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1.

図書

図書
Frédéric Hélein
出版情報: Cambridge : Cambridge University Press, 2002  xxv, 264 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 150
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2.

図書

図書
Yasumasa Nishiura ; translated by Kunimochi Sakamoto
出版情報: Providence, R.I. : American Mathematical Society, c2002  xx, 311 p. ; 22 cm
シリーズ名: Translations of mathematical monographs ; v. 209
Iwanami series in modern mathematics
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Separation and unification of scales
Amplitude equations
Marginal stability criterion and pattern selection
Pattern formation
Method of singular limit analysis
Transient dynamics
Future perspectives
Bibliography
Index
Separation and unification of scales
Amplitude equations
Marginal stability criterion and pattern selection
3.

図書

図書
Claus Hertling
出版情報: Cambridge : Cambridge University Press, 2002  ix, 270 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 151
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Multiplication on the Tangent Bundle / Part I:
Introduction to part 1 / 1:
Definition and first properties of F-manifolds / 2:
Massive F-manifolds and Lagrange maps / 3:
Discriminants and modality of F-manifolds / 4:
Singularities and Coxeter groups / 5:
Frobenius Manifolds, Gauss-Manin Connections, and Moduli Spaces for Hypersurface Singularities / Part II:
Introduction to part 2 / 6:
Connections on the punctured plane / 7:
Meromorphic connections / 8:
Frobenius manifolds ad second structure connections / 9:
Gauss-Manin connections for hypersurface singularities / 10:
Frobenius manifolds for hypersurface singularities / 11:
âê´Î¼Ïà-constant stratum / 12:
Moduli spaces for singularities / 13:
Variance of the spectral numbers / 14:
Multiplication on the Tangent Bundle / Part I:
Introduction to part 1 / 1:
Definition and first properties of F-manifolds / 2:
4.

図書

図書
Wolfgang Lück
出版情報: Berlin ; Tokyo : Springer, c2002  xv, 595 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, v. 44
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5.

図書

図書
Jan Cnops
出版情報: Boston : Birkhäuser, c2002  x, 211 p. ; 24 cm
シリーズ名: Progress in mathematical physics / editors-in-chief, Anne Boutet de Monvel, Gerald Kaiser ; v. 24
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Introduction
Clifford Algebras
Manifolds
Dirac Operators
Conformal Maps
Unique Continuation and the Cauchy Kernel
Boundary Values
Appendix
General Manifolds
The Additional Canterbury Tales
List of Symbols
Bibliography
Index
Introduction
Clifford Algebras
Manifolds
6.

図書

図書
Donggao Deng ... [et al.], editors
出版情報: Providence, R.I. : American Mathematical Society : International Press, c2002  xvi, 326 p. ; 26 cm
シリーズ名: AMS/IP studies in advanced mathematics ; v. 25
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7.

図書

図書
Janet Whalen Kammeyer, Daniel J. Rudolph
出版情報: Cambridge : Cambridge University Press, 2002  vi, 201 p. ; 24 cm
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Preface / 1:
Definitions and examples / 2:
The Ornstein-Weiss machinery / 3:
Copying lemmas / 4:
m-entropy / 5:
m-joinings / 6:
The equivalence theorem / 7:
Appendix / 8:
Preface / 1:
Definitions and examples / 2:
The Ornstein-Weiss machinery / 3:
8.

図書

図書
Andrew J. Majda, Andrea L. Bertozzi
出版情報: Cambridge : Cambridge University Press, 2002  xii, 545 p. ; 26 cm
シリーズ名: Cambridge texts in applied mathematics
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Preface
An introduction to vortex dynamics for incompressible fluid flows / 1:
The vorticity-stream formulation of the Euler and the Navier-Stokes equations / 2:
Energy methods for the Euler and the Navier-Stokes equations / 3:
The particle-trajectory method for existence and uniqueness of solutions to the Euler equation / 4:
The search for singular solutions to the 3D Euler equations / 5:
Computational vortex methods / 6:
Simplified asympototic equations for slender vortex filaments / 7:
Weak solutions to the 2D Euler equations with initial vorticity in Lâê  / 8:
Introduction to vortex sheets, weak solutions and approximate-solution sequences for the Euler equation / 9:
Weak solutions and solution sequences in two dimensions / 10:
The 2D Euler equation: concentrations and weak solutions with vortex-sheet initial data / 11:
Reduced Hausdorff dimension, oscillations and measure-valued solutions of the Euler equations in two and three dimensions / 12:
The Vlasov-Poisson equations as an analogy to the Euler equations for the study of weak solutions / 13:
Index
Preface
An introduction to vortex dynamics for incompressible fluid flows / 1:
The vorticity-stream formulation of the Euler and the Navier-Stokes equations / 2:
9.

図書

図書
David F. Walnut
出版情報: Boston : Birkhäuser, c2002  xvii, 449 p. ; 25 cm
シリーズ名: Applied and numerical harmonic analysis / series editor, John J. Benedetto
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Preface
Preliminaries / Part I:
Functions and Convergence
Fourier Series
The Fourier Transform
Signals and Systems
The Haar System / Part II:
The Discrete Haar Transform
Orthonormal Wavelet Bases / Part III:
Mulitresolution Analysis
The Discrete Wavelet Transform
Smooth, Compactly Supported Wavelets
Other Wavelet Constructions / Part IV:
Biorthogonal Wavelets
Wavelet Packets
Applications / Part V:
Image Compression
Integral Operators
Review of Advanced Calculus and Linear Algebra / Appendix A:
Excursions in Wavelet Theory / Appendix B:
References Cited in the Text / Appendix C:
Index
Preface
Preliminaries / Part I:
Functions and Convergence
10.

図書

図書
M. Takesaki
出版情報: Berlin ; Tokyo : Springer, c2002-c2003  3 v. ; 25 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 124-125, 127 . Operator algebras and non-commutative geometry ; 5-6, 8
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Preface
Ergodic Transformaton Groups and the Associated von Neumann Algebras / Chapter XIII:
Approximately Finite Dimensional von Neumann Algebras / Chapter XIV:
Nuclear C*-Algebras / Chapter XV:
Injective von Neumann Algebras / Chapter XVI:
Non-Commutative Ergodic Theory / Chapter XVII:
Structure of Approximately Finite Dimensional Factors / Chapter XVIII:
Subfactors of a Factor of Tape II1 / Chapter XIX:
Fundaments of Banach Algebras and C*-Algebras / Appendix:
Topologies and Density Theorems in Operator Algebras
Conjugate Spaces
Tensor Products of Operator Algebras and Direct Integrals
Types of von Neumann Algebras and Traces
Appendix: Polish Spaces and Standard Borel Spaces
Preface
Ergodic Transformaton Groups and the Associated von Neumann Algebras / Chapter XIII:
Approximately Finite Dimensional von Neumann Algebras / Chapter XIV:
11.

