1.
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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2.
図書
Yu.L. Pavlov
出版情報:
Utrecht : VSP, 2000 122 p. ; 26 cm
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3.
図書
Jean-Pierre Serre ; translated from the French by Chee Whye Chin
目次情報:
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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
J. Frédéric Bonnans, Alexander Shapiro
5.
図書
Masaki Kashiwara, Tetsuji Miwa, editors
6.
図書
Luis Ribes, Pavel Zalesskii
目次情報:
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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
M. Rørdam, F. Larsen, N. Laustsen
目次情報:
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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
Nicolae Dinculeanu
目次情報:
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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
edited by N. Kenmochi
10.
図書
D. Bao, S.-S. Chern, Z. Shen
目次情報:
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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：
11.
図書
H. Hauser ... [et al.], editors
12.
図書
Steven Weinberg
目次情報:
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Preface to Volume III
Notation
Historical introduction / 24：
Supersymmetry algebras / 25：
Supersymmetric field theories / 26：
Supersymmetric gauge theories / 27：
Supersymmetric versions of the standard model / 28：
Beyond perturbation theory / 29：
Supergraphs / 30：
Supergravity / 31：
Supersymmetry in higher dimensions / 32：
Author index
Subject index
Preface to Volume III
Notation
Historical introduction / 24：
13.
図書
Frank den Hollander
目次情報:
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Preface
Theory / Part A.：
Large Deviations for I.I.D. Sequences: Part 1 / Chapter I.：
Introduction / I.1.：
An example: coin tossing / I.2.：
Cramer's Theorem for the empirical average / I.3.：
Comments / I.4.：
A toy application of Cramer / I.5.：
Large Deviations for I.I.D. Sequences: Part 2 / Chapter II.：
Sanov's Theorem for the empirical measure / II.1.：
The pair empirical measure / II.2.：
A toy application of Sanov for pairs / II.3.：
A contraction principle / II.4.：
The empirical process / II.5.：
Extension to countable state space / II.6.：
General Theory / Chapter III.：
The large deviation principle (LDP) / III.1.：
Varadhan's Lemma / III.2.：
The LDP for integrals of exponential functionals / III.4.：
The Contraction Principle / III.5.：
The weak LDP / III.6.：
Convexity / III.7.：
Relation to earlier results / III.8.：
Large Deviations for Markov Sequences / Chapter IV.：
Radon-Nikodym formula / IV.1.：
The LDP for discrete-time Markov chains / IV.2.：
The LDP for continuous-time Markov chains / IV.3.：
Large Deviations for Dependent Sequences / Chapter V.：
Preliminaries / V.1.：
The Gartner-Ellis Theorem / V.2.：
Conclusion / V.3.：
Applications / Part B.：
Statistical Hypothesis Testing / Chapter VI.：
The statistical problem / VI.1.：
Large deviation estimates on test optimality / VI.2.：
Random Walk in Random Environment / Chapter VII.：
Random drifts / VII.1.：
The LDP for the speed / VII.2.：
The LDP for the hitting times / VII.3.：
From hitting times to speed / VII.4.：
Random continued fractions / VII.5.：
Analysis of the rate functions / VII.6.：
Comparison with homogeneous random walk / VII.7.：
Concluding remarks / VII.8.：
Heat Conduction with Random Sources and Sinks / Chapter VIII.：
The parabolic Anderson model / VIII.1.：
Growth rate of the moments / VIII.2.：
Analysis of the variational problem / VIII.3.：
Correlation structure / VIII.4.：
Derivation of the growth rate / VIII.5.：
Transformation of the variational problem / VIII.6.：
Polymer Chains / VIII.7.：
A polymer model: self-repellent random walk / IX.1.：
Linear speed / IX.2.：
The LDP for bridges / IX.3.：
Step 1: Adding drift / IX.4.：
Step 2: Markovian nature of the total local times / IX.5.：
Step 3: Key variational problem / IX.6.：
Step 4: Analysis of the rate function for bridges / IX.7.：
Step 5: Identification of the speed / IX.8.：
The LDP without the bridge condition / IX.9.：
Interacting Diffusions / IX.10.：
The interaction Hamiltonian / X.1.：
The LDP for the double layer empirical measure / X.2.：
A simpler representation for the rate function / X.4.：
McKean-Vlasov equation / X.5.：
The Kuramoto model / X.6.：
Solutions to the Exercises / X.7.：
Bibliography
Index
Glossary of Symbols
Errata
Preface
Theory / Part A.：
Large Deviations for I.I.D. Sequences: Part 1 / Chapter I.：
14.
