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1.

図書

図書
Alexander Prestel, Charles N. Delzell
出版情報: Berlin : Springer, c2001  viii, 267 p. ; 24 cm
シリーズ名: Springer monographs in mathematics
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目次情報: 続きを見る
Introduction
Real Fields / 1:
Ordered Fields / 1.1:
Extensions of Orderings / 1.2:
The Real Closure / 1.3:
Exercises / 1.4:
Bibliographical and Historical Comments / 1.5:
Semialgebraic Sets / 2:
Ultraproducts / 2.1:
Elimination of Quanti ers / 2.3:
The "Finiteness Theorem" / 2.4:
Quadratic Forms over Real Fields / 2.5:
Witt Decomposition / 3.1:
The Witt Ring of a Field / 3.2:
Signatures / 3.3:
Quadratic Forms Over Real Function Fields / 3.4:
Generalization of HilbertÆs 17th Problem / 3.5:
Real Rings / 3.6:
The Real Spectrum of a Commutative Ring / 4.1:
The Positivstellensatz / 4.2:
öContinuousö Representation of Polynomials / 4.3:
-Fields / 4.4:
The Real Spectrum of R[X1;: : : ;Xn / 4.5:
Archimedean Rings / 4.6:
Quadratic Modules and Semiorderings / 5.1:
Rings with Archimedean Preorderings / 5.2:
Rings with Archimedean Quadratic Modules / 5.3:
Rings with Archimedean Preprimes / 5.4:
Positive Polynomials on Semialgebraic Sets / 5.5:
Semiorderings and Weak Isotropy / 6.1:
Archimedean Quadratic Modules on R[X1;: : : ;Xn / 6.2:
Distinguished Representations of Positive Polynomials / 6.3:
Applications to the Moment Problem / 6.4:
Sums of 2mth Powers / 6.5:
Preorderings and Semiorderings of Level 2m / 7.1:
Semiorderings of Level 2m on Fields / 7.2:
Archimedean Modules of Level 2m / 7.3:
Bounds / 7.4:
Length of Sums of Squares / 8.1:
Existence of Degree Bounds / 8.2:
Positive Polynomials over Non-Archimedean Fields / 8.3:
Distinguished Representations in the Non-Archimedean Case / 8.4:
Exercise / 8.5:
Appendix: Valued Fields / 8.6:
Valuations / A.1:
Algebraic Extensions / A.2:
Henselian Fields / A.3:
Complete Fields / A.4:
Dependence and Composition of Valuations / A.5:
Transcendental Extensions / A.6:
Bibliographical Comments / A.7:
References
Glossary of Notations
Index
Introduction
Real Fields / 1:
Ordered Fields / 1.1:
2.

図書

図書
Teo Mora
出版情報: Cambridge, U.K. : Cambridge University Press, 2003  xiii, 423 p. ; 24 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 88
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目次情報:
The Kronecker-Duval philosophy
Factorization
The Kronecker-Duval philosophy
Factorization
3.

図書

図書
Andrew J. Sommese, Charles W. Wampler,II
出版情報: New Jersey : World Scientific, c2005  xxii, 401 p. ; 26 cm
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4.

図書

図書
by Jacek Graczyk and Grzegorz Świa̦tek
出版情報: Princeton, N.J. : Princeton University Press, 1998  viii, 148 p. ; 24 cm
シリーズ名: Annals of mathematics studies ; no. 144
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目次情報: 続きを見る
Review of Concepts / 1:
Theory of Quadratic Polynomials / 1.1:
Dense Hyperbolicity / 1.2:
Steps of the Proof of Dense Hyperbolicity / 1.3:
Quasiconformal Gluing / 2:
Extendibility and Distortion / 2.1:
Saturated Maps / 2.2:
Gluing of Saturated Maps / 2.3:
Polynomial-Like Property / 3:
Domains in the Complex Plane / 3.1:
Cutting Times / 3.2:
Linear Growth of Moduli / 4:
Box Maps and Separation Symbols / 4.1:
Conformal Roughness / 4.2:
Growth of the Separation Index / 4.3:
Quasiconformal Techniques / 5:
Initial Inducing / 5.1:
Quasiconformal Pull-back / 5.2:
Gluing Quasiconformal Maps / 5.3:
Regularity of Saturated Maps / 5.4:
Straightening Theorem / 5.5:
Bibliography
Index
Review of Concepts / 1:
Theory of Quadratic Polynomials / 1.1:
Dense Hyperbolicity / 1.2:
5.