図書

図書
Zhuoqun Wu ... [et al.]
出版情報: Singapore : World Scientific, c2001  xvii, 502 p. ; 23 cm
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Preface
Newtonian Filtration Equations / Chapter 1:
Introduction / 1.1:
Physical examples / 1.1.1:
Definitions of generalized solutions / 1.1.2:
Special solutions / 1.1.3:
Existence and Uniqueness of Solutions: One Dimensional Case / 1.2:
Uniqueness of solutions / 1.2.1:
Existence of solutions / 1.2.2:
Comparison theorems / 1.2.3:
Some extensions / 1.2.4:
Existence and Uniqueness of Solutions: Higher Dimensional Case / 1.3:
Comparison theorem and uniqueness of solutions / 1.3.1:
Regularity of Solutions: One Dimensional Case / 1.3.2:
Lemma / 1.4.1:
Regularity of solutions / 1.4.2:
Regularity of Solutions: Higher Dimensional Case / 1.4.3:
Generalized class B[subscript 2] / 1.5.1:
Some lemmas / 1.5.2:
Properties of functions in the generalized class B[subscript 2] / 1.5.3:
Holder continuity of solutions / 1.5.4:
Properties of the Free Boundary: One Dimensional Case / 1.6:
Finite propagation of disturbances / 1.6.1:
Localization and extinction of disturbances / 1.6.2:
Differential equation on the free boundary / 1.6.3:
Continuously differentiability of the free boundary / 1.6.4:
Some further results / 1.6.5:
Properties of the Free Boundary: Higher Dimensional Case / 1.7:
Monotonicity and Holder continuity of the free boundary / 1.7.1:
Lipschitz continuity of the free boundary / 1.7.2:
Initial Trace of Solutions / 1.7.3:
Harnack inequality / 1.8.1:
Main result / 1.8.2:
Extension of existence and uniqueness theorem / 1.8.3:
Other Problems / 1.9:
Equations with strongly nonlinear sources / 1.9.1:
Asymptotic properties of solutions / 1.9.2:
Non-Newtonian Filtration Equations / Chapter 2:
Introduction Preliminary Knowledge / 2.1:
Introduction Physical example / 2.1.1:
Basic spaces and some lemmas / 2.1.2:
Existence of Solutions / 2.1.3:
The case u[subscript 0] [set membership] C[superscript [infinity] subscript 0](R[superscript N]) or u[subscript 0] [set membership] L[superscript 1](R[superscript N]) [intersection of] L[superscript [infinity](R[superscript N]) / 2.2.1:
The case u[subscript 0] [set membership] L[superscript 1 subscript loc](R[superscript N]) / 2.2.2:
Some remarks / 2.2.3:
Harnack Inequality and the Initial Trace of Solutions / 2.3:
Local Harnack inequality / 2.3.1:
Global Harnack inequality / 2.3.2:
Initial trace of solutions / 2.3.3:
Regularity of Solutions / 2.4:
Boundedness of solutions / 2.4.1:
Boundedness of the gradient of solutions / 2.4.2:
Holder continuity of the gradient of solutions / 2.4.3:
Uniqueness of Solutions / 2.5:
Auxiliary propositions / 2.5.1:
Uniqueness theorem and its proof / 2.5.2:
Properties of the Free Boundary / 2.6:
p-Laplacian equation with strongly nonlinear sources / 2.6.1:
General Quasilinear Equations of Second Order / 2.7.2:
Weakly Degenerate Equations in One Dimension / 3.1:
Uniqueness of bounded and measurable solutions / 3.2.1:
Existence of continuous solutions / 3.2.2:
Weakly Degenerate Equations in Higher Dimension / 3.2.3:
Existence of continuous solutions for equations with two points of degeneracy / 3.3.1:
Uniqueness of BV solutions / 3.3.2:
Existence of BV solutions / 3.3.3:
Strongly Degenerate Equations in One Dimension / 3.3.4:
Definitions of solutions with discontinuity / 3.4.1:
Interior discontinuity condition / 3.4.2:
Uniqueness of BV solutions of the Cauchy problem / 3.4.3:
Formulation of the boundary value problem / 3.4.4:
Boundary discontinuity condition / 3.4.5:
Uniqueness of BV solutions of the first boundary value problem / 3.4.6:
Existence of BV solutions of the first boundary value problem / 3.4.7:
Equations with degeneracy at infinity / 3.4.8:
Properties of the curves of discontinuity / 3.4.10:
Degenerate Equations in Higher Dimension without Terms of Lower Order / 3.5:
Uniqueness of bounded and integrable solutions / 3.5.1:
A lemma on weak convergence / 3.5.2:
General Strongly Degenerate Equations in Higher Dimension / 3.5.3:
Appendix Classes BV and BV[subscript x] / 3.6.1:
Nonlinear Diffusion Equations of Higher Order / Chapter 4:
Similarity Solutions of a Fourth Order Equation / 4.1:
Definition of similarity solutions / 4.2.1:
Existence and uniqueness of global solutions of the Cauchy problem / 4.2.2:
Properties of solutions at zero points / 4.2.3:
Properties of unbounded solutions / 4.2.5:
Bounded solutions on the half line / 4.2.6:
Bounded solutions on the whole line / 4.2.7:
Properties of solutions in typical cases k = 1,2,3,4 / 4.2.8:
Behavior of similarity solutions as t [right arrow] 0[superscript +] / 4.2.9:
Equations with Double-Degeneracy / 4.3:
Weighted energy equality of solutions / 4.3.1:
Some auxiliary inequalities / 4.3.4:
Asymptotic behavior of solutions / 4.3.5:
Extinction of solutions at finite time / 4.3.7:
Nonexistence of nonnegative solutions / 4.3.8:
Infinite propagation case / 4.3.9:
Cahn-Hilliard Equation with Constant Mobility / 4.4:
Existence of classical solutions / 4.4.1:
Blowing-up of solutions / 4.4.2:
Global existence of solutions for small initial value / 4.4.3:
Cahn-Hilliard Equations with Positive Concentration Dependent Mobility / 4.5:
A modified Campanato space / 4.5.1:
Holder norm estimates for a linear problem / 4.5.2:
Zero potential case / 4.5.3:
General case / 4.5.4:
Thin Film Equation / 4.6:
Definition of generalized solutions / 4.6.1:
Approximate solutions / 4.6.2:
Nonnegativity of solutions / 4.6.3:
Zeros of nonnegative solutions / 4.6.5:
Monotonicity of the support of solutions / 4.6.6:
Cahn-Hilliard Equation with Degenerate Mobility / 4.7:
Models with degenerate mobility / 4.7.1:
Definition of physical solutions / 4.7.2:
Physical solutions / 4.7.3:
Bibliography
Preface
Newtonian Filtration Equations / Chapter 1:
Introduction / 1.1:
12.

