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1.

図書

図書
ビラン・ドゥ・アーン [著]
出版情報: 東京 : 技報堂, 1953.9  xiv, 727p ; 22cm
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2.

図書

図書
Joachim Kock, Israel Vainsencher
出版情報: Boston : Birkhäuser, c2007  xii, 159 p. ; 25 cm
シリーズ名: Progress in mathematics ; v. 249
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Preface
Introduction
Prologue: Warming up with Cross Ratios, and the Definition of Moduli Space / 0:
Cross ratios / 0.1:
Definition of moduli space / 0.2:
Stable n-pointed Curves / 1:
n-pointed smooth rational curves / 1.1:
Stable n-pointed rational curves / 1.2:
Stabilization, forgetting marks, contraction / 1.3:
Sketch of the construction of [Characters not reproducible subscript 0,n] / 1.4:
The boundary / 1.5:
Generalizations and references / 1.6:
Stable Maps / 2:
Maps P[superscript 1 Characters not reproducible] P[superscript r] / 2.1:
1-parameter families / 2.2:
Kontsevich stable maps / 2.3:
Idea of the construction of [Characters not reproducible subscript 0,n] (P[superscript r], d) / 2.4:
Evaluation maps / 2.5:
Forgetful maps / 2.6:
Easy properties and examples / 2.7:
Complete conics / 2.9:
Enumerative Geometry via Stable Maps / 2.10:
Classical enumerative geometry / 3.1:
Counting conics and rational cubics via stable maps / 3.2:
Kontsevich's formula / 3.3:
Transversality and enumerative significance / 3.4:
Stable maps versus rational curves / 3.5:
Gromov-Witten Invariants / 3.6:
Definition and enumerative interpretation / 4.1:
Properties of Gromov-Witten invariants / 4.2:
Recursion / 4.3:
The reconstruction theorem / 4.4:
Quantum Cohomology / 4.5:
Quick primer on generating functions / 5.1:
The Gromov-Witten potential and the quantum product / 5.2:
Associativity / 5.3:
Kontsevich's formula via quantum cohomology / 5.4:
Bibliography / 5.5:
Index
Preface
Introduction
Prologue: Warming up with Cross Ratios, and the Definition of Moduli Space / 0:
3.

図書

図書
Yu.V. Shestopalov, Yu.G. Smirnov and E.V. Chernokozhin
出版情報: Utrecht : VSP, 2000  vii, 117 p. ; 26 cm
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4.

図書

図書
Yu.L. Pavlov
出版情報: Utrecht : VSP, 2000  122 p. ; 26 cm
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5.

図書

図書
Grigor A. Barsegian
出版情報: London : Taylor & Francis, c2002  ix, 176 p. ; 25 cm
シリーズ名: Asian mathematics series / edited by Chung-Chun Yang ; vol. 5
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Preface
Tangent Variation Principle
Satellite Principles
Modification of Length-area Principle
Estimates for collections of Gamma-Lines
Estimates of lengths of Gamma-Lines for angular-quasiconformal mappings
Remarks on applying of estimates of L (D, Gamma)
Nevanlinna and Ahilfors Theories
Additions
Basic concepts and outcomes of Nevanlinna Value Distribution theory and Ahlfors theory of covering surfaces
Geometric deficient values
On some
Preface
Tangent Variation Principle
Satellite Principles
6.

図書

図書
Abdul-Majid Wazwaz
出版情報: Lisse ; Tokyo : A.A. Balkema, c2002  xi, 459 p. ; 25 cm
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7.

図書

図書
M.S. Howe
出版情報: Cambridge, U.K. : Cambridge University Press, 2003  xiv, 216 p. ; 23 cm
シリーズ名: Cambridge texts in applied mathematics
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Preface
Introduction / 1:
Lighthill's theory / 2:
The compact Green's function / 3:
Vorticity / 4:
Vortex sound / 5:
Vortex-surface interaction noise in two-dimensions / 6:
Problems in three-dimensions / 7:
Further worked examples / 8:
Bibliography
Preface
Introduction / 1:
Lighthill's theory / 2:
8.

図書

図書
by Lord Kelvin and Peter Guthrie Tait
出版情報: Cambridge : At the University Press, 1879-1883  v. ; 23 cm
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9.

図書

図書
Giuliana Davidoff, Peter Sarnak, Alain Valette
出版情報: Cambridge : Cambridge University Press, 2003  viii, 144 p. ; 24 cm
シリーズ名: London Mathematical Society student texts ; 55
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An overview
Graph theory / 1:
Number theory / 2:
PSL2(q) / 3:
The graphs Xp, q / 4:
4-regular graphs with large girth / Appendix A:
Index
Bibliography
An overview
Graph theory / 1:
Number theory / 2:
10.

図書

図書
Robert Botet, Marek Płoszajczak
出版情報: Singapore ; River Edge, N.J. : World Scientific, c2002  xix, 369 p. ; 24 cm
シリーズ名: World Scientific lecture notes in physics ; v. 65
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11.

図書

図書
Andrew Majda
出版情報: New York : Courant Institute of Mathematical Sciences, New York University , Providence, R.I : American Mathematical Society, 2003  ix, 234 p. ; 26 cm
シリーズ名: Courant lecture notes in mathematics ; 9
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Preface
Introduction / Chapter 1.:
Basic Properties of the Equations with Rotation and Stratification / 1.1.:
Two-Dimensional Exact Solutions / 1.2.:
Buoyancy and Stratification / 1.3.:
Jet Flows with Rotation and Stratification / 1.4.:
From Vertical Stratification to Shallow Water / 1.5.:
Some Remarkable Features of Stratified Flow / Chapter 2.:
Energy Principle / 2.1.:
Vorticity in Stratified Fluids and Exact Solutions Motivated by Local Analysis / 2.2.:
Use of Theorem 2.4: Exact Two-Dimensional Solutions / 2.3.:
Nonlinear Plane Waves in Stratified Flow: Internal Gravity Waves / 2.4.:
Exact Solutions with Large-Scale Motion and Nonlinear Plane Waves / 2.5.:
More Details for Theorem 2.7 on Special Exact Solutions for the Boussinesq Equations Including Plane Waves / 2.6.:
Linear and Nonlinear Instability of Stratified Flows with Strong Stratification / Chapter 3.:
Boussinesq Equations and Vorticity Stream Formulation / 3.1.:
Nonlinear Instability of Stratified Flows / 3.2.:
Shear Flows / 3.3.:
Some Background Facts on ODEs / 3.4.:
Rotating Shallow Water Theory / Chapter 4.:
Rotating Shallow Water Equations / 4.1.:
Conservation of Potential Vorticity / 4.2.:
Nonlinear Conservation of Energy / 4.3.:
Linear Theory for the Rotating Shallow Water Equations / 4.4.:
Nondimensional Form of the Rotating Shallow Water Equations / 4.5.:
Derivation of the Quasi-Geostrophic Equations / 4.6.:
The Quasi-Geostrophic Equations as a Singular PDE Limit / 4.7.:
The Model Rotating Shallow Water Equations / 4.8.:
Preliminary Mathematical Considerations / 4.9.:
Regorous Convergence of the Model Rotating Shallow Water Equations to the Quasi-Geostrophic Equations / 4.10.:
Proof of the Convergence Theorem / 4.11.:
Linear and Weakly Nonlinear Theory of Dispersive Waves with Geophysical Examples / Chapter 5.:
Linear Wave Midlatitude Planetary Equations / 5.1.:
Dispersive Waves: General Properties / 5.2.:
Interpretation of Group Velocity / 5.3.:
Distant Propagation from a Localized Source / 5.4.:
WKB Methods for Linear Dispersive Waves / 5.5.:
Beyond Caustics: Eikonal Equation Revisited / 5.6.:
Weakly Nonlinear WKB for Perturbations Around a Constant State / 5.7.:
Nonlinear WKB and the Boussinesq Equations / 5.8.:
Simplified Equations for the Dynamics of Strongly Stratified Flow / Chapter 6.:
Nondimensionalization of the Boussinesq Equations for Stably Stratified Flow / 6.1.:
The Vorticity Stream Formulation and Elementary Properties of the Limit Equations for Strongly Stratified Flow / 6.2.:
Solutions of the Limit Dynamics with Strong Stratification as Models for Laboratory Experiments / 6.3.:
The Stratified Quasi-Geostrophic Equations as a Singular Limit of the Rotating Boussinesq Equations / Chapter 7.:
The Rotating Boussinesq Equations / 7.1.:
The Nondimensional Rotating Boussinesq Equations / 7.3.:
Formal Asymptotic Derivation of the Quasi-Geostrophic Equations as a Distinguished Asymptotic Limit of Small Rossby and Froude Numbers / 7.4.:
Rigorous Convergence of the Rotating Boussinesq Equations to the Quasi-Geostrophic Equations / 7.5.:
Introduction to Averaging over Fast Waves for Geophysical Flows / 7.6.:
Motivation for Fast-Wave Averaging / 8.1.:
A General Framework for Averaging over Fast Waves / 8.3.:
Elementary Analytic Models for Comparing Instabilities at Low Froude Numbers with the Low Froude Number Limit Dynamics / 8.4.:
The Rapidly Rotating Shallow Water Equations with Unbalanced Initial Data in the Quasi-Geostrophic Limit / 8.5.:
The Interaction of Fast Waves and Slow Dynamics in the Rotating Stratified Boussinesq Equations / 8.6.:
Waves and PDEs for the Equatorial Atmosphere and Ocean / Chapter 9.:
Introduction to Equatorial Waves for Rotating Shallow Water / 9.1.:
The Equatorial Primitive Equations / 9.2.:
The Nonlinear Equatorial Long-Wave Equations / 9.3.:
A Simple Model for the Steady Circulation of the Equatorial Atmosphere / 9.4.:
Bibliography
Preface
Introduction / Chapter 1.:
Basic Properties of the Equations with Rotation and Stratification / 1.1.:
12.

図書

図書
Christopher Parker, Peter Rowley
出版情報: London : Springer, c2002  xi, 361 p. ; 24 cm
シリーズ名: Springer monographs in mathematics
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13.

図書

図書
Ken A. Brown, Ken R. Goodearl
出版情報: Basel : Birkhäuser, c2002  ix, 348 p. ; 24 cm
シリーズ名: Advanced courses in mathematics CRM Barcelona
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14.