図書
Hari Bercovici, Ciprian Foias, editors
15.
図書
Israel Gohberg, Seymour Goldberg, Nahum Krupnik
16.
図書
by Han-lin Chen
出版情報:
Dordrecht ; Boston : Kluwer Academic, c2000 xii, 226 p. ; 25 cm
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17.
図書
Tai-Ping Liu
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Preface
Hyperbolic Conservation Laws / Chapter 1.：
Preliminaries / 1.1：
Riemann Problem / 1.2：
Wave Interactions / 1.3：
Random Choice Method / 1.4：
Nonlinear Superposition / 1.5：
Large-Time Behavior and Regularity / 1.6：
Viscous Conservation Laws / Chapter 2.：
The Burgers Equation / 2.1：
Diffusion Waves / 2.3：
Viscous Shocks / 2.4：
Viscous Rarefaction Waves / 2.5：
Concluding Remarks / 2.6：
Bibliography
Index
Preface
Hyperbolic Conservation Laws / Chapter 1.：
Preliminaries / 1.1：
18.
図書
R. MacKenzie, M.B. Paranjape, W.J. Zakrzewski, [editors]
19.
図書
E.B. Dynkin ; A.A. Yushkevich, G.M. Seitz, A.L. Onishchik, editors
出版情報:
Providence, R.I. : American Mathematical Society , Cambridge, Mass. : International Press, c2000 xxvi, 798 p. ; 27 cm
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Lie groups and Lie algebras: Dynkin and Lie theory / G. M. SeitzPart I：
On the work of E. B. Dynkin in the theory of Lie groups / F. I. Karpelevich ; A. L. Onishchik ; E. B. Vinberg
Correction to On the work of E. B. Dynkin in the theory of Lie groups
Classification of simple Lie groups / E. B. Dynkin
Calculation of the coefficients in the Campbell-Hausdorff formula
The maximal subgroups of the classical groups
Comments on Maximal subgroups of the classical groups
Semisimple subalgebras of semisimple Lie algebras
Comments on the paper Semisimple subalgebras of semisimple Lie algebras
Construction of primitive cycles in compact Lie groups
Topological characteristics of homomorphisms of compact Lie groups
Comments on the paper Topological characteristics of homomorphisms of compact Lie groups
Dynkin and modern Lie theory / B. Kostant
Comments on the impact of Dynkin's work on current research in representation theory / D. A. Vogan
Coxeter-Dynkin diagrams and singularities / A. Gabrielov
Lie groups in physics / K. Gottfried
Dynkin diagrams in the physics of particles, fields and strings / Y. Ne'eman
Probability theory: Dynkin and probability theory / A. A. YushkevichPart II：
Necessary and sufficient statistics for a family of probability distributions
Some limit theorems for sums of independent random variables with infinite mathematical expectations
Markov processes and semigroups of operators
Strong Markov processes
Infinitesimal operators of Markov processes
The natural topology and excessive functions connected with a Markov process
Random walk on groups with a finite number of generators / M. B. Malyutov
The optimum choice of the instant for stopping a Markov process
Brownian motion in certain symmetric spaces and nonnegative eigenfunctions of the Laplace-Beltrami operator
Diffusion of tensors
Game variant of a problem on optimal stopping
Determining functions of Markov processes and corresponding dual regular classes / S. E. Kuznetsov
Economic equilibrium under uncertainty
Comments on Economic equilibrium under uncertainty / I. V. Evstigneev
Markov processes and random fields
Green's and Dirichlet spaces associated with fine Markov processes
Markov processes as a tool in field theory
Symmetric statistics, Poisson point processes, and multiple Wiener integrals / A. Mandelbaum
Gaussian and non-Gaussian random fields associated with Markov processes
Author's correction to Guassian and non-Gaussian random fields associated with Markov processes.