図書

図書
George Greaves
出版情報: Berlin ; Tokyo : Springer, c2001  xii, 304 p. ; 24 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, v. 43
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Introduction
The Structure of Sifting Arguments / 1:
The Sieves of Eratosthenes and Legendre / 1.1:
The Contribution of Eratosthenes / 1.1.1:
Legendre's Sieve / 1.1.2:
An Estimate for n(X) / 1.1.3:
The Distribution of Primes / 1.1.4:
Examples of Sifting Situations / 1.2:
Notations / 1.2.1:
The Integers in an Interval (Y - X, Y ) / 1.2.2:
Numbers Given by Polynomial Expressions / 1.2.3:
Arithmetic Progressions / 1.2.4:
Sums of Two Squares / 1.2.5:
Polynomials with Prime Arguments / 1.2.6:
A General Formulation of a Sifting Situation / 1.3:
The Basic Formulation / 1.3.1:
Legendre's Sieve in a General Setting / 1.3.2:
A Generalised Formulation / 1.3.3:
A Further Generalisation / 1.3.4:
Sifting Density / 1.3.5:
The Sifting Limit Β(k) / 1.3.6:
Composition of Sieves / 1.3.7:
Notes on Chapter 1 / 1.4:
Selberg's Upper Bound Method / 2:
The Sifting Apparatus / 2.1:
Selberg's Theorem / 2.1.1:
The Numbers (lambda)(d) / 2.1.2:
A Simple Application / 2.1.3:
General Estimates of G(x) and E(D, P) / 2.2:
An Estimate by Rankin's Device / 2.2.1:
Asymptotic Formulas / 2.2.2:
The Error Term / 2.2.3:
Applications / 2.3:
Prime Twins and Goldbach's Problem / 2.3.1:
Polynomial Sequences / 2.3.3:
Notes on Chapter 2 / 2.4:
Combinatorial Methods / 3:
The Construction of Combinatorial Sieves / 3.1:
Preliminary Discussion of Brun's Ideas / 3.1.1:
Fundamental Inequalities and Identities / 3.1.2:
Buchstab's Identity / 3.1.3:
The Combinatorial Sieve Lemma / 3.1.4:
Brun's Pure Sieve / 3.2:
Inequalities and Identities / 3.2.1:
The "Pure Sieve" Theorem / 3.2.2:
A Corollary / 3.2.3:
Prime Twins / 3.2.4:
A Modern Edition of Brun's Sieve / 3.3:
Rosser's Choice of X / 3.3.1:
A Technical Estimate / 3.3.2:
A Simplifying Approximation / 3.3.3:
A Combinatorial Sieve Theorem / 3.3.4:
Brun's Version of his Method / 3.3.5:
Brun's Choice of x / 3.4.1:
The Estimations / 3.4.2:
The Result / 3.4.3:
Notes on Chapter 3 / 3.5:
Rosser's Sieve / 4:
Approximations by Continuous Functions / 4.1:
The Recurrence Relations / 4.1.1:
Partial Summation / 4.1.2:
The Leading Terms / 4.1.3:
The Functions F and f / 4.2:
The Difference-Differential Equations / 4.2.1:
The Adjoint Equation and the Inner Product / 4.2.2:
Solutions of the Adjoint Equation / 4.2.3:
Particular Values of F(s) and f(s) / 4.2.4:
Asymptotic Analysis as k -> $(infinity$) / 4.2.5:
The Convergence Problem / 4.3:
The Auxiliary Functions / 4.3.1:
Adjoints and Inner Products / 4.3.2:
The Case k
A Sieve Theorem Following Rosser / 4.4:
The Case k >/= 1/2: a First Result / 4.4.1:
Theorem 1 when k
An Improved Version of Proposition 1 / 4.4.3:
A Two-Sided Estimate / 4.4.4:
Extremal Examples / 4.5:
The Linear Case / 4.5.1:
The Case k=1/2 / 4.5.2:
Notes on Chapter 4 / 4.6:
The Sieve with Weights / 5:
Simpler Weighting Devices / 5.1:
Logarithmic Weights / 5.1.1:
Modified Logarithmic Weights / 5.1.2:
Some Applications / 5.1.3:
More Elaborate Weighted Sieves / 5.2:
An Improved Weighting Device / 5.2.1:
Buchstab's Weights / 5.2.2:
A Weighted Sieve Following Rosser / 5.3:
Combining Sieving and Weighting / 5.3.1:
The Reduction Identities / 5.3.2:
An Identity for the Main Term / 5.3.3:
The Estimate for the Main Term / 5.3.4:
Notes on Chapter 5 / 5.4:
The Remainder Term in the Linear Sieve / 6:
The Bilinear Nature of Rosser's Construction / 6.1:
The Factorisation of x.d / 6.1.1:
Discretisations of Rosser's Sieve / 6.1.2:
Specification of Details / 6.1.3:
The Leading Contributions to the Main Term / 6.1.4:
The Remainder Term / 6.1.5:
Sifting Short Intervals / 6.2:
The Smoothed Formulation / 6.2.1:
The Remainder Sums / 6.2.2:
Trigonometrical Sums / 6.2.3:
Notes on Chapter 6 / 6.3:
Lower Bound Sieves when k > 1 / 7:
An Extension of Selberg's Upper Bound / 7.1:
The Integral Equation and the Function $(sigma$) (s) / 7.1.1:
The Estimation of G(s) / 7.1.2:
A Lower Bound Sieve via Buchstab's Identity / 7.2:
Buchstab's Iterations / 7.2.1:
The Buchstab Transform of the $(lambda$)2 Method / 7.2.2:
The Sifting Limit as k -> $(infinity$) / 7.2.3:
Selberg's a2 a" Method / 7.3:
The Improved Sifting Limit for Large k / 7.3.1:
Notes on Chapter 7 / 7.4:
References
Index
Introduction
The Structure of Sifting Arguments / 1:
The Sieves of Eratosthenes and Legendre / 1.1:
13.