図書

図書
Michael Frame and Benoit B. Mandelbrot, editors ; foreword by Lynn Arthur Steen
出版情報: [Washington, D.C.] : Mathematical Association of America, c2002  xiii, 206 p., [4] p. of plates ; 28 cm
シリーズ名: MAA notes ; 58
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Foreword / Lynn Arthur Steen
Preface
Introductory Essays
Some Reasons for the Effectiveness of Fractals in Mathematics Education / Benoit B. Mandelbrot ; Michael Frame1.:
Unsolved Problems and Still-Emerging Concepts in Fractal Geometry / 2.:
Fractals, Graphics, and Mathematics Education / 3.:
Mathematics and Society in the 20th Century / 4.:
Classroom Experiences
Teaching Fractals and Dynamical Systems at The Hotchkiss School / Melkana Brakalova ; David Coughlin5.:
Reflecting on Wada Basins: Some Fractals with a Twist / Dane Camp6.:
Learning and Teaching about Fractals / Donald M. Davis7.:
The Fractal Geometry of the Mandelbrot Set: Periods of the Bulbs / Robert L. Devaney8.:
Fractals--Energizing the Mathematics Classroom / Vicki Fegers ; Mary Beth Johnson9.:
Other Chaos Games / Sandy Fillebrown10.:
Creating and Teaching Undergraduate Courses and Seminars in Fractal Geometry: a Personal Experience / Michel Lapidus11.:
Exploring Fractal Dimensions by Experiment / Ron Lewis12.:
Fractal Themes at Every Level / Kenneth G. Monks13.:
Art and Fractals: Artistic Explorations of Natural Self-Similarity / Brianna Murratti14.:
Order and Chaos, Art and Magic: a First College Course in Quantitative Reasoning Based on Fractals and Chaos / David Peak15.:
A Software Driven Undergraduate Fractals Course / Douglas C. Ravenel16.:
A Final Word
The Fractal Ring from Art to Art through Mathematics, Finance, and the Sciences / 17.:
Appendices
Panorama of Fractals and Their Uses. An Alphabetic Wordbook-Index / 18.:
Reports of Some Field Experiences / 19.:
Guide to Topics
References
About the Editors and Other Contributors
Index
Foreword / Lynn Arthur Steen
Preface
Introductory Essays
15.

図書

図書
A. Galves, J.K. Hale, C. Rocha, editors
出版情報: Providence, R.I. : American Mathematical Society, c2002  xiv, 353 p. ; 26 cm
シリーズ名: Fields Institute communications ; 31
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16.

図書

図書
M. O. Deville, P. F. Fischer, E. H. Mund
出版情報: Cambridge : Cambridge University Press, 2002  xxvii, 499 p. ; 24 cm.
シリーズ名: Cambridge monographs on applied and computational mathematics ; 9
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Preface
Fluid mechanics and computation: an introduction / 1:
Approximation methods for elliptic problems / 2:
Parabolic and hyperbolic problems / 3:
Mutidimensional problems / 4:
Steady Stokes and Navier-Stokes equations / 5:
Unsteady Stokes and Navier-Stokes equations / 6:
Domain decomposition / 7:
Vector and parallel implementations / 8:
Preliminary mathematical concepts / Appendix A:
Orthogonal polynomials and discrete transforms / Appendix B:
Preface
Fluid mechanics and computation: an introduction / 1:
Approximation methods for elliptic problems / 2:
17.

図書

図書
Prem K. Kythe, Pratap Puri
出版情報: Boston : Birkhäuser, c2002  xviii, 508 p. ; 25 cm
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18.

図書

図書
by J. Harkness and F. Marley
出版情報: London : Macmillan, 1898  xv, 336 p. ; 23 cm
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19.

図書

図書
M. Göckeler, T. Schücker
出版情報: Cambridge ; New York : Cambridge University Press, 1989  xii, 230 p. ; 23 cm
シリーズ名: Cambridge monographs on mathematical physics
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Preface
Exterior algebra / 1:
Differential forms on open subsets of Rn / 2:
Metric structures / 3:
Gauge theories / 4:
Einstein-Cartan theory / 5:
The Lie derivative / 6:
Manifolds / 7:
Lie groups / 8:
Fibre bundles / 9:
Monopoles, instantons, and related fibre bundles / 10:
Spin / 11:
An algebraic approach to anomalies / 12:
Anomalies from graphs / 13:
References
Bibliography
Notation
Index
Preface
Exterior algebra / 1:
Differential forms on open subsets of Rn / 2:
20.

図書

図書
by Bertrand A.W. Russell
出版情報: Cambridge : University press, 1897  xvi, 201 p. ; 23 cm
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21.

図書

図書
by Nikolay Sidorov ... [et al.]
出版情報: Dordrecht ; London : Kluwer Academic Publishers, c2002  xx, 548 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 550
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Preface
On Regularization of Linear Equations on the Basis of Perturbation Theory / 1.:
Generalised Jordan chains, sets and root numbers of linear operators
Regularization of linear equations with Fredholm operators / 2.:
Principal theorem on regularization of linear equations by the perturbation method / 3.:
Regularization of linear equations on the basis of perturbation theory in Hilbert spaces / 4.:
Computation of eigenvalues and eigenvectors of linear operators by pseudo-perturbation method / 5.:
Notes / 6.:
Investigation of Bifurcation Points of a Nonlinear Equations
Lyapunov-Schmidt BEq in the problem of a bifurcation point
General existence theorems for the bifurcation points
Construction of asymptotics in a neighborhood of a bifurcation point
Asymptotic bifurcation points
On perturbation of the branch points of nonlinear equations
Notes and generalization
Regularization of Computation of Solutions in a Neighborhood of the Branch Point
Construction of the regularizing equation in the problem at a branch point
Definition and properties of simple solutions
Regularization of calculations of simple solutions of nonlinear equations
Regularization of method for continuation along parameter in a neighborhood of a branch point
Notes and remarks
Iterations, Interlaced Equations and Lyapunov Convex Majorants in Nonlinear Analysis
Iterations and uniformization of branching solutions in nonlinear analysis
BEq and the selection of the initial approximation / 1.1:
On the role of supporting lines and Newton diagrams in the construction of the initial approximation / 1.2:
A one-step iteration method / 1.3:
An N-step iteration method / 1.4:
On regularization in the sense of Tikhonov, modifications and possible generalizations of an N-step method / 1.5:
Remarks / 1.6:
Interlaced and potential BEq
The property of (S, K)-interlacing of an equation and its inheritance by the BEq / 2.1:
(T, M)-interlaced and (T[superscript 2], M)-interlaced BEq / 2.2:
[alpha]-parametric interlaced BEq / 2.3:
Interlaced BEq of potential type / 2.4:
Surface bundle of a domain of free parameters / 2.5:
Parametrization of solutions and the method of successive approximations / 2.6:
On the role of Lyapunov convex majorants in the nonlocal existence theorems of implicit functions
Majorants independent of parameters / 3.1:
Majorants depending on a parameter / 3.2:
Investigation of the existence domain of the solution of equation F(u, [varepsilon]) = 0. / 3.3:
Methods of Representation Theory and Group Analysis in Bifurcation Theory
Nonlinear equations invariant under transformation groups
Lyapounov-Schmidt BEq and some methods of their reduction
Some applications
Hereditary symmetry of branching equations and resolving systems
Invariance properties of BEq
Resolving systems for differential equations with Fredholm operator at the derivative and their symmetry
On the Grobman-Hartman theorem for equations with degenerate operator at the derivative
Construction and investigation of the branching equation by group analysis methods
BEq of solutions invariant relative to subgroups of the original equation group symmetry
Potential BEq
Direct methods of BEq group invariance usage for its general form construction by admitted group symmetry
Applications of Lie--Ovsyannikov theorem about invariant manifolds for the construction of BEq general form by allowing group symmetry / 4.1:
Non-linearly perturbed Helmholtz equations
Domain symmetry and bifurcational solutions asymptotics / 5.1:
Periodic solutions / 5.2:
Capillary--gravity waves in fluid layers
Capillary--gravity waves in a floating fluid spatial layer / 6.1:
Capillary--gravity waves at the interface of two fluids flow / 6.2:
Capillary--gravity waves on a cylindrical surface / 6.3:
Ferrofluid layer in a magnetic field / 6.4:
Fluid phase state crystallization problem in statistical crystal theory / 7.:
The statement of the problem / 7.1:
Subspaces N(B[subscript s]). Their expansions on irreducible subspaces relative to O[subscript h] / 7.2:
The BEq construction / 7.3:
Asymptotics of small solutions families for n[subscript s] = 1, 3 / 7.4:
Solutions invariant relative to normal divisors O[subscript h] / 7.5:
Andronov--Hopf bifurcation under group symmetry conditions / 8.:
BEq derivation in non-stationary bifurcation / 8.1:
Symmetry inheritance theorem / 8.2:
BEq construction by group analysis methods / 8.3:
On the asymptotics of small solutions / 8.4:
Stability of the bifurcating solutions / 9.:
Singular Differential Equations in Banach Spaces
Fundamental operator functions
Generalized functions in Banach spaces
Fundamental operator functions of singular differential operators
Fundamental operator functions of singular integral and integro-differential operators
The initial value problem for a differential equation having a Noetherian operator at the derivative. Periodic solutions and the property of convergence
Auxiliary information on Jordan sets of Noetherian operators
The initial value problem for a linear differential equation
The initial value problem for a nonlinear differential equation
Integral pseudo-solutions
Non-stationary differential equations with singularities
The initial value problem for a non-stationary linear equation and systems of 1st kind integral Volterra equations
The initial value problem for a non-stationary linear differential equation and a system of integral Volterra equations with a singularity
Branching differential equations of the initial value problem with singularity
The initial value problem for a nonlinear differential equation and equations with a singular point / 3.4:
Partial differential equations with the Fredholm operator in the main part
The theory of semigroups and groups of operators with kernels
Relative resolvents. Relatively adjoint elements
Relatively spectrally bounded operators and analytical groups of operators with kernells
Relatively sectorial operators and analytical semigroups of operators with kernels / 5.3:
Steady-State Solutions of the Vlasov--Maxwell System
Introduction
Stationary solutions of a VM system
The reduction of VM system to the resolving elliptic system (2.28), (2.29)
The reduction of the resolving system to the unique resolving equation
Existence of solutions of the boundary value problem (2.40)-(2.42)
Applications of the reduction theorems
Normalized solutions for a one-component distribution function
Non-stationary problem
Bifurcation points and nontrivial solutions of the stationary VM system
Statement of the boundary value problem and the problem at a bifurcation point / 4.2:
Resolution of the bifurcation equation / 4.3:
The existence theorem for bifurcation points and the construction of asymptotic solutions / 4.4:
Appendices
Positive solutions of the nonlinear singular boundary value problem of magnetic insulation / A:
References
Preface
On Regularization of Linear Equations on the Basis of Perturbation Theory / 1.:
Generalised Jordan chains, sets and root numbers of linear operators
22.