図書

図書
J.S. Lomont, John Brillhart
出版情報: Boca Raton : Chapman & Hall/CRC, c2001  xxiii, 289 p. ; 25 cm
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目次情報: 続きを見る
Contents
Tables
Preface
Introduction
Binomial Sequences of Polynomials / 1.:
The functions F / (a):
The functions F[subscript 0]--The sequences {G[subscript m](z)} and {H[subscript m](z)} / (b):
The Binomial Sequences Generated from f[superscript -1], f [set membership] F[superscript 0] / 2.:
The Functions F[subscript 1]--Elliptic Polynomials of the First Kind / 3.:
The Moment Polynomials--P[subscript n](x,y), Q[subscript n](x,y), and R[subscript n](x,y) / 4.:
The Functions F[superscript -1 subscript 1]--Elliptic Polynomials of Second Kind / 5.:
Inner Products, Integrals, and Moments--Favard's Theorem / 6.:
The Functions F[subscript 2]--Orthogonal Sequences {G[subscript m](z)}, {H[subscript m](z)} / 7.:
The Functions in Classes I and II / 8.:
Class I Functions--The elliptic functions sn (t,k)
Class II Functions--The polynomials f*(t,k)
The Tangent Numbers / 9.:
Class III Functions--The [delta subscript n](x) Polynomials / 10.:
Coefficients of the [delta subscript n](x) Polynomials / 11.:
The [lambda subscript n](x) Polynomials / 12.:
The Orthogonal Sequences {A[subscript m](z)} and {B[subscript m](z)} / 13.:
The Weight Functions for {A[subscript m](z)} and {B[subscript m](z)} / 14.:
Miscellaneous Results / 15.:
Uniqueness and Completion Results / 16.:
Polynomial Inequalities / 17.:
Some Concluding Questions / 18.:
References
Name Index
Subject Index
Symbol Index
Contents
Tables
Preface
6.

図書

図書
A. Schinzel
出版情報: Cambridge : Cambridge University Press, 2000  x, 558 p. ; 24 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 77
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7.

図書

図書
Theodore J. Rivlin, Edward B. Saff, editors
出版情報: New York : Springer, c2000  xliv, 682 p. ; 25 cm
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8.

図書

図書
Martin Dietzfelbinger
出版情報: Berlin : Springer, 2004  x, 147 p. ; 29 cm.
シリーズ名: Lecture notes in computer science ; 3000
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9.

図書

図書
T. Sheil-Small
出版情報: Cambridge : Cambridge University Press, 2002  xix, 428 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 75
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目次情報: 続きを見る
Preface
List of notation
The algebra of polynomials / 1:
The degree principle and the fundamental theorem of algebra / 2:
The Jacobian problem / 3:
Analytic and harmonic functions in the unit disc / 4:
Circular regions and Grace's theorem / 5:
The Ilieff-Sendov conjecture / 6:
Self-inversive polynomials / 7:
Duality and an extension of Grace's theorem to rational functions / 8:
Real polynomials / 9:
Level curves / 10:
Miscellaneous topics / 11:
References
Index
Preface
List of notation
The algebra of polynomials / 1:
10.

図書

図書
Eduardo D. Sontag
出版情報: Berlin ; New York : Springer-Verlag, 1979  viii, 168 p. ; 25 cm
シリーズ名: Lecture notes in control and information sciences ; 13
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