図書

図書
Alexei Skorobogatov
出版情報: Cambridge : Cambridge University Press, 2001  viii, 187 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 144
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Introduction / 1:
Torsors / Part 1:
Torsors: general theory / 2:
Torsors over a field / 2.1:
Torsors and Cech cohomology / 2.2:
Torsors under groups of multiplicative type / 2.3:
Obstructions to existence of rational points over arbitrary fields / 2.4:
Examples of torsors / 3:
Torsors in geometric invariant theory / 3.1:
Classification of Del Pezzo surfaces of degree 5 / Appendix:
Homogeneous spaces and central extensions / 3.2:
Torsors under abelian varieties / 3.3:
Equations for 2- and 4-coverings of elliptic curves
Abelian torsors / 4:
From abelian torsors to Azumaya algebras / 4.1:
A commutative diagram / 4.2:
Local description of abelian torsors / 4.3:
Torsors associated with a dominant morphism to P[superscript 1 subscript k] / 4.4:
Descent and Manin Obstruction / Part 2:
Obstructions over number fields / 5:
The Hasse principle, weak and strong approximation / 5.1:
The Manin obstruction / 5.2:
Descent obstructions / 5.3:
Abelian descent and Manin obstruction / 6:
Descent theory / 6.1:
Manin obstruction and global duality pairings / 6.2:
Compactifications of torsors under tori / 6.3:
Abelian descent on conic bundle surfaces / 7:
Brauer group of conic bundles / 7.1:
Chatelet surfaces / 7.2:
Some intersections of two quadrics in P[superscript 5 subscript k] / 7.3:
Conic bundles with six singular fibres / 7.4:
Non-abelian descent on bielliptic surfaces / 8:
Beyond the Manin obstruction / 8.1:
An example of 4-torsion in III (E)
Interpretation in terms of non-abelian torsors / 8.2:
Homogeneous spaces and non-abelian cohomology / 9:
Liens and non-abelian H[superscript 2] / 9.1:
The Springer class of a homogeneous space / 9.2:
Abelianization of non-abelian H[superscript 2] / 9.3:
Hasse principle for non-abelian H[superscript 2] / 9.4:
Descent on homogeneous spaces / 9.5:
References
Index
Introduction / 1:
Torsors / Part 1:
Torsors: general theory / 2:
14.

図書

図書
Peter Jan Pahl, Rudolf Damrath ; [translation, Felix Pahl]
出版情報: Berlin : Springer, c2001  xviii, 1008 p. ; 24 cm
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15.

図書

図書
by Ravi P. Agarwal and Donal O'Regan
出版情報: Dordrecht : Kluwer Academic, c2001  x, 341 p. ; 25 cm
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16.

図書

図書
J. Eells, B. Fuglede ; with a preface by M. Gromov
出版情報: Cambridge ; New York : Cambridge University Press, 2001  xii, 296 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 142
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GromovÆs preface
Preface
Introduction / 1:
Domains, Targets, Examples / Part 1:
Harmonic spaces, Dirichlet spaces and geodesic spaces / 2:
Examples of domains and targets / 3:
Riemannian polyhedra / 4:
Potential Theory on Polyhedra / Part 2:
The Sobolev space W1,2(X). Weakly harmonic functions / 5:
Potential theory on Riemannian polyhedra / 7:
Examples of Riemannian polyhedra and related spaces / 8:
Maps between Polyhedra / Part 3:
Energy of maps / 9:
Hölder continuity of energy minimizers / 10:
Existence of energy minimizers / 11:
Harmonic maps - totally geodesic maps / 12:
Harmonic morphisms / 13:
Energy according to Korevaar-Schoen / 14Appendix A:
Minimizers with small energy decay / 15Appendix B:
Bibliography
Special symbols
Index
GromovÆs preface
Preface
Introduction / 1:
17.

図書

図書
J.M.T. Thompson and H.B. Stewart
出版情報: Chichester [West Sussex] : Wiley, c2002  xxii, 437 p. ; 23 cm
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Preface
Preface to the First Edition
Acknowledgements from the First Edition
Introduction / 1:
Historical background / 1.1:
Chaotic dynamics in Duffing's oscillator / 1.2:
Attractors and bifurcations / 1.3:
Basic Concepts of Nonlinear Dynamics / Part I:
An overview of nonlinear phenomena / 2:
Undamped, unforced linear oscillator / 2.1:
Undamped, unforced nonlinear oscillator / 2.2:
Damped, unforced linear oscillator / 2.3:
Damped, unforced nonlinear oscillator / 2.4:
Forced linear oscillator / 2.5:
Forced nonlinear oscillator: periodic attractors / 2.6:
Forced nonlinear oscillator: chaotic attractor / 2.7:
Point attractors in autonomous systems / 3:
The linear oscillator / 3.1:
Nonlinear pendulum oscillations / 3.2:
Evolving ecological systems / 3.3:
Competing point attractors / 3.4:
Attractors of a spinning satellite / 3.5:
Limit cycles in autonomous systems / 4:
The single attractor / 4.1:
Limit cycle in a neural system / 4.2:
Bifurcations of a chemical oscillator / 4.3:
Multiple limit cycles in aeroelastic galloping / 4.4:
Topology of two-dimensional phase space / 4.5:
Periodic attractors in driven oscillators / 5:
The Poincare map / 5.1:
Linear resonance / 5.2:
Nonlinear resonance / 5.3:
The smoothed variational equation / 5.4:
Variational equation for subharmonics / 5.5:
Basins of attraction by mapping techniques / 5.6:
Resonance of a self-exciting system / 5.7:
The ABC of nonlinear dynamics / 5.8:
Chaotic attractors in forced oscillators / 6:
Relaxation oscillations and heartbeat / 6.1:
The Birkhoff-Shaw chaotic attractor / 6.2:
Systems with nonlinear restoring force / 6.3:
Stability and bifurcations of equilibria and cycles / 7:
Liapunov stability and structural stability / 7.1:
Centre manifold theorem / 7.2:
Local bifurcations of equilibrium paths / 7.3:
Local bifurcations of cycles / 7.4:
Basin changes at local bifurcations / 7.5:
Prediction of incipient instability / 7.6:
Iterated Maps as Dynamical Systems / Part II:
Stability and bifurcation of maps / 8:
Stability of one-dimensional maps / 8.1:
Bifurcations of one-dimensional maps / 8.3:
Stability of two-dimensional maps / 8.4:
Bifurcations of two-dimensional maps / 8.5:
Basin changes at local bifurcations of limit cycles / 8.6:
Chaotic behaviour of one- and two-dimensional maps / 9:
General outline / 9.1:
Theory for one-dimensional maps / 9.2:
Bifurcations to chaos / 9.3:
Bifurcation diagram of one-dimensional maps / 9.4:
Henon map / 9.5:
Flows, Outstructures, and Chaos / Part III:
The geometry of recurrence / 10:
Finite-dimensional dynamical systems / 10.1:
Types of recurrent behaviour / 10.2:
Hyperbolic stability types for equilibria / 10.3:
Hyperbolic stability types for limit cycles / 10.4:
Implications of hyperbolic structure / 10.5:
The Lorenz system / 11:
A model of thermal convection / 11.1:
First convective instability / 11.2:
The chaotic attractor of Lorenz / 11.3:
Geometry of a transition to chaos / 11.4:
Rossler's band / 12:
The simply folded band in an autonomous system / 12.1:
Return map and bifurcations / 12.2:
Smale's horseshoe map / 12.3:
Transverse homoclinic trajectories / 12.4:
Spatial chaos and localized buckling / 12.5:
Geometry of bifurcations / 13:
Local bifurcations / 13.1:
Global bifurcations in the phase plane / 13.2:
Bifurcations of chaotic attractors / 13.3:
Applications in the Physical Sciences / Part IV:
Subharmonic resonances of an offshore structure / 14:
Basic equation and non-dimensional form / 14.1:
Analytical solution for each domain / 14.2:
Digital computer program / 14.3:
Resonance response curves / 14.4:
Effect of damping / 14.5:
Computed phase projections / 14.6:
Multiple solutions and domains of attraction / 14.7:
Chaotic motions of an impacting system / 15:
Resonance response curve / 15.1:
Application to moored vessels / 15.2:
Period-doubling and chaotic solutions / 15.3:
Escape from a potential well / 16:
Analytical formulation / 16.1:
Overview of the steady-state response / 16.3:
The two-band chaotic attractor / 16.4:
Resonance of the steady states / 16.5:
Transients and basins of attraction / 16.6:
Homoclinic phenomena / 16.7:
Heteroclinic phenomena / 16.8:
Indeterminate bifurcations / 16.9:
Appendix
Illustrated Glossary
Bibliography
Online Resources
Index
Preface
Preface to the First Edition
Acknowledgements from the First Edition
18.