図書

図書
edited by Ugo Bruzzo, Vittorio Gorini and Ugo Moschella
出版情報: Bristol ; Philadelphia : Institute of Physics Pub., c2003  x, 282 p. ; 25 cm
シリーズ名: Studies in high energy physics, cosmology and gravitation
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Preface
An elementary introduction to branes in string theory / Alberto LerdaPart 1:
Introduction / 1:
Branes in string theory / 2:
The superstring effective actions of type II / 2.1:
Type IIA / 2.1.1:
Type IIB / 2.1.2:
General construction / 2.2:
Explicit solutions / 2.3:
Fundamental string / 2.3.1:
NS 5-brane / 2.3.2:
D p-branes / 2.3.3:
The geometry of the D3-brane of type IIB / 2.3.4:
The boundary state description of D-branes / 3:
The boundary state with an external field / 3.1:
The effective action of D-branes / 4:
Classical D-branes from the boundary state / 5:
References
Physical aspects / Yassen Stanev ; Cesar Gomez ; Pedro RescoPart 2:
Two-dimensional conformal field theory on open and unoriented surfaces / 6:
General properties of two-dimensional CFT / 6.1:
The stress-energy tensor in two dimensions / 6.2.1:
Rational conformal field theories / 6.2.2:
Non-Abelian conformal current algebras / 6.2.3:
Partition function, modular invariance / 6.2.4:
Correlation functions in current algebra models / 6.3:
Properties of the chiral conformal blocks / 6.3.1:
Regular basis of 4-point functions in the SU (2) model / 6.3.2:
Matrix representation of the exchange algebra / 6.3.3:
Two-dimensional braid invariant Green functions / 6.3.4:
CFT on surfaces with holes and crosscaps / 6.4:
Open sector, sewing constraints / 6.4.1:
Closed unoriented sector, crosscap constraint / 6.4.2:
Partition functions / 6.5:
Klein bottle projection / 6.5.1:
Annulus partition function / 6.5.2:
Mobius strip projection / 6.5.3:
Solutions for the partition functions / 6.5.4:
Acknowledgments
Topics in string tachyon dynamics / 7:
Why tachyons? / 7.1:
Tachyons in AdS: The c = 1 barrier / 7.3:
Tachyon [sigma]-model beta-functions / 7.4:
Open strings and cosmological constant: the Fischler-Susskind mechanism / 7.5:
Fischler-Susskind mechanism: closed-string case / 7.5.1:
Open-string contribution to the cosmological constant: the filling brane / 7.5.2:
The effective action / 7.6:
A warming-up exercise / 7.6.1:
Non-critical dimension and tachyon condensation / 7.6.2:
D-branes, tachyon condensation and K-theory / 7.7:
Extended objects and topological stability / 7.7.1:
A gauge theory analogue for D-branes in type II strings / 7.7.2:
K-theory version of Sen's conjecture / 7.7.3:
Type IIA strings / 7.7.4:
Some final comments on gauge theories / 7.8:
Mathematical developments / Kenji Fukaya ; Antonella Grassi ; Michele RossiPart 3:
Deformation theory, homological algebra and mirror symmetry / 8:
Classical deformation theory / 8.1:
Holomorphic structure on vector bundles / 8.2.1:
Families of holomorphic structures on vector bundles / 8.2.2:
Cohomology and deformations / 8.2.3:
Bundle valued harmonic forms / 8.2.4:
Construction of a versal family and Feynman diagrams / 8.2.5:
The Kuranishi family / 8.2.6:
Formal deformations / 8.2.7:
Homological algebra and deformation theory / 8.3:
Homotopy theory of A[subscript infinity] and L[subscript infinity] algebras / 8.3.1:
Maurer-Cartan equation and moduli functors / 8.3.2:
Canonical model, Kuranishi map and moduli space / 8.3.3:
Superspace and odd vector fields--an alternative formulation of L[subscript infinity] algebras / 8.3.4:
Application to mirror symmetry / 8.4:
Novikov rings and filtered A[subscript infinity], L[subscript infinity] algebras / 8.4.1:
Review of a part of global symplectic geometry / 8.4.2:
From Lagrangian submanifold to A[subscript infinity] algebra / 8.4.3:
Maurer-Cartan equation for filtered A[subscript infinity] algebras / 8.4.4:
Homological mirror symmetry / 8.4.5:
Large N dualities and transitions in geometry / 9:
Geometry and topology of transitions / 9.1:
The local topology of a conifold transition / 9.1.1:
Transitions of Calabi-Yau threefolds / 9.1.2:
Transitions and mirror symmetry / 9.1.3:
Transitions, black holes etc / 9.1.4:
Chern-Simons theory / 9.2:
Chern-Simons' form and action / 9.2.1:
The Hamiltonian formulation of the Chern-Simons QFT (following Witten's canonical quantization) / 9.2.2:
Computability and link invariants / 9.2.3:
The Gopakumar-Vafa conjecture / 9.3:
Matching the free energies / 9.3.1:
The matching of expectation values / 9.3.2:
Lifting to M-theory / 9.4:
Riemannian Holonomy, G[subscript 2] manifolds and Calabi-Yau, revisited / 9.4.1:
The geometry / 9.4.2:
Branes and M-theory lifts / 9.4.3:
M-theory lift and M-theory flop / 9.4.4:
Appendix: Some notation on singularities and their resolutions / 9.5:
Appendix: More on the Greene-Plesser construction / 9.6:
Appendix: More on transitions in superstring theory / 9.7:
Appendix: Principal bundles, connections etc / 9.8:
Appendix: More on Witten's open-string theory interpretation of QFT / 9.9:
Index
Preface
An elementary introduction to branes in string theory / Alberto LerdaPart 1:
Introduction / 1:
23.

図書

図書
edited by S. Müller-Stach and C. Peters
出版情報: Cambridge : Cambridge University Press, 2004  xix, 290 p., [1] p. of plates ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 313
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Introductory Material / Part I:
Chow varieties, the Euler-Chow series and the total coordinate ring / J. Elizondo1:
Introduction to Lawson homology / C. Peters ; S. Kosarew2:
Lawson (Co)homology / Part II:
Topological properties of the algebraic cycles functor / P. Lima-Filho3:
Motives and Motivic Cohomology / Part III:
Lectures on motives / J. P. Murre4:
A short introduction to higher Chow groups / P. Elbaz-Vincent5:
Hodge Theoretic Invariants of Cycles / Part IV:
Three lectures on the Hodge conjecture / J. D. Lewis6:
Lectures on Nori's connectivity theorem / J. Nagel7:
Beilinson's Hodge and Tate conjectures / S. Saito8:
Introductory Material / Part I:
Chow varieties, the Euler-Chow series and the total coordinate ring / J. Elizondo1:
Introduction to Lawson homology / C. Peters ; S. Kosarew2:
24.

図書

図書
Ayalvadi Ganesh, Neil O'Connell, Damon Wischik
出版情報: Berlin ; Tokyo : Springer, c2004  xi, 254 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1838
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25.

図書

図書
Rolf Gohm
出版情報: Berlin ; Tokyo : Springer, c2004  viii, 170 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1839
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26.

図書

図書
Simon Tavaré, Ofer Zeitouni ; editor, Jean Picard
出版情報: Berlin ; Tokyo : Springer, c2004  314 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1837
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Simon Tavare: Ancestral Inference in Population Genetics Contents / Part I:
Introduction / 1:
The Wright-Fisher model / 2:
The Ewens Sampling Formula / 3:
The Coalescent / 4:
The Infinitely-many-sites Model / 5:
Estimation in the Infinitely-many-sites Model / 6:
Ancestral Inference in the Infinitely-many-sites Model / 7:
The Age of a Unique Event Polymorphism / 8:
Markov Chain Monte Carlo Methods / 9:
Recombination / 10:
ABC: Approximate Bayesian Computation / 11:
Afterwords / 12:
References
Ofer Zeitouni: Random Walks in Random Environment Contents / Part II:
RWRE - d=1
RWRE - d > 1
List of Participants
List of Short Lectures
Simon Tavare: Ancestral Inference in Population Genetics Contents / Part I:
Introduction / 1:
The Wright-Fisher model / 2:
27.

図書

図書
von Hans Wussing
出版情報: Aachen : J. A. Mayer, 1962  viii, 245 p. ; 24 cm
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28.

図書

図書
by Titus Petrila, Damian Trif
出版情報: New York, N.Y. : Spinger, c2005  xiv, 500 p. ; 25 cm
シリーズ名: Numerical methods and algorithms ; v. 3
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29.

図書

図書
A. D. Alexandrov ; [english translation by N.S. Dairbekov, S.S. Kutateladze and A.B. Sossinsky]
出版情報: Berlin : Springer-Verlag, c2005  xi, 539 p ; 25 cm
シリーズ名: Springer monographs in mathematics
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Introduction
Basic Concepts and Simplest Properties of Convex Polyhedra
Methods and Results
Uniqueness of Polyhedra with Prescribed Development
Existence of Polyhedra with Prescribed Development
Gluing and Flexing Polyhedra with Boundary
Conditions for Congruence of Polyhedra with Parallel Faces
Existence Theorems for Polyhedra with Prescribed Face Directions
Relationship Between the Congruence Condition for Polyhedra with Parallel Faces and Other Problems
Polyhedra with Vertices on Prescribed Rays
Infinitesimal Rigidity of Convex Polyhedra with Stationary Development
Infinitesimal Rigidity Conditions for Polyhedra with Prescribed Face Directions
Supplements
References
Subject Index
Introduction
Basic Concepts and Simplest Properties of Convex Polyhedra
Methods and Results
30.

