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1.

図書
図書
1. Logarithmic integral equations in electromagnetics
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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2.

図書
図書
2. Random forests
Yu.L. Pavlov
出版情報: Utrecht : VSP, 2000  122 p. ; 26 cm
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3.

図書
図書
3. Local algebra
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
4.

図書
図書
4. Perturbation analysis of optimization problems
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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5.

図書
図書
5. Physical combinatorics (: us ; : sz)
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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6.

図書
図書
6. Profinite groups
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：
7.

図書
図書
7. An introduction to K-theory for C*-algebras (: hbk ; : pbk)
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：
8.

図書
図書
8. Vector integration and stochastic integration in Banach spaces
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.：
9.

図書
図書
9. Proceedings of International Conference on: Free Boundary Problems : Theory and Applications (I ; II)
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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10.

図書
図書
10. An introduction to Riemann-Finsler geometry (: hbk)
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：
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