図書

図書
Martin Golubitsky, Ian Stewart
出版情報: Basel ; Boston : Birkhäuser, c2002  xvii, 325 p. ; 24 cm
シリーズ名: Progress in mathematics ; v. 200
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19.

図書

図書
Washek F. Pfeffer
出版情報: Cambridge : Cambridge University Press, 2001  xvi, 266 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 140
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Preface
Acknowledgements
Preliminaries / 1.:
The setting / 1.1.:
Topology / 1.2.:
Measures / 1.3.:
Covering theorems / 1.4.:
Densities / 1.5.:
Lipschitz maps / 1.6.:
BV functions / 1.7.:
BV sets / 1.8.:
Slices of BV sets / 1.9.:
Approximating BV sets / 1.10.:
Charges / 2.:
The definition and examples / 2.1.:
Spaces of charges / 2.2.:
Derivates / 2.3.:
Derivability / 2.4.:
Reduced charges / 2.5.:
Partitions / 2.6:
Variations of charges / 3.:
Some classical concepts / 3.1.:
The essential variation / 3.2.:
The integration problem / 3.3.:
An excursion to Hausdorff measures / 3.4.:
The critical variation / 3.5.:
AC[subscript *] charges / 3.6.:
Essentially clopen sets / 3.7.:
Charges and BV functions / 4.:
The charge F x L[superscript 1] / 4.1.:
The space (CH[subscript *](E),S) / 4.2.:
Duality / 4.3.:
More on BV functions / 4.4.:
The charge F [angle] g / 4.5.:
Lipeomorphisms / 4.6.:
Integration / 5.:
The R-integral / 5.1.:
Multipliers / 5.2.:
Change of variables / 5.3.:
Averaging / 5.4.:
The Riemann approach / 5.5.:
Charges as distributional derivatives / 5.6.:
The Lebesgue integral / 5.7.:
Extending the integral / 6.:
Buczolich's example / 6.1.:
I-convergence / 6.2.:
The GR-integral / 6.3.:
Additional properties / 6.4.:
Bibliography
List of symbols
Index
Preface
Acknowledgements
Preliminaries / 1.:
20.

図書

図書
V.A. Vassiliev ; translated by A. Sossinski
出版情報: Providence, R.I. : American Mathematical Society, c2001  xiii, 149 p. ; 22 cm
シリーズ名: Student mathematical library ; v. 14
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Topological spaces and operations with them
Homotopy groups and homotopy equivalence
Coverings Cell spaces ($CW$-complexes)
Relative homotopy groups and the exact sequence of a pair
Fiber bundles
Smooth manifolds
The degree of a map
Homology: Basic definitions and examples
Main properties of singular homology groups and their computation
Homology of cell spaces
Morse theory
Cohomology and Poincare duality
Some applications of homology theory
Multiplication in cohomology (and homology)
Index of notations Subject
Index
Topological spaces and operations with them
Homotopy groups and homotopy equivalence
Coverings Cell spaces ($CW$-complexes)
21.

図書

図書
Seán Dineen
出版情報: London ; Tokyo : Springer, c2001  xii, 254 p. ; 24 cm
シリーズ名: Springer undergraduate mathematics series
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Introduction to Differentiable Functions / 1:
Level Sets and Tangent Spaces / 2:
Lagrange Multipliers / 3:
Maxima and Minima on Open Sets / 4:
Curves in Rn / 5:
Line Integrals / 6:
The Frenet-Serret Equations / 7:
Geometry of Curves in R3 / 8:
Double Integration / 9:
Parametrised Surfaces in R3 / 10:
Surface Area / 11:
Surface Integrals / 12:
Stokes'Theorem / 13:
Triple Integrals / 14:
The Divergence Theorem / 15:
Geometry of Surfaces in R3 / 16:
Gaussian Curvature / 17:
Geodesic Curvature / 18:
Solutions
Index
Introduction to Differentiable Functions / 1:
Level Sets and Tangent Spaces / 2:
Lagrange Multipliers / 3:
22.

図書

図書
Jun Kigami
出版情報: Cambridge : Cambridge University Press, 2001  viii, 226 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 143
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23.

図書

図書
W.J. Kaczor, M.T. Nowak
出版情報: Providence, R.I. : American Mathematical Society, c2001  xiv, 398 p. ; 22 cm
シリーズ名: Student mathematical library ; v. 12 . Problems in mathematical analysis ; 2
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Problems: Limits and continuity
Differentiation Sequences and series of functions
Solutions: Limits and continuity
Bibliography
Index
Problems: Real numbers
Sequence of real numbers
Series of real numbers
Solutions: Real numbers
Sequences of real numbers
Problems: Limits and continuity
Differentiation Sequences and series of functions
Solutions: Limits and continuity
24.