図書

図書
Donald E. Knuth
出版情報: Stanford, Calif. : CSLI Publications, c2003  xvi, 812 p. ; 23 cm
シリーズ名: CSLI lecture notes ; no. 106
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Combinatorial Analysis and Computers / 1:
Two Notes on Notation / 2:
Bracket Notation for the 'Coefficient of' Operator / 3:
Johann Faulhaber and Sums of Powers / 4:
Notes on Thomas Harriot / 5:
A Permanent Inequality / 6:
Overlapping Pfaffians / 7:
The Sandwich Theorem / 8:
Combinatorial Matrices / 9:
Aztec Diamonds, Checkerboard Graphs, and Spanning Trees / 10:
Partitioned Tensor Products and Their Spectra / 11:
Oriented Subtrees of an Arc Digraph / 12:
Another Enumeration of Trees / 13:
Abel Identities and Inverse Relations / 14:
Convolution Polynomials / 15:
Polynomials Involving the Floor Function / 16:
Construction of a Random Sequence / 17:
An Imaginary Number System / 18:
Tables of Finite Fields
Finite Semifields and Projective Planes / 20:
A Class of Projective Planes / 21:
Notes on Central Groupoids / 22:
Huffman's Algorithm via Algebra / 23:
Wheels Within Wheels / 24:
Complements and Transitive Closures / 25:
Random Matroids / 26:
The Asymptotic Number of Geometries / 27:
Permutations with Nonnegative Partial Sums / 28:
Efficient Balanced Codes / 29:
The Knowlton - Graham Partition Problem / 30:
Permutations, Matrices, and Generalized Young Tableaux / 31:
Enumeration of Plane Partitions / 32:
A Note on Solid Partitions / 33:
Identities from Partition Involutions / 34:
Subspaces, Subsets, and Partitions / 35:
The Power of a Prime That Divides a Generalized Coefficient / 36:
An Almost Linear Recurrence / 37:
Recurrence Relations Based on Minimization / 38:
A Recurrence Related to Trees / 39:
The First Cycles in an Evolving Graph / 40:
The Birth of the Giant Component / 41:
Index
Combinatorial Analysis and Computers / 1:
Two Notes on Notation / 2:
Bracket Notation for the 'Coefficient of' Operator / 3:
31.

図書

図書
Harry Kesten (editor)
出版情報: Berlin ; Tokyo : Springer, c2004  vi, 351 p. ; 25 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 110 . Probability theory ; 1
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The Random-Cluster Model / Geoffrey Grimmett
Models of First-Passage Percolation / C. Douglas Howard
Relaxation Times of Markov Chains in Statistical Mechanics and Combinatorial Structures / Fabio Martinelli
Random Walks on Finite Groups / Laurent Saloff-Coste
Index
Introduction / 1:
A Motivating Example: the Assignment Problem / 1.1:
A Stalking Horse: the Partial Matching Problem / 1.2:
Organization of the Survey / 1.3:
Geometric Graphs and Local Weak Convergence / 2:
Geometric Graphs / 2.1:
<$>{\cal G}^\ast<$> as a Metric Space / 2.2:
Local Weak Convergence / 2.3:
The Standard Construction / 2.4:
A Prototype: The Limit of Uniform Random Trees / 2.5:
Maximal Weight Partial Matching on Random Trees / 3:
Weighted Matchings of Graphs in General / 3.1:
Our Case: Random Trees with Random Edge Weights / 3.2:
Two Obvious Guesses: One Right, One Wrong / 3.3:
Not Your Grandfather's Recursion / 3.4:
A Direct and Intuitive Plan / 3.5:
Characterization of the Limit of <$>B(T_n^{small})<$> / 3.6:
Characterization of the Limit of <$>B(T_n^{big})<$> / 3.7:
The Limit Theorem for Maximum Weight Partial Matchings / 3.8:
Closing the Loop: Another Probabilistic Solution of a Fixed-Point Equation / 3.9:
From Coupling to Stability - Thence to Convergence / 3.10:
Looking Back: Perspective on a Case Study / 3.11:
The Mean-Field Model of Distance / 4:
From Poisson Points in <$>{\op R}^{d}<$> to a Simple Distance Model / 4.1:
The Poisson Weighted Infinite Tree - or, the PWIT / 4.2:
The Cut-off Components of a Weighted Graph and a PWIT / 4.3:
The Minimum Spanning Forests of an Infinite Graph / 4.4:
The Average Length Per Vertex of the MSF of a PWIT / 4.5:
The Connection to Frieze's ζ(3) Theorem / 4.6:
Minimal Cost Perfect Matchings / 5:
A Natural Heuristic - Which Fails for a Good Reason / 5.1:
Involution Invariance and the Standard Construction / 5.2:
Involution Invariance and the Convergence of MSTs / 5.3:
A Heuristic That Works by Focusing on the Unknown / 5.4:
A Distributional Identity with a Logistic Solution / 5.5:
A Stochastic Process that Constructs a Matching / 5.6:
Calculation of a Limiting Constant: <$>\pi^{2}/6<$> / 5.7:
Passage from a PWIT Matching to a Kn Matching / 5.8:
Finally - Living Beyond One's Means / 5.9:
Problems in Euclidean Space / 6:
A Motivating Problem / 6.1:
Far Away Places and Their Influence / 6.2:
Euclidean Methods and Some Observations in Passing / 6.3:
Recurrence of Random Walks in Limits of Planar Graphs / 6.4:
Limitations, Challenges, and Perspectives / 7:
References
Potts and random-cluster processes
Random-cluster measures
Ising and Potts models
Random-cluster and Ising-Potts coupled
The limit as <$>q \downarrow 0<$>
Rank-generating functions
Infinite-volume random-cluster measures
Stochastic ordering
A differential formula
Conditional probabilities
Infinite-volume weak limits
Random-cluster measures on infinite graphs
The case q < 1
Phase transition, the big picture
Infinite open clusters
First- and second-order phase transition
General results in d (≥ 2) dimensions
The subcritical phase, p < pc(q)
The supercritical phase, p > pc(q)
Near the critical point, p ≃ pc(q)
In two dimensions
Graphical duality
Value of the critical point
First-order phase transition
SLE limit when q ≤ 4
On complete graphs and trees
On complete graphs / 7.1:
On trees and non-amenable graphs / 7.2:
Time-evolutions of random-cluster models / 8:
Reversible dynamics / 8.1:
Coupling from the past / 8.2:
Swendsen-Wang dynamics / 8.3:
The Basic Model and Some Fundamental Questions
Notation
The Time Constant
The Fundamental Processes of Hammersley and Welsh
About μ
Minimizing Paths
Asymptotic Shape and Shape Fluctuations
Shape Theorems for Standard FPP
About the Asymptotic Shape for Lattice FPP
FPP Based on Poisson Point Processes
Upper Bounds on Shape Fluctuations
Some Related Longitudinal Fluctuation Exponents
Monotonicity
Transversal Fluctuations and the Divergence of Shape Fluctuations
Transversal Fluctuation Exponents
Upper Bounds on <$>\xi<$>
Lower Bounds on <$>\chi<$>
Lower Bounds on <$>\xi<$>
Fluctuations for Other Related Models
Infinite Geodesics and Spanning Trees
Semi-Infinite Geodesics and Spanning Trees
Coalescence and Another Spanning Tree in 2 Dimensions
Doubly-Infinite Geodesics
Summary of Some Open Problems
Mixing times for reversible, continuous-time Markov chains
Analytic methods
Tensorization of the Poincaré and logarithmic Sobolev inequalities
Geometric tools
Comparison methods
Coupling methods and block dynamics
Statistical mechanics models in <$>{\op Z}^d<$>
Grand canonical Gibbs measures
Mixing conditions and absence of long-range order
Canonical Gibbs measures for lattice gases
The ferromagnetic Ising and Potts models
FK representation of Potts models
Antiferromagnetic models on an arbitrary graph: Potts and hard-core models
Model with random interactions
Unbounded spin systems
Ground states of certain quantum Heisenberg models as classical Gibbs measures
Glauber dynamics in <$>{\op Z}^d<$>
The dynamics in a finite volume
The dynamics in an infinite volume
Graphical construction
Uniform ergodicity and logarithmic Sobolev constant
Mixing property versus logarithmic Sobolev constant in <$>{\op Z}^d<$>
The auxiliary chain and sweeping out relations method
The renormalization group approach
The martingale method
The recursive analysis
Rapid mixing for unbounded spin systems
Torpid mixing in the phase coexistence region
Torpid mixing for the Ising model in <$>\Lambda \subset {\op Z}^{d}<$> with free boundary conditions
Interface driven mixing inside one phase
Torpid mixing for Potts model in <$>{\op Z}^d<$>
Glauber dynamics for certain random systems in <$>{\op Z}^d<$>
Combination of torpid and rapid mixing: the dilute Ising model
Relaxation to equilibrium for spin glasses
Glauber dynamics for more general structures
Glauber dynamics on trees and hyperbolic graphs
Glauber dynamics for the hard-core model
Cluster algorithms: the Swendsen-Wang dynamics for Potts models
Mixing time for conservative dynamics / 9:
Random transposition, Bernoulli-Laplace and symmetric simple exclusion / 9.1:
The asymmetric simple exclusion / 9.2:
The Kac model for the Boltzmann equation / 9.3:
Adsorbing staircase walks / 9.4:
Kawasaki dynamics for lattice gases / 10:
Diffusive scaling of the mixing time in the one-phase region / 10.1:
Background and Notation / 10.2:
Finite Markov Chains
Invariant Markov Chains on Finite Groups
Shuffling Cards and the Cut-off Phenomenon
Three Examples of Card Shuffling
Exact Computations
The Cut-off Phenomenon
Probabilistic Methods
Coupling
Strong Stationary Times
Spectrum and Singular Values
General Finite Markov Chains
The Random Walk Case
Lower Bounds
Eigenvalue Bounds Using Paths
Cayley Graphs
The Second Largest Eigenvalue
The Lowest Eigenvalue
Diameter Bounds, Isoperimetry and Expanders
Results Involving Volume Growth Conditions
Moderate Growth
Nilpotent Groups
Nilpotent Groups with many Generators / 7.3:
Representation Theory for Finite Groups
The General Set-up
Abelian Examples
Random Random Walks
Central Measures and Bi-invariant Walks
Characters and Bi-invariance
Random Transposition on the Symmetric Group
Walks Based on Conjugacy Classes of the Symmetric Group
Finite Classical Groups
Fourier Analysis for Non-central Measures / 9.5:
Comparison Techniques
The min-max Characterization of Eigenvalues
Comparing Dirichlet Forms Using Paths
Comparison for Non-symmetric Walks / 10.3:
The Random-Cluster Model / Geoffrey Grimmett
Models of First-Passage Percolation / C. Douglas Howard
Relaxation Times of Markov Chains in Statistical Mechanics and Combinatorial Structures / Fabio Martinelli
32.

