denominators -- 2.2.2 Degree Bounds -- 2.3 The Gap Between PSD and SOS Polynomials -- References -- 3 Global Certificates of Positivity -- 3.1 The Gram Matrix Method -- 3.2 From Gram Matrices to Certificates -- 3.3 Application: Global Optimization of Polynomials -- References -- 4 Positive Semidefinite Ternary Quartics -- 4.1 Proofs of Hilbert's Theorem on Ternary Quartics -- 4.2 Finding and Counting Sum of Squares Representations -- References -- 5 Positivity on Semialgebraic Sets -- 5.1 Semialgebraic Sets -- 5.2 Preorders and Quadratic Modules -- 5.3 Positivity Properties -- 5.4 Saturated Quadratic Modules and Preorders -- 5.5 The Positivstellensatz -- 5.6 Sums of Squares and Positivity on Algebraic Sets -- 5.7 Application: The Moment Problem -- References -- 6 The Archimedean Property -- 6.1 Archimedean T-Modules -- 6.2 Marshall's Representation Theorem -- 6.3 Application: Theorems of |
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Handelman and Pólya -- References -- 7 Theorems of Schmüdgen and Putinar -- 7.1 Schmüdgen's Positivstellensatz -- 7.1.1 Wörmann's Proof -- 7.2 Putinar's Positivstellenstz -- 7.3 Minimal Representations -- 7.4 Constructive Proofs -- 7.4.1 Degree Bounds -- 7.5 Application: Polynomial Optimization on Compact Semialgebraic Sets -- References -- 8 The Dimension One Case -- 8.1 Positivity on a Closed Interval -- 8.1.1 Bernstein Representations -- 8.2 Basic Closed Semialgebraic Subsets of mathbbR -- 8.3 Positivity on Curves in the Plane -- References -- 9 Positivity on Polytopes -- 9.1 Pólya's Theorem. |
9.1.1 Pólya's Theorem with Zeros -- 9.2 Certificates in Preprimes and Quadratic Modules -- 9.3 Applications -- 9.3.1 Approximating the Stability Number of a Graph -- 9.3.2 Minimization of Polynomials on Polytopes -- References -- 10 The Noncompact Case -- 10.1 Saturation in the Noncompact Case -- 10.2 Stability and Open Cones -- 10.3 Cylinders with Compact Cross-Section -- References -- 11 Sums of Squares of Rational Polynomials -- 11.1 Weighted Sums of Squares Representations -- 11.2 The Univariate Case -- 11.3 Sums of Rational Squares -- 11.4 Algorithmic Approaches -- References -- 12 Positive Polynomials with Special Structure -- 12.1 Symmetric Polynomials -- 12.2 Diagonal-Tail Forms -- 12.3 Agiforms -- 12.4 Circuit Polynomials -- 12.5 Application: Global Optimization Using Geometric Programming -- References -- Appendix A Real Algebra and Algebraic Geometry -- A.1 Algebraic Sets -- A.2 Real Fields -- A.3 Tarski-Seidenberg Theorem -- A.4 The Real Spectrum -- References -- Appendix Index of Notation -- Index. |
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2. |
Record Nr. |
UNINA9910348249103321 |
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Autore |
Achard-Bayle Guy |
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Titolo |
Genres & textes : Déterminations, évolutions, confrontations / / Michèle Monte, Gilles Philippe |
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Pubbl/distr/stampa |
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Lyon, : Presses universitaires de Lyon, 2018 |
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ISBN |
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Descrizione fisica |
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1 online resource (358 p.) |
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Altri autori (Persone) |
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AdamJean-Michel |
Badiou-MonferranClaire |
BonhommeMarc |
BronckartJean-Paul |
CalameClaude |
CharaudeauPatrick |
CombettesBernard |
CoutinhoMaria Antónia |
FenoglioIrène |
FløttumKjersti |
Gomes da Silva NetoJoão |
Graças Soares RodriguesMaria das |
JaubertAnna |
Lorda MurClara Ubaldina |
LundquistLita |
MaingueneauDominique |
MoliniéGeorges |
MonteMichèle |
NølkeHenning |
PasseggiLuis |
PétillonSabine |
PetitjeanAndré |
RabatelAlain |
RevazFrançoise |
PhilippeGilles |
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Soggetti |
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Linguistics |
analyse textuelle |
discours |
genre |
textualisation |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Sommario/riassunto |
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En dialogue avec l'analyse textuelle des discours défendue et illustrée par Jean-Michel Adam, les vingt contributions de ce volume, dues à des chercheurs renommés, s'interrogent sur l'articulation entre les normes textuelles et discursives découlant de l'appartenance d'un texte à un genre et les faits linguistiques locaux résultant des impératifs de la textualisation. L'ouvrage propose des réflexions théoriques sur les concepts de genre, texte et discours, des analyses partant de faits textuels tels que la ponctuation, les reformulations sur manuscrit ou l'usage des connecteurs, et des études de cas portant sur des genres oraux ou écrits (notamment le débat, les blogs, la tragédie grecque, le feuilleton) dans des sphères discursives variées (littérature, publicité, médias, discours institutionnels et politiques). |
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