図書

図書
M.C. Irwin
出版情報: Singapore : World Scientific, c2001  xii, 259 p. ; 23 cm
シリーズ名: Advanced series in nonlinear dynamics ; v. 17
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Foreword
Preface
Introduction
The simple pendulum / I.:
A dissipative system / II.:
The spherical pendulum / III.:
Vector fields and dynamical systems / IV.:
Some Simple Examples / Chapter 1.:
Flows and homeomorphisms
Orbits
Examples of dynamical systems
Constructing systems
Properties of orbits / V.:
Appendix 1
Group actions
Equivalent Systems / Chapter 2.:
Topological conjugacy
Homeomorphisms of the circle
Flow equivalence and topological equivalence
Local equivalence
Limit sets of flows
Limit sets of homeomorphisms / VI.:
Non-wandering sets / VII.:
Appendix 2
Two topological lemmas
Oriented orbits in Hausdorff spaces
Compactification
Integration of Vector Fields / Chapter 3.:
Vector fields
Velocity vector fields and integral flows
Ordinary differential equations
Local integrals
Global integrals
Appendix 3
Integrals of perturbed vector fields
First integrals
Linear Systems / Chapter 4.:
Linear flows on R[superscript n]
Linear automorphisms of R[superscript n]
The spectrum of a linear endomorphism
Hyperbolic linear automorphisms
Hyperbolic linear vector fields
Appendix 4
Spectral Theory
Linearization / Chapter 5.:
Regular points
Hartman's theorem
Hartman's theorem for flows
Hyperbolic closed orbits
Appendix 5
Smooth linearization
Liapunov stability
The index of a fixed point
Stable Manifolds / Chapter 6.:
The stable manifold at a hyperbolic fixed point of a diffeomorphism
Stable manifold theory for flows
The generalized stable manifold theorem
Appendix 6
Perturbed stable manifolds
Stable Systems / Chapter 7.:
Low dimensional systems
Anosov systems
Characterization of structural stability
Density
Omega stability
Bifurcation
Theory of Manifolds / Appendix A.:
Topological manifolds
Smooth manifolds and maps
Smooth vector bundles
The tangent bundle
Immersions, embeddings and submersions
Sections of vector bundles
Tensor bundles
Riemannian manifolds / VIII.:
Map Spaces / Appendix B.:
Spaces of smooth maps
Composition theorems
Spaces of sections
Spaces of dynamical systems
The Contraction Mapping Theorem / Appendix C.:
Bibliography
Subject Index
Foreword
Preface
Introduction
25.

図書

図書
Jean-Pierre Tignol
出版情報: Singapore : World Scientific, c2001  xiii, 333 p. ; 22 cm
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26.

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図書
C.G. Gibson
出版情報: Cambridge, [Eng.] : Cambridge University Press, 2001  xvii, 216 p. ; 24 cm
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The Euclidean plane / 1:
Parametrized curves / 2:
Classes of special curves / 3:
Arc length / 4:
Curvature / 5:
Existence and uniqueness / 6:
Contact with lines / 7:
Contact with circles / 8:
Vertices / 9:
Envelopes / 10:
Orthotomics / 11:
Caustics by reflexion / 12:
Planar kinematics / 13:
Centrodes / 14:
Geometry of trajectories / 15:
The Euclidean plane / 1:
Parametrized curves / 2:
Classes of special curves / 3:
27.

図書

図書
Isaac Chavel
出版情報: Cambridge : Cambridge University Press, 2001  xii, 268 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 145
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28.

図書

図書
Judith N. Cederberg
出版情報: New York : Springer, c2001  xix, 442 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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29.

図書

図書
Michael Douglas, Jerome Gauntlett, Mark Gross, editors
出版情報: Providence, RI : American Mathematical Society , Cambridge, MA : Clay Mathematics Institute, c2004  ix, 376 p. ; 26 cm
シリーズ名: Clay mathematics proceedings ; v. 3
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30.

図書

図書
Stuart S. Antman
出版情報: New York : Springer, c2005  xviii, 831 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 107
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31.

図書

図書
Suresh Sethi, Hanqin Zhang, Qing Zhang
出版情報: New York : Springer, c2005  xv, 324 p. ; 25 cm
シリーズ名: Stochastic modelling and applied probability ; 54
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Preface
Notation
Introduction and Models of Manufacturing Systems / Part I:
Concept of Near-Optimal Control / 1:
Introduction / 1.1:
A Brief Review of the Related Literature / 1.2:
Plan of the Book / 1.3:
Models of Manufacturing Systems / 2:
A Parallel-Machine, Single Product Model / 2.1:
A Parallel-Machine, Multiproduct Model / 2.3:
A Single Product Dynamic Flowshop / 2.4:
A Dynamic Jobshop / 2.5:
Optimal Control of Manufacturing Systems: Existence and Characterization / Part II:
Optimal Control of Parallel-Machine Systems / 3:
Problem Formulation / 3.1:
Estimates for Discounted Cost Value Functions / 3.3:
Verification Theorem / 3.4:
Existence and Characterization of Optimal Policy / 3.5:
Turnpike Set Analysis / 3.6:
Multiproduct Systems / 3.7:
Notes / 3.8:
Optimal Control of Dynamic Flowshops / 4:
Verification Theorem and HJBDD Equations / 4.1:
Two-Machine Flowshop with Finite Internal Buffer / 4.5:
Optimal Controls of Dynamic Jobshops / 4.6:
A Graph-Theoretic Framework and Problem Formulation / 5.1:
Risk-Sensitive Control / 5.3:
HJB Equations / 6.1:
Near-Optimal Controls / 6.4:
Near-Optimal Control of Parallel-Machine Systems / 7:
The Limiting Control Problem / 7.1:
Convergence of the Minimum Average Expected Cost / 7.4:
Asymptotic Optimal Controls / 7.5:
Parallel-Machine Systems without Attrition / 7.6:
Near-Optimal Control of Dynamic Flowshops / 7.7:
Construction of a Near-Optimal Control / 8.1:
Near-Optimal Controls of Dynamic Jobshops / 8.6:
The Optimization Problem / 9.1:
Near-Optimal Risk-Sensitive Control / 9.3:
The Limiting Problem / 10.1:
Conclusions / 10.4:
Further Extensions and Open Research Problems / 11:
Multilevel Systems / 11.1:
Asymptotic Optimal Feedback Controls / 11.3:
Robust Controls / 11.4:
General Systems / 11.5:
Final Thoughts / 11.6:
Appendices / Part V:
Finite State Markov Chains / A:
Convergence and Error Estimates of Markov Chains / B:
Convex Sets and Functions / C:
Viscosity Solutions of HJB Equations / D:
Discounted Cost Problems / E:
Miscellany / F:
References
Author Index
Subject Index
Copyright Permissions
Preface
Notation
Introduction and Models of Manufacturing Systems / Part I:
32.

図書

図書
by Jose Labastida and Marcos Marino
出版情報: Dordrecht : Springer, c2005  x, 222 p. ; 25 cm
シリーズ名: Mathematical physics studies ; v. 25
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From the contents:Topological Aspects of Four-Manifolds
The Theory of Donaldson Invariants
The Theory of Seiberg-Witten Invariants
Supersymmetry in Four Dimensions
Topological Quantum Field Theories in Four Dimensions
The Mathai-Quillen Formalism
The Seiberg-Witten Solution of N = 2 SUSY Yang-Mills Theory
The u-plane Integral
Some Applications of the u-plane Integral
Further Developments in Donaldson-Witten Theory
Spinors in Four Dimensions / Appendix A:
Elliptic Functions and Modular Forms / Appendix B:
Bibliography
From the contents:Topological Aspects of Four-Manifolds
The Theory of Donaldson Invariants
The Theory of Seiberg-Witten Invariants
33.