図書

図書
Jean-Philippe Anker, Bent Orsted, editors
出版情報: Boston : Birkhäuser, c2005  x, 207 p. ; 25 cm
シリーズ名: Progress in mathematics ; v. 229
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Preface / Ji
Introduction to Symmetric Spaces and Their Compactifications / Borel/Ji
Compactifications of Symmetric and Locally Symmetric Spaces / Kobayashi
Restrictions of Unitary Representations of Real Reductive Groups
Preface / Ji
Introduction to Symmetric Spaces and Their Compactifications / Borel/Ji
Compactifications of Symmetric and Locally Symmetric Spaces / Kobayashi
33.

図書

図書
S. Ramanan
出版情報: Providence, R.I. : American Mathematical Society, c2005  xi, 316 p. ; 27 cm
シリーズ名: Graduate studies in mathematics ; v. 65
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Preface
Sheaves and Differential Manifolds: Definitions and Examples / Chapter 1:
Sheaves and Presheaves / 1:
Basic Constructions / 2:
Differential Manifolds / 3:
Lie Groups; Action on a Manifold / 4:
Exercises
Differential Operators / Chapter 2:
First Order Differential Operators
Locally Free Sheaves and Vector Bundles
Flow of a Vector Field
Theorem of Frobenius
Tensor Fields; Lie Derivative / 5:
The Exterior Derivative; de Rham Complex / 6:
Differential Operators of Higher Order / 7:
Integration on Differential Manifolds / Chapter 3:
Integration on a Manifold
Sheaf of Densities
Adjoints of Differential Operators
Cohomology of Sheaves and Applications / Chapter 4:
Injective Sheaves
Sheaf Cohomology
Cohomology through Other Resolutions
Singular and Sheaf Cohomologies
Cech and Sheaf Cohomologies
Differentiable Simplices; de Rham's Theorem
Connections on Principal and Vector Bundles; Lifting of Symbols / Chapter 5:
Connections in a Vector Bundle
The Space of All Connections on a Bundle
Principal Bundles
Connections on Principal Bundles
Curvature
Chern-Weil Theory
Holonomy Group; Ambrose-Singer Theorem
Linear Connections / Chapter 6:
Lifting of Symbols and Torsion
Manifolds with Additional Structures / Chapter 7:
Reduction of the Structure Group
Torsion Free G-Connections
Complex Manifolds
The Outer Gauge Group
Riemannian Geometry
Riemannian Curvature Tensor
Ricci, Scalar and Weyl Curvature Tensors
Clifford Structures and the Dirac Operator / 8:
Local Analysis of Elliptic Operators / Chapter 8:
Regularisation
A Characterisation of Densities
Schwartz Space of Functions and Densities
Fourier Transforms
Distributions
Theorem of Sobolev
Interior Regularity of Elliptic Solutions
Vanishing Theorems and Applications / Chapter 9:
Elliptic Operators on Differential Manifolds
Elliptic Complexes
Composition Formula
A Vanishing Theorem
Hodge Decomposition
Lefschetz Decomposition
Kodaira's Vanishing Theorem
The Imbedding Theorem
Appendix
Algebra
Topology
Analysis
Bibliography
Index
Preface
Sheaves and Differential Manifolds: Definitions and Examples / Chapter 1:
Sheaves and Presheaves / 1:
34.

図書

図書
Burak Ozbagci, András I. Stipsicz
出版情報: Berlin : Springer , Budapest : János Bolyai Mathematical Society, c2004  281 p. ; 24 cm
シリーズ名: Bolyai Society mathematical studies ; 13
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Preface
Introduction
Topological Surgeries
Symplectic 4-Manifolds
Contact 3-Manifolds
Convex Surfaces in Contact 3-Manifolds
Spinc Structures on 3- and 4-Manifolds
Symplectic Surgery
Stein Manifolds
Open Books and Contact Structures
Lefschetz Fibrations on 4-Manifolds
Contact Dehn Surgery
Fillings of Contact 3-Manifolds
Appendix: Seiberg-Witten Invariants
Appendix: Heegaard Floer Theory
Appendix: Mapping Class Groups
Bibliography
Index
Preface
Introduction
Topological Surgeries
35.

図書

図書
Jean-Pierre Serre ; translated from the French by Chee Whye Chin
出版情報: Berlin : Springer, 2000  xiii, 128 p. ; 24 cm
シリーズ名: Springer monographs in mathematics
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Preface
Contents
Introduction
Prime Ideals and Localization / I:
Notation and definitions /  1:
Nakayama's lemma /  2:
Localization /  3:
Noetherian rings and modules /  4:
Spectrum /  5:
The noetherian case /  6:
Associated prime ideals /  7:
Primary decompositions /  8:
Tools / II:
Filtrations and Gradings / A:
Filtered rings and modules
Topology defined by a filtration
Completion of filtered modules
Graded rings and modules
Where everything becomes noetherian again - <$>\mathfr {q}<$> -adic filtrations
Hilbert-Samuel Polynomials / B:
Review on integer-valued polynomials
Polynomial-like functions
The Hilbert polynomial
The Samuel polynomial
Dimension Theory / III:
Dimension of Integral Extensions
Definitions
Cohen-Seidenberg first theorem
Cohen-Seidenberg second theorem
Dimension in Noetherian Rings
Dimension of a module
The case of noetherian local rings
Systems of parameters
Normal Rings / C:
Characterization of normal rings
Properties of normal rings
Integral closure
Polynomial Rings / D:
Dimension of the ring A[X1, ..., Xn]
The normalization lemma
Applications. I. Dimension in polynomial algebras
Applications. II. Integral closure of a finitely generated algebra
Applications. III. Dimension of an intersection in affine space
Homological Dimension and Depth / IV:
The Koszul Complex
The simple case
Acyclicity and functorial properties of the Koszul complex
Filtration of a Koszul complex
The depth of a module over a noetherian local ring
Cohen-Macaulay Modules
Definition of Cohen-Macaulay modules
Several characterizations of Cohen-Macaulay modules
The support of a Cohen-Macaulay module
Prime ideals and completion
Homological Dimension and Noetherian Modules
The homological dimension of a module
The local case
Regular Rings
Properties and characterizations of regular local rings
Permanence properties of regular local rings
Delocalization
A criterion for normality
Regularity in ring extensions
Minimal Resolutions / Appendix I:
Definition of minimal resolutions
Application
The case of the Koszul complex
Positivity of Higher Euler-Poincare Characteristics / Appendix II:
Graded-polynomial Algebras / Appendix III:
Notation
Graded-polynomial algebras
A characterization of graded-polynomial algebras
Ring extensions
Application: the Shephard-Todd theorem
Multiplicities / V:
Multiplicity of a Module
The group of cycles of a ring
Multiplicity of a module
Intersection Multiplicity of Two Modules
Reduction to the diagonal
Completed tensor products
Regular rings of equal characteristic
Conjectures
Regular rings of unequal characteristic (unramified case)
Arbitrary regular rings
Connection with Algebraic Geometry
Tor-formula
Cycles on a non-singular affine variety
Basic formulae
Proof of theorem 1
Rationality of intersections
Direct images
Pull-backs
Extensions of intersection theory
Bibliography
Index
Index of Notation
Preface
Contents
Introduction
36.

図書

図書
J. Frédéric Bonnans, Alexander Shapiro
出版情報: New York : Springer, c2000  xviii, 601 p. ; 24 cm
シリーズ名: Springer series in operations research
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37.

図書

図書
by William Snow Burnside and Arthur William Panton
出版情報: Dublin : Hodges, Figgis , London : Longmans, Green, 1886  xvi, 448 p. ; 23 cm
シリーズ名: Dublin University Press series
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38.

図書

図書
V.Ostrovskyi, Yu. Samoilenko
出版情報: Amsterdam : Harwood Academic Pub., c1999  iii, 261 p. ; 22 cm
シリーズ名: Reviews in mathematics and mathematical physics ; v. 11, pt. 1
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39.

図書

図書
Masaki Kashiwara, Tetsuji Miwa, editors
出版情報: Boston : Birkhäuser, c2000  viii, 317 p. ; 25 cm
シリーズ名: Progress in mathematics ; v. 191
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40.

図書

図書
Luis Ribes, Pavel Zalesskii
出版情報: Berlin ; Tokyo : Springer, c2000  xiv, 435 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, v. 40
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Preface
Inverse and Direct Limits / 1:
Inverse or Projective Limits / 1.1:
Direct or Inductive Limits / 1.2:
Notes, Comments and Further Reading / 1.3:
Profinite Groups / 2:
Pro- <$>{\cal C}<$> Groups / 2.1:
Basic Properties of Pro- <$>{\cal C}<$> Groups / 2.2:
Existence of Sections
Exactness of Inverse Limits of Profinite Groups
The Order of a Profinite Group and Sylow Subgroups / 2.3:
Generators / 2.4:
Finitely Generated Profinite Groups / 2.5:
Generators and Chains of Subgroups / 2.6:
Procyclic Groups / 2.7:
The Frattini Subgroup of a Profinite Group / 2.8:
Pontryagin Duality for Profinite Groups / 2.9:
Pullbacks and Pushouts / 2.10:
Profinite Groups as Galois Groups / 2.11:
Free Profinite Groups / 2.12:
Profinite Topologies / 3.1:
The Pro-<$>{\cal C}<$> Completion / 3.2:
The Completion Functor
Free Pro-<$>{\cal C}<$> Groups / 3.3:
Free Pro - <$>{\cal C}<$> Group on a Set Converging to 1
Maximal Pro- <$>{\cal C}<$> Quotient Groups / 3.4:
Characterization of Free Pro-<$>{\cal C}<$> Groups / 3.5:
Open Subgroups of Free Pro-<$>{\cal C}<$> Groups / 3.6:
Some Special Profinite Groups / 3.7:
Powers of Elements with Exponents from <$>\hat {\rm Z}<$> / 4.1:
Subgroups of Finite Index in a Profinite Group / 4.2:
Profinite Abelian Groups / 4.3:
Automorphism Group of a Profinite Group / 4.4:
Automorphism Group of a Free Pro-p Group / 4.5:
Profinite Frobenius Groups / 4.6:
Torsion in the Profinite Completion of a Group / 4.7:
Discrete and Profinite Modules / 4.8:
Profinite Rings and Modules / 5.1:
Duality Between Discrete and Profinite Modules
Free Profinite Modules / 5.2:
G-modules and Complete Group Algebras / 5.3:
The Complete Group Algebra
Projective and Injective Modules / 5.4:
Complete Tensor Products / 5.5:
Profinite G-spaces / 5.6:
Free Profinite <$$$>[[RG]]-modules / 5.7:
Diagonal Actions / 5.8:
Homology and Cohomology of Profinite Groups / 5.9:
Review of Homological Algebra / 6.1:
Right and Left Derived Functors
Bifunctors
The Ext Functors
The Tor Functors
Cohomology with Coefficients in DMod(<$$$>[[RG]]) / 6.2:
Standard Resolutions
Homology with Coefficients in PMod(<$$$>[[RG]]) / 6.3:
Cohomology Groups with Coefficients in DMod(G) / 6.4:
The Functorial Behavior of Hn(G, A) and Hn(G, A) / 6.5:
The Inflation Map
Hn(G,A) as Derived Functors on DMod(G) / 6.6:
Special Mappings / 6.7:
The Restriction Map in Cohomology
The Corestriction Map in Cohomology
The Corestriction Map in Homology
The Restriction Map in Homology
Homology and Cohomology Groups in Low Dimensions / 6.8:
H2 (G, A) and Extensions of Profinite Groups
Extensions of Profinite Groups with Abelian Kernel / 6.9:
Induced and Coinduced Modules / 6.10:
The Induced Module <$>{\rm Ind}_H^G<$> (B) for H Open / 6.11:
Cohomological Dimension / 6.12:
Basic Properties of Dimension / 7.1:
The Lyndon-Hochschild-Serre Spectral Sequence / 7.2:
Cohomological Dimension of Subgroups / 7.3:
Cohomological Dimension of Normal Subgroups and Quotients / 7.4:
Groups G with cdp(G) ≤ 1 / 7.5:
Projective Profinite Groups / 7.6:
Free Pro-p Groups and Cohomological Dimension / 7.7:
Generators and Relators for Pro-p Groups / 7.8:
Cup Products / 7.9:
Normal Subgroups of Free Pro - <$>{\cal C}<$> Groups / 7.10:
Normal Subgroup Generated by a Subset of a Basis / 8.1:
The S-rank / 8.2:
Accessible Subgroups / 8.3:
Accessible Subgroups H with w0(F/H) < rank(F) / 8.4:
Homogeneous Pro- <$>{\cal C}<$> Groups / 8.5:
Normal Subgroups / 8.6:
Proper Open Subgroups of Normal Subgroups / 8.7:
The Congruence Kernel of SL2(Z) / 8.8:
Sufficient Conditions for Freeness / 8.9:
Characteristic Subgroups of Free Pro- <$>{\cal C}<$> Groups / 8.10:
Free Constructions of Profinite Groups / 8.11:
Free Pro- <$>{\cal C}<$> Products / 9.1:
Amalgamated Free Pro- <$>{\cal C}<$> Products / 9.2:
Cohomological Characterizations of Amalgamated Products / 9.3:
Pro- <$>{\cal C}<$> HNN extensions / 9.4:
Open Questions / 9.5:
Appendix
Spectral Sequences / A1:
Positive Spectral Sequences / A2:
Spectral Sequence of a Filtered Complex / A3:
Spectral Sequences of a Double Complex / A4:
Bibliography / A5:
Index of Symbols
Index of Authors
Index of Terms
Preface
Inverse and Direct Limits / 1:
Inverse or Projective Limits / 1.1:
41.

図書

図書
M. Rørdam, F. Larsen, N. Laustsen
出版情報: Cambridge, UK ; New York, NY : Cambridge University Press, 2000  xii, 242 p. ; 24 cm
シリーズ名: London Mathematical Society student texts ; 49
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Preface
C*-Algebra Theory / 1:
C*-algebras and *-homomorphisms / 1.1:
Spectral theory / 1.2:
Matrix algebras / 1.3:
Exercises / 1.4:
Projections and Unitary Elements / 2:
Homotopy classes of unitary elements / 2.1:
Equivalence of projections / 2.2:
Semigroups of projections / 2.3:
The K[subscript 0]-Group of a Unital C*-Algebra / 2.4:
Definition of the K[subscript 0]-group of a unital C*-algebra / 3.1:
Functoriality of K[subscript 0] / 3.2:
Examples / 3.3:
The Functor K[subscript 0] / 3.4:
Definition and functoriality of K[subscript 0] / 4.1:
The standard picture of the group K[subscript 0](A) / 4.2:
Half and split exactness and stability of K[subscript 0] / 4.3:
The Ordered Abelian Group K[subscript 0](A) / 4.4:
The ordered K[subscript 0]-group of stably finite C*-algebras / 5.1:
States on K[subscript 0](A) and traces on A / 5.2:
Inductive Limit C*-Algebras / 5.3:
Products and sums of C*-algebras / 6.1:
Inductive limits / 6.2:
Continuity of K[subscript 0] / 6.3:
Stabilized C*-algebras / 6.4:
Classification of AF-Algebras / 6.5:
Finite dimensional C*-algebras / 7.1:
AF-algebras / 7.2:
Elliott's classification theorem / 7.3:
UHF-algebras / 7.4:
The Functor K[subscript 1] / 7.5:
Definition of the K[subscript 1]-group / 8.1:
Functoriality of K[subscript 1] / 8.2:
K[subscript 1]-groups and determinants / 8.3:
The Index Map / 8.4:
Definition of the index map / 9.1:
The index map and partial isometries / 9.2:
An exact sequence of K-groups / 9.3:
Fredholm operators and Fredholm index / 9.4:
The Higher K-Functors / 9.5:
The isomorphism between K[subscript 1](A) and K[subscript 0](SA) / 10.1:
The long exact sequence in K-theory / 10.2:
Bott Periodicity / 10.3:
The Bott map / 11.1:
The proof of Bott periodicity / 11.2:
Applications of Bott periodicity / 11.3:
Homotopy groups and K-theory / 11.4:
The holomorphic function calculus / 11.5:
The Six-Term Exact Sequence / 11.6:
The exponential map and the six-term exact sequence / 12.1:
An explicit description of the exponential map / 12.2:
Inductive Limits of Dimension Drop Algebras / 12.3:
Dimension drop algebras / 13.1:
Countable Abelian groups as K-groups / 13.2:
References / 13.3:
Table of K-groups
Index of symbols
General index
Preface
C*-Algebra Theory / 1:
C*-algebras and *-homomorphisms / 1.1:
42.

図書

図書
Judy L. Walker
出版情報: Providence, R.I. : American Mathematical Society, c2000  xii, 66 p. ; 22 cm
シリーズ名: Student mathematical library ; v. 7 . IAS/Park City mathematical subseries
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Introduction to coding theory
Bounds on codes
Algebraic curves
Nonsingularity and the genus
Points, functions, and divisors on curves
Algebraic geometry codes
Good codes from algebraic geometry
Abstract algebra review
Finite fields Projects
Bibliography
Introduction to coding theory
Bounds on codes
Algebraic curves
43.

図書

図書
by George Biddell Airy
出版情報: London : Macmillan, 1866  viii, 58 p., [4] leaves of plates ; 20 cm
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44.