図書

図書
Roger Knobel
出版情報: Providence, R.I. : American Mathematical Society , Princeton, N.J. : Institute for Advanced Study, c2000  xiv, 196 p. ; 22 cm
シリーズ名: Student mathematical library ; v. 3 . IAS/Park City mathematical subseries
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Introduction
Introduction to waves
A mathematical representation of waves
Partial differential equation
Traveling and standing waves: Traveling waves
The Korteweg-de Vries equation
The Sine-Gordon equation
The wave equation D'Alembert's solution of the wave equation
Vibrations of a semi-infinite string
Characteristic lines of the wave equation
Standing wave solutions of the wave equation
Standing waves of a nonhomogeneous string
Superposition of standing waves
Fourier series and the wave equation
Waves in conservation laws: Conservation laws
Examples of conservation laws
The method of characteristics
Gradient catastrophes and breaking times
Shock waves Shock wave example: Traffic at a red light
Shock waves and the viscosity method
Rarefaction waves An example with rarefaction and shock waves
Nonunique solutions and the entropy condition
Weak solutions of conservation laws
Bibliography
Index
Introduction
Introduction to waves
A mathematical representation of waves
34.

図書

図書
Martin R. Bridson, André Haefliger
出版情報: Berlin ; Tokyo : Springer, c1999  xxi, 643 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 319
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35.

図書

図書
V.I. Bernik, M.M. Dodson
出版情報: Cambridge [Cambridgeshire] : Cambridge University Press, 1999  xi, 172 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; v. 137
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Preface
Notation
Diophantine approximation and manifolds / Chapter 1.:
Introduction / 1.1.:
Diophantine approximation in one dimension / 1.2.:
Approximation in higher dimensions / 1.3.:
Euclidean submanifolds / 1.4.:
Metric Diophantine approximation on manifolds / 1.5.:
Notes / 1.6.:
Khintchine's and Groshev's theorems for manifolds / Chapter 2.:
Extremal manifolds / 2.1.:
Khintchine and Groshev type manifolds / 2.3.:
Baker's conjecture / 2.4.:
Higher dimensional manifolds / 2.5.:
Hausdorff measure and dimension / 2.6.:
Hausdorff measure / 3.1.:
Hausdorff dimension / 3.3.:
Properties of Hausdorff dimension / 3.4.:
Determining the Hausdorff dimension / 3.5.:
Hausdorff dimension on manifolds / 3.6.:
Upper bounds for Hausdorff dimension / 3.7.:
Diophantine approximation on manifolds / 4.1.:
Smooth manifolds of dimension at least 2 / 4.3.:
Simultaneous Diophantine approximation / 4.4.:
Lower bounds for Hausdorff dimension / 4.5.:
Regular systems / 5.1.:
Ubiquitous systems / 5.3.:
Simultaneous Diophantine approximation on manifolds / 5.4.:
Diophantine approximation over the p-adic field / 5.5.:
Introduction to p-adic numbers / 6.1.:
Diophantine approximation in Q[subscript p] / 6.2.:
Integral polynomials with small p-adic values / 6.3.:
Applications / 6.4.:
Diophantine type and very well approximable numbers / 7.1.:
A wave equation / 7.3.:
The rotation number / 7.4.:
Dynamical systems / 7.5.:
Linearising diffeomorphisms / 7.6.:
Diophantine approximation in hyperbolic space / 7.7.:
References / 7.8.:
Index
Preface
Notation
Diophantine approximation and manifolds / Chapter 1.:
36.

図書

図書
James J. Callahan
出版情報: New York : Springer, c2000  xvi, 451 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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Relativity before 1905
Special relativityùkinematics
Special relativityùkinetics
Arbitrary frames
Surfaces and curvatures
Intrinsic geometry
General relativity
Consequences
Relativity before 1905
Special relativityùkinematics
Special relativityùkinetics
37.

図書

図書
Anton Bovier, Pierre Picco, editors
出版情報: Boston : Birkhauser, c1998  viii, 382 p. ; 25 cm
シリーズ名: Progress in probability / series editors, Thomas Liggett, Charles Newman, Loren Pitt ; 41
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38.

図書

図書
William Fulton
出版情報: Berlin ; Tokyo : Springer, c1998  xiii, 470 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 2
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39.

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図書
Rami Shakarchi
出版情報: New York : Springer-Verlag, c1998  xii, 368 p. ; 24 cm
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40.

図書

図書
Wolfgang Tomé
出版情報: Singapore : World Scientific, c1998  xviii, 213 p. ; 23 cm
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41.

図書

図書
Paul C. Roberts
出版情報: Cambridge, UK : Cambridge University Press, 1998  xi, 303 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 133
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Prime ideals and the Chow group / 1:
Graded rings and Samuel multiplicity / 2:
Complexes and derived functors / 3:
Homological properties of rings and modules / 4:
Intersection multiplicities / 5:
The homological conjectures / 6:
The Frobenius map / 7:
Projective schemes / 8:
Chern classes of locally free sheaves / 9:
The Grassmannian / 10:
Local Chern characters / 11:
Properties of local Chern characters / 12:
Applications and examples. / 13:
Prime ideals and the Chow group / 1:
Graded rings and Samuel multiplicity / 2:
Complexes and derived functors / 3:
42.

図書

図書
Andrei Marshakov
出版情報: Farrer Road, Singapore : World Scientific, c1999  253 p. ; 23 cm
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43.

図書

図書
by Igor E. Shparlinski
出版情報: Dordrecht : Kluwer Academic Publishers, c1999  xiv, 528 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 477
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Preface
Acknowledgments
Notation
Introduction
Links flowchart
Polynomial Factorization / 1:
Finding Irreducible and Primitive Polynomials / 2:
The Distribution of Irreducible, Primitive and Other Special Polynomials and Matrices / 3:
Bases and Computation in Finite Fields / 4:
Coding Theory and Algebraic Curves / 5:
Elliptic Curves / 6:
Recurrence Sequences in Finite Fields and Cyclic Linear Codes / 7:
Finite Fields and Discrete Mathematics / 8:
Congruences / 9:
Some Related Problems / 10:
References / Appendix 1:
Index.
Preface
Acknowledgments
Notation
44.

図書

図書
Elton P. Hsu, S.R.S. Varadhan, editors
出版情報: Providence, R.I. : American Mathematical Society , [Princeton] : Institute for Advanced Study, c1999  x, 374 p. ; 26 cm
シリーズ名: IAS/Park City mathematics series / [Dan Freed, series editor] ; v. 6
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45.

図書

図書
Junjiro Noguchi ; translated by Junjiro Noguchi
出版情報: Providence, R.I. : American Mathematical Society, c1998  xi, 250 p. ; 26 cm
シリーズ名: Translations of mathematical monographs ; v. 168
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46.

図書

図書
R. Tyrrell Rockafellar, Roger J.-B. Wets
出版情報: Berlin ; New York : Springer, c1998  xiii, 733 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 317
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47.