図書

図書
Nicolae Dinculeanu
出版情報: New York : Wiley, c2000  xv, 424 p. ; 25 cm
シリーズ名: Pure and applied mathematics
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Preface
Vector Integration / Chapter 1:
Preliminaries / 1.:
Banach spaces / A.:
Classes of sets / B.:
Measurable functions / C.:
Simple measurability of operator-valued functions / D.:
Weak measurability / E.:
Integral of step functions / F.:
Totally measurable functions and the immediate integral / G.:
The Riesz representation theorem / H.:
The classical integral / I.:
The Bochner integral / J.:
Convergence theorems / K.:
Measures with finite variation / 2.:
The variation of vector measures
Boundedness of [sigma]-additive measures
Variation of real-valued measures
Integration with respect to vector measures with finite variation
The indefinite integral
Integration with respect to gm
The Radon-Nikodym theorem
Conditional expectations
[sigma]-additive measures / 3.:
[sigma]-additive measures on [sigma]-rings
Uniform [sigma]-additivity
Uniform absolute continuity and uniform [sigma]-additivity
Weak [sigma]-additivity
Uniform [sigma]-additivity of indefinite integrals
Weakly compact sets in L[superscript 1 subscript F] ([mu])
Measures with finite semivariation / 4.:
The semivariation
Semivariation and norming spaces
The semivariation of [sigma]-additive measures
The family m[subscript F,Z] of measures
Integration with respect to a measure with finite semivariation / 5.:
Measurability with respect to a vector measure
The seminorm m[subscript F,G](f)
The space of integrable functions
The integral
Properties of the space F[subscript D] (B, m[subscript F,G])
Relationship between the spaces F[subscript D](m)
The indefinite integral of measures with finite semivariation
Strong additivity / 6.:
Extension of measures / 7.:
Applications / 8.:
Integral representation of continuous linear operations on L[superscript p]-spaces
Random Gaussian measures
The Stochastic Integral / Chapter 2:
Summable processes / 9.:
Notations
The measure I[subscript X]
Computation of I[subscript X] for predictable rectangles
Computation of I[subscript X] for stochastic intervals
The stochastic integral / 10.:
The space F[subscript D] [characters not reproducible]
The integral [function of] HdI[subscript X]
A convergence theorem
The stochastic integral H - X
The stochastic integral and stopping times / 11.:
Stochastic integral of elementary processes
Stopping the stochastic integral
Summability of stopped processes
The jumps of the stochastic integral
The completeness of the space L[superscript 1 subscript F,G](X) / 12.:
The Uniform Convergence Theorem
The Vitali and the Lebesgue Convergence Theorems
The stochastic integral of [sigma]-elementary and of caglad processes as a pathwise Stieltjes integral
Summability of the stochastic integral / 13.:
Summability criterion / 14.:
Quasimartingales and the Doleans measure
The summability criterion
Local summability and local integrability / 15.:
Definitions
Basic properties
Additional properties
Martingales / Chapter 3:
Stochastic integral of martingales / 16.:
Square integrable martingales / 17.:
Extension of the measure I[subscript M]
Summability of square integrable martingales
Properties of the space F[subscript F,G](M)
Isometrical isomorphism of L[superscript 1 subscript F,G](M) and L[superscript 2 subscript F]([mu subscript [M]])
Processes with Finite Variation / Chapter 4:
Functions with finite variation and their Stieltjes integral / 18.:
Functions with finite variation
The variation function |g|
The measure associated to a function
The Stieltjes integral
Processes with finite variation / 19.:
Definition and properties
Optional and predictable measures
The measure [mu subscript X]
Summability of processes with integrable variation
The stochastic integral as a Stieltjes integral
The pathwise stochastic integral
Semilocally summable processes
Processes with Finite Semivariation / Chapter 5:
Functions with finite semivariation and their Stieltjes integral / 20.:
Functions with finite semivariation
The Stieltjes integral with respect to a function with finite semivariation
Processes with finite semivariation / 21.:
The semivariation process
The measure [mu]x
Summability of processes with integrable semivariation
Dual projections / 22.:
Dual projection of measures
Dual projections of processes
Existence of dual projections
Processes with locally integrable variation or semivariation
Examples of processes with locally integrable variation or semivariation
Decomposition of local martingales
The Ito Formula / Chapter 6:
The Ito formula / 23.:
Preliminary results
The vector quadratic variation
The quadratic variation
The process of jumps
Ito's formula
Stochastic Integration in the Plane / Chapter 7:
Order relation in R[superscript 2] / 24.:
The increment [Delta subscript zz], g
Right continuity
The filtration
The predictable [Sigma]-algebra
Stopping times
Stochastic processes
Extension of processes from R[superscript 2 subscript +] [times] [Omega] to R[superscript 2] [times] [Omega]
The seminorm I[subscript X] and the space F[subscript F,G](X) / 25.:
Properties of the stochastic integral / 26.:
Extension of I[subscript X] to P([infinity])
Existence of left limits of X in L[superscript p subscript E]
Some properties of the integral [function of] HdI[subscript X]
Two-Parameter Martingales / Chapter 8:
A decomposition theorem / 27.:
The measures [characters not reproducible] and [mu subscript [M]]
Summability of the square integrable martingales in Hilbert spaces
The space F[subscript F,G](I[subscript M])
Isometric isomorphism of L[superscript 1 subscript F,G](M) and L[superscript 2 subscript F]([mu subscript [M]])
Two-Parameter Processes with Finite Variation / Chapter 9:
Functions with finite variation in the plane / 29.:
Monotone functions
Partitions
Variation corresponding to a partition
Variation of a function on a rectangle
Limits of the variation
Functions vanishing outside a quadrant
Variation of real-valued functions
Lateral limits
Measures associated to functions
[sigma]-additivity of the measure m[subscript g] / L.:
Processes with integrable variation / M.:
Two-Parameter Processes with Finite Semivariation / Chapter 10:
Functions with finite semivariation in the plane / 31.:
The Stieltjes integral for functions with finite semivariation in R[superscript 2]
Processes with finite semivariation in the plane / 32.:
References
Preface
Vector Integration / Chapter 1:
Preliminaries / 1.:
45.

図書

図書
edited by N. Kenmochi
出版情報: Tokyo : Gakkōtosho, 2000  2 v. ; 27 cm
シリーズ名: GAKUTO international series ; . Mathematical sciences and applications ; vol. 13-14
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46.

図書

図書
edited by Ravi P. Agarwal and Donal O'Regan
出版情報: Amsterdam : Gordon & Breach, 2000  xi, 326 p. ; 26 cm
シリーズ名: Series in mathematical analysis and applications / Edited by Ravi P. Agarwal and Donal O'Regan ; v. 2
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47.

図書

図書
D. Bao, S.-S. Chern, Z. Shen
出版情報: New York : Springer-Verlag, c2000  xx, 431 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 200
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Preface
Acknowledgments
Finsler Manifolds and Their Curvature / Part 1:
Finsler Manifolds and the Fundamentals of Minkowski Norms / Chapter 1:
Physical Motivations / 1.0:
Finsler Structures: Definitions and Conventions / 1.1:
Two Basic Properties of Minkowski Norms / 1.2:
Euler's Theorem / 1.2 A.:
A Fundamental Inequality / 1.2 B.:
Interpretations of the Fundamental Inequality / 1.2 C.:
Explicit Examples of Finsler Manifolds / 1.3:
Minkowski and Locally Minkowski Spaces / 1.3 A.:
Riemannian Manifolds / 1.3 B.:
Randers Spaces / 1.3 C.:
Berwald Spaces / 1.3 D.:
Finsler Spaces of Constant Flag Curvature / 1.3 E.:
The Fundamental Tensor and the Cartan Tensor / 1.4:
References for Chapter 1
The Chern Connection / Chapter 2:
Prologue / 2.0:
The Vector Bundle [pi]*TM and Related Objects / 2.1:
Coordinate Bases Versus Special Orthonormal Bases / 2.2:
The Nonlinear Connection on the Manifold TM \ 0 / 2.3:
The Chern Connection on [pi]*TM / 2.4:
Index Gymnastics / 2.5:
The Slash (...)[subscript / 2.5 A.:
Covariant Derivatives of the Fundamental Tensor g / 2.5 B.:
Covariant Derivatives of the Distinguished l / 2.5 C.:
References for Chapter 2
Curvature and Schur's Lemma / Chapter 3:
Conventions and the hh-, hv-, vv-curvatures / 3.1:
First Bianchi Identities from Torsion Freeness / 3.2:
Formulas for R and P in Natural Coordinates / 3.3:
First Bianchi Identities from "Almost" g-compatibility / 3.4:
Consequences from the dx[superscript k] [logical and] dx[superscript l] Terms / 3.4 A.:
Consequences from the dx[superscript k] [logical and] 1/F[delta]y[superscript 1] Terms / 3.4 B.:
Consequences from the 1/F[delta]y[superscript k] [logical and] 1/F[delta]y[superscript 1] Terms / 3.4 C.:
Second Bianchi Identities / 3.5:
Interchange Formulas or Ricci Identities / 3.6:
Lie Brackets among the [delta]/[delta]x and the F[characters not reproducible] / 3.7:
Derivatives of the Geodesic Spray Coefficients G[superscript i] / 3.8:
The Flag Curvature / 3.9:
Its Definition and Its Predecessor / 3.9 A.:
An Interesting Family of Examples of Numata Type / 3.9 B.:
Schur's Lemma / 3.10:
References for Chapter 3
Finsler Surfaces and a Generalized Gauss-Bonnet Theorem / Chapter 4:
Minkowski Planes and a Useful Basis / 4.0:
Rund's Differential Equation and Its Consequence / 4.1 A.:
A Criterion for Checking Strong Convexity / 4.1 B.:
The Equivalence Problem for Minkowski Planes / 4.2:
The Berwald Frame and Our Geometrical Setup on SM / 4.3:
The Chern Connection and the Invariants I, J, K / 4.4:
The Riemannian Arc Length of the Indicatrix / 4.5:
A Gauss-Bonnet Theorem for Landsberg Surfaces / 4.6:
References for Chapter 4
Calculus of Variations and Comparison Theorems / Part 2:
Variations of Arc Length, Jacobi Fields, the Effect of Curvature / Chapter 5:
The First Variation of Arc Length / 5.1:
The Second Variation of Arc Length / 5.2:
Geodesics and the Exponential Map / 5.3:
Jacobi Fields / 5.4:
How the Flag Curvature's Sign Influences Geodesic Rays / 5.5:
References for Chapter 5
The Gauss Lemma and the Hopf-Rinow Theorem / Chapter 6:
The Gauss Lemma / 6.1:
The Gauss Lemma Proper / 6.1 A.:
An Alternative Form of the Lemma / 6.1 B.:
Is the Exponential Map Ever a Local Isometry? / 6.1 C.:
Finsler Manifolds and Metric Spaces / 6.2:
A Useful Technical Lemma / 6.2 A.:
Forward Metric Balls and Metric Spheres / 6.2 B.:
The Manifold Topology Versus the Metric Topology / 6.2 C.:
Forward Cauchy Sequences, Forward Completeness / 6.2 D.:
Short Geodesics Are Minimizing / 6.3:
The Smoothness of Distance Functions / 6.4:
On Minkowski Spaces / 6.4 A.:
On Finsler Manifolds / 6.4 B.:
Long Minimizing Geodesics / 6.5:
The Hopf-Rinow Theorem / 6.6:
References for Chapter 6
The Index Form and the Bonnet-Myers Theorem / Chapter 7:
Conjugate Points / 7.1:
The Index Form / 7.2:
What Happens in the Absence of Conjugate Points? / 7.3:
Geodesics Are Shortest Among "Nearby" Curves / 7.3 A.:
A Basic Index Lemma / 7.3 B.:
What Happens If Conjugate Points Are Present? / 7.4:
The Cut Point Versus the First Conjugate Point / 7.5:
Ricci Curvatures / 7.6:
The Ricci Scalar Ric and the Ricci Tensor Ric[subscript ij] / 7.6 A.:
The Interplay between Ric and Ric[subscript ij] / 7.6 B.:
The Bonnet-Myers Theorem / 7.7:
References for Chapter 7
The Cut and Conjugate Loci, and Synge's Theorem / Chapter 8:
Definitions / 8.1:
The Cut Point and the First Conjugate Point / 8.2:
Some Consequences of the Inverse Function Theorem / 8.3:
The Manner in Which c[subscript y] and i[subscript y] Depend on y / 8.4:
Generic Properties of the Cut Locus Cut[subscript x] / 8.5:
Additional Properties of Cut[subscript x] When M Is Compact / 8.6:
Shortest Geodesics within Homotopy Classes / 8.7:
Synge's Theorem / 8.8:
References for Chapter 8
The Cartan-Hadamard Theorem and Rauch's First Theorem / Chapter 9:
Estimating the Growth of Jacobi Fields / 9.1:
When Do Local Diffeomorphisms Become Covering Maps? / 9.2:
Some Consequences of the Covering Homotopy Theorem / 9.3:
The Cartan-Hadamard Theorem / 9.4:
Prelude to Rauch's Theorem / 9.5:
Transplanting Vector Fields / 9.5 A.:
A Second Basic Property of the Index Form / 9.5 B.:
Flag Curvature Versus Conjugate Points / 9.5 C.:
Rauch's First Comparison Theorem / 9.6:
Jacobi Fields on Space Forms / 9.7:
Applications of Rauch's Theorem / 9.8:
References for Chapter 9
Special Finsler Spaces over the Reals / Part 3:
Berwald Spaces and Szabo's Theorem for Berwald Surfaces / Chapter 10:
Various Characterizations of Berwald Spaces / 10.0:
Examples of Berwald Spaces / 10.3:
A Fact about Flat Linear Connections / 10.4:
Characterizing Locally Minkowski Spaces by Curvature / 10.5:
Szabo's Rigidity Theorem for Berwald Surfaces / 10.6:
The Theorem and Its Proof / 10.6 A.:
Distinguishing between y-local and y-global / 10.6 B.:
References for Chapter 10
Randers Spaces and an Elegant Theorem / Chapter 11:
The Importance of Randers Spaces / 11.0:
Randers Spaces, Positivity, and Strong Convexity / 11.1:
A Matrix Result and Its Consequences / 11.2:
The Geodesic Spray Coefficients of a Randers Metric / 11.3:
The Nonlinear Connection for Randers Spaces / 11.4:
A Useful and Elegant Theorem / 11.5:
The Construction of y-global Berwald Spaces / 11.6:
The Algorithm / 11.6 A.:
An Explicit Example in Three Dimensions / 11.6 B.:
References for Chapter 11
Constant Flag Curvature Spaces and Akbar-Zadeh's Theorem / Chapter 12:
Characterizations of Constant Flag Curvature / 12.0:
Useful Interpretations of E and E / 12.2:
Growth Rates of Solutions of E + [lambda]E = 0 / 12.3:
Akbar-Zadeh's Rigidity Theorem / 12.4:
Formulas for Machine Computations of K / 12.5:
The Geodesic Spray Coefficients / 12.5 A.:
The Predecessor of the Flag Curvature / 12.5 B.:
Maple Codes for the Gaussian Curvature / 12.5 C.:
A Poincare Disc That Is Only Forward Complete / 12.6:
The Example and Its Yasuda-Shimada Pedigree / 12.6 A.:
The Finsler Function and Its Gaussian Curvature / 12.6 B.:
Geodesics; Forward and Backward Metric Discs / 12.6 C.:
Consistency with Akbar-Zadeh's Rigidity Theorem / 12.6 D.:
Non-Riemannian Projectively Flat S[superscript 2] with K = 1 / 12.7:
Bryant's 2-parameter Family of Finsler Structures / 12.7 A.:
A Specific Finsler Metric from That Family / 12.7 B.:
References for Chapter 12
Riemannian Manifolds and Two of Hopf's Theorems / Chapter 13:
The Levi-Civita (Christoffel) Connection / 13.1:
Curvature / 13.2:
Symmetries, Bianchi Identities, the Ricci Identity / 13.2 A.:
Sectional Curvature / 13.2 B.:
Ricci Curvature and Einstein Metrics / 13.2 C.:
Warped Products and Riemannian Space Forms / 13.3:
One Special Class of Warped Products / 13.3 A.:
Spheres and Spaces of Constant Curvature / 13.3 B.:
Standard Models of Riemannian Space Forms / 13.3 C.:
Hopf's Classification of Riemannian Space Forms / 13.4:
The Divergence Lemma and Hopf's Theorem / 13.5:
The Weitzenbock Formula and the Bochner Technique / 13.6:
References for Chapter 13
Minkowski Spaces, the Theorems of Deicke and Brickell / Chapter 14:
Generalities and Examples / 14.1:
The Riemannian Curvature of Each Minkowski Space / 14.2:
The Riemannian Laplacian in Spherical Coordinates / 14.3:
Deicke's Theorem / 14.4:
The Extrinsic Curvature of the Level Spheres of F / 14.5:
The Gauss Equations / 14.6:
The Blaschke-Santalo Inequality / 14.7:
The Legendre Transformation / 14.8:
A Mixed-Volume Inequality, and Brickell's Theorem / 14.9:
References for Chapter 14
Bibliography
Index
Preface
Acknowledgments
Finsler Manifolds and Their Curvature / Part 1:
48.

図書

図書
Franco Vivaldi
出版情報: Boca Raton, Fla. : Chapman & Hall/CRC, c2001  xi, 223 p. ; 24 cm
シリーズ名: Chapman & Hall/CRC mathematics
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What is Maple? / 1:
Integers and rationals / 2:
Integers / 2.1:
Arithmetical expressions / 2.2:
Some Maple / 2.3:
Divisibility / 2.4:
Rationals / 2.5:
Primes / 2.6:
Standard library functions / 2.7:
Sets and functions / 3:
Sets / 3.1:
Sets with Maple / 3.2:
Functions / 3.3:
User-defined functions / 3.4:
Sequences / 4:
Basics / 4.1:
Sequences with Maple / 4.2:
Plotting the elements of a sequence / 4.3:
Periodic and eventually periodic sequences / 4.4:
Some non-periodic sequences / 4.5:
Basic counting sequences / 4.6:
Sequences defined recursively / 4.7:
Real and complex numbers / 5:
Digits of rationals / 5.1:
Real numbers / 5.2:
Random and pseudo-random digits* / 5.3:
Complex numbers / 5.4:
Structure of expressions / 5.5:
Analysis of an expression / 6.1:
More on substitutions / 6.2:
Functions acting on operands of expressions / 6.3:
Polynomials and rational functions / 7:
Polynomials / 7.1:
Polynomial arithmetic / 7.2:
Rational functions / 7.3:
Basic manipulations / 7.4:
Partial fractions decomposition* / 7.5:
Finite sums and products / 8:
Sums and products with Maple / 8.1:
Symbolic evaluation of sums and products / 8.3:
Double sums and products / 8.4:
Sums and products as recursive sequences / 8.5:
Elements of programming / 9:
Iteration / 9.1:
Study of an eventually periodic sequence / 9.2:
Conditional execution* / 9.3:
Procedures* / 9.4:
Vector spaces / 10:
Cartesian product of sets / 10.1:
Vectors with Maple / 10.2:
Matrices / 10.4:
Matrices with Maple / 10.5:
Modular arithmetic* / 11:
A modular system / 11.1:
Arithmetic of equivalence classes / 11.2:
Some arithmetical constructions in F[subscript p] / 11.3:
Some abstract structures* / 12:
The axioms of arithmetic / 12.1:
Metric spaces / 12.2:
Rings and fields / 12.3:
What is Maple? / 1:
Integers and rationals / 2:
Integers / 2.1:
49.

図書

図書
Kai-Seng Chou, Xi-Ping Zhu
出版情報: Boca Raton, Flo. : Chapman & Hall/CRC, c2001  ix, 255 p. ; 24 cm
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Preface
Basic Results / 1:
Short time existence / 1.1:
Facts from the parabolic theory / 1.2:
The evolution of geometric quantities / 1.3:
Invariant Solutions for the Curve Shortening Flow / 2:
Travelling waves / 2.1:
Spirals / 2.2:
The support function of a convex curve / 2.3:
Self-similar solutions / 2.4:
The Curvature-Eikonal Flow for Convex Curves / 3:
Blaschke Selection Theorem / 3.1:
Preserving convexity and shrinking to a point / 3.2:
Gage-Hamilton Theorem / 3.3:
The contracting case of the ACEF / 3.4:
The stationary case of the ACEF / 3.5:
The expanding case of the ACEF / 3.6:
The Convex Generalized Curve Shortening Flow / 4:
Results from the Brunn-Minkowski Theory / 4.1:
The AGCSF for [sigma] in (1/3, 1) / 4.2:
The affine curve shortening flow / 4.3:
Uniqueness of self-similar solutions / 4.4:
The Non-convex Curve Shortening Flow / 5:
An isoperimetric ratio / 5.1:
Limits of the rescaled flow / 5.2:
Classification of singularities / 5.3:
A Class of Non-convex Anisotropic Flows / 6:
The decrease in total absolute curvature / 6.1:
The existence of a limit curve / 6.2:
Shrinking to a point / 6.3:
A whisker lemma / 6.4:
The convexity theorem / 6.5:
Embedded Closed Geodesics on Surfaces / 7:
Basic results / 7.1:
The limit curve / 7.2:
Convergence to a geodesic / 7.3:
The Non-convex Generalized Curve Shortening Flow / 8:
The number of convex arcs / 8.1:
Removal of interior singularities / 8.3:
The almost convexity theorem / 8.5:
Bibliography
Index
Preface
Basic Results / 1:
Short time existence / 1.1:
50.

図書

図書
Mohamed A. Khamsi, William A. Kirk
出版情報: New York : J. Wiley, c2001  x, 302 p. ; 25 cm
シリーズ名: A Wiley-Interscience publication
Pure and applied mathematics
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Preface
Metric Spaces
Introduction
Metric Contraction Principles
Hyperconvex Spaces
"Normal" Structures in Metric Spaces
Banach Spaces
Banach Spaces: Introduction
Continuous Mappings in Banach Spaces
Metric Fixed Point Theory
Banach Space Ultrapowers
Appendix: Set Theory
Bibliography
Index
Preface
Metric Spaces
Introduction
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