図書

図書
Joseph Polchinski
出版情報: Cambridge ; New York : Cambridge University Press, 1998  xix, 402 p. ; 26 cm
シリーズ名: Cambridge monographs on mathematical physics ; . String theory / Joseph Polchinski ; v. 1
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Foreword
Preface
Notation
A first look at strings / 1:
Why strings? / 1.1:
Action principles / 1.2:
The open string spectrum / 1.3:
Closed and unoriented strings / 1.4:
Exercises
Conformal field theory / 2:
Massless scalars in two dimensions / 2.1:
The operator product expansion / 2.2:
Ward identities and Noether's theorem / 2.3:
Conformal invariance / 2.4:
Free CFTs / 2.5:
The Virasoro algebra / 2.6:
Mode expansions / 2.7:
Vertex operators / 2.8:
More on states and operators / 2.9:
The Polyakov path integral / 3:
Sums over world-sheets / 3.1:
Gauge fixing / 3.2:
The Weyl anomaly / 3.4:
Scattering amplitudes / 3.5:
Strings in curved spacetime / 3.6:
The string spectrum / 4:
Old covariant quantization / 4.1:
BRST quantization / 4.2:
BRST quantization of the string / 4.3:
The no-ghost theorem / 4.4:
The string S-matrix / 5:
The circle and the torus / 5.1:
Moduli and Riemann surfaces / 5.2:
The measure for moduli / 5.3:
More about the measure / 5.4:
Exercise
Tree-level amplitudes / 6:
Riemann surfaces / 6.1:
Scalar expectation values / 6.2:
The bc CFT / 6.3:
The Veneziano amplitude / 6.4:
Chan-Paton factors and gauge interactions / 6.5:
Closed string tree amplitudes / 6.6:
General results / 6.7:
One-loop amplitudes / 7:
CFT on the torus / 7.1:
The torus amplitude / 7.3:
Open and unoriented one-loop graphs / 7.4:
Toroidal compactification and T-duality / 8:
Toroidal compactification in field theory / 8.1:
Toroidal compactification in CFT / 8.2:
Closed strings and T-duality / 8.3:
Compactification of several dimensions / 8.4:
Orbifolds / 8.5:
Open strings / 8.6:
D-branes / 8.7:
T-duality of unoriented theories / 8.8:
Higher order amplitudes / 9:
General tree-level amplitudes / 9.1:
Higer genus Riemann surfaces / 9.2:
Sewing and cutting world-sheets / 9.3:
Sewing and cutting CFTs / 9.4:
General amplitudes / 9.5:
String field theory / 9.6:
Large order behavior / 9.7:
High energy and high temperature / 9.8:
Low dimensions and noncritical strings / 9.9:
A short course on path integrals / Appendix A:
Bosonic fields / A.1:
Fermionic fields / A.2:
References
Glossary
Index
Foreword
Preface
Notation
48.

図書

図書
Joseph Polchinski
出版情報: Cambridge ; New York : Cambridge University Press, 1998  xix, 531 p. ; 26 cm
シリーズ名: Cambridge monographs on mathematical physics ; . String theory / Joseph Polchinski ; v. 2
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Foreword
Preface
Notation
Type I and type II superstrings / 10:
The superconformal algebra / 10.1:
Ramond and Neveu-Schwarz sectors / 10.2:
Vertex operators and bosonization / 10.3:
The superconformal ghosts / 10.4:
Physical states / 10.5:
Superstring theories in ten dimensions / 10.6:
Modular invariance / 10.7:
Divergences of type I theory / 10.8:
Exercises
The heterotic string / 11:
World-sheet supersymmetries / 11.1:
The SO(32) and E[subscript 8] x E[subscript 8] heterotic strings / 11.2:
Other ten-dimensional heterotic strings / 11.3:
A little Lie algebra / 11.4:
Current algebras / 11.5:
The bosonic construction and toroidal compactification / 11.6:
Superstring interactions / 12:
Low energy supergravity / 12.1:
Anomalies / 12.2:
Superspace and superfields / 12.3:
Tree-level amplitudes / 12.4:
General amplitudes / 12.5:
One-loop amplitudes / 12.6:
D-branes / 13:
T-duality of type II strings / 13.1:
T-duality of type I strings / 13.2:
The D-brane charge and action / 13.3:
D-brane interactions: statics / 13.4:
D-brane interactions: dynamics / 13.5:
D-brane interactions: bound states / 13.6:
Strings at strong coupling / 14:
Type IIB string and SL(2,Z) duality / 14.1:
U-duality / 14.2:
SO(32) type I-heterotic duality / 14.3:
Type IIA string and M-theory / 14.4:
The E[subscript 8] x E[subscript 8] heterotic string / 14.5:
What is string theory? / 14.6:
Is M for matrix? / 14.7:
Black hole quantum mechanics / 14.8:
Advanced CFT / 15:
Representations of the Virasoro algebra / 15.1:
The conformal bootstrap / 15.2:
Minimal models / 15.3:
Coset models / 15.4:
Representations of the N = 1 superconformal algebra / 15.6:
Rational CFT / 15.7:
Renormalization group flows / 15.8:
Statistical mechanics / 15.9:
Orbifolds / 16:
Orbifolds of the heterotic string / 16.1:
Spacetime supersymmetry / 16.2:
Examples / 16.3:
Low energy field theory / 16.4:
Calabi-Yau compactification / 17:
Conditions for N = 1 supersymmetry / 17.1:
Calabi-Yau manifolds / 17.2:
Massless spectrum / 17.3:
Higher corrections / 17.4:
Generalizations / 17.6:
Physics in four dimensions / 18:
Continuous and discrete symmetries / 18.1:
Gauge symmetries / 18.2:
Mass scales / 18.3:
More on unification / 18.4:
Conditions for spacetime supersymmetry / 18.5:
Low energy actions / 18.6:
Supersymmetry breaking in perturbation theory / 18.7:
Supersymmetry beyond perturbation theory / 18.8:
Advanced topics / 19:
The N = 2 superconformal algebra / 19.1:
Type II strings on Calabi-Yau manifolds / 19.2:
Heterotic string theories with (2,2) SCFT / 19.3:
N = 2 minimal models / 19.4:
Gepner models / 19.5:
Mirror symmetry and applications / 19.6:
The conifold / 19.7:
String theories on K3 / 19.8:
String duality below ten dimensions / 19.9:
Conclusion / 19.10:
Spinors and SUSY in various dimensions / Appendix B:
Spinors in various dimensions / B.1:
Introduction to supersymmetry: d = 4 / B.2:
Supersymmetry in d = 2 / B.3:
Differential forms and generalized gauge fields / B.4:
Thirty-two supersymmetries / B.5:
Sixteen supersymmetries / B.6:
Eight supersymmetries / B.7:
References
Glossary
Index
Foreword
Preface
Notation
49.

図書

図書
editors, M.-H. Saito, Y. Shimizu & K. Ueno
出版情報: Singapore : World Scientific, c1998  xii, 480 p. ; 23 cm
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50.

図書

図書
Robert Goldblatt
出版情報: New York : Springer, c1998  xiv, 289 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 188
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