An application of flows to time shift and time reversal in stochastic processes
Author's comments on An application of flows to time shift and time reversal in stochastic processes
Representation for functionals of superprocesses by multiple stochastic integrals, with applications to self-intersection local times
A probabilistic approach to one class of nonlinear differential equations
Superdiffusions and parabolic nonlinear differential equations
Comments on Superdiffusions and parabolic nonlinear differential equations
Dynkin and the theory of Markov processes / P. A. Meyer
To the history of strong Markov property
On compactifications of symmetric spaces / M. A. Olshanetsky
Dynkin's contributions to superprocesses and partial differential equations / J.-F. Le Gall
Dynkin's work in mathematical economics
Acknowledgments
Lie groups and Lie algebras: Dynkin and Lie theory / G. M. SeitzPart I：
On the work of E. B. Dynkin in the theory of Lie groups / F. I. Karpelevich ; A. L. Onishchik ; E. B. Vinberg
Correction to On the work of E. B. Dynkin in the theory of Lie groups
20.
図書
Yun Fan, Q.Y. Xiong, Y.L. Zheng
出版情報:
Farrer Road, Singapore : World Scientific, c2000 x, 246 p. ; 23 cm
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Preface
Preliminaries / 1：
Sets / 1.1：
Logic / 1.2：
Relations / 1.3：
Maps / 1.4：
Zorn's Lemma / 1.5：
Groups / 2：
Transformations and Permutations / 2.1：
Subgroups / 2.2：
Homomorphisms, Isomorphisms / 2.4：
Cosets / 2.5：
Normal Subgroups, Quotient Groups / 2.6：
Homomorphism Theorems / 2.7：
Cyclic Groups, Orders of Elements / 2.8：
Direct Products / 2.9：
Rings / 3：
Fundamentals / 3.1：
Zero Divisors, Invertible Elements / 3.2：
Ideals, Residue Rings / 3.3：
Prime Ideals, Maximal Ideals / 3.4：
Direct Sums / 3.6：
Fraction Fields of Integral Domains / 3.7：
Polynomial Rings / 3.8：
Factorial Domains / 3.9：
Polynomial Rings over Factorial Rings / 3.10：
Modules / 4：
Homomorphisms / 4.1：
Direct Products, Direct Sums / 4.3：
Exact Sequences of Homomorphisms / 4.4：
Free Modules, Matrices over Rings / 4.5：
Matrices over Division Rings / 4.6：
Matrices over Commutative Rings / 4.7：
Algebras over Commutative Rings / 4.8：
Tensor Products / 4.9：
Projective Modules, Injective Modules / 4.10：
Fields / 5：
Subfields and Extensions / 5.1：
Single Extensions / 5.2：
Algebraic Extensions / 5.3：
Splitting Fields, Normal Extensions / 5.4：
Two Applications / 5.5：
Separability, Multiple Roots / 5.6：
Finite Fields / 5.7：
Coding / 5.8：
p-adic Numbers / 5.9：
Quaternions / 5.10：
Index
Preface
Preliminaries / 1：
Sets / 1.1：
21.
図書
Frank C. Hoppensteadt
目次情報:
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Linear Systems
Dynamical Systems
Stability Methods for Nonlinear Systems
Bifurcation and Topological Methods
Regular Perturbation Methods
Iterations and Perturbations
Methods of Averaging
Quasistatic-State Approximations
References
Index
Linear Systems
Dynamical Systems
Stability Methods for Nonlinear Systems
22.
図書
edited by Toshiyuki Kobayashi ... [et al.]
目次情報:
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Preface
Characters of non-linear groups / Jeffrey Adams
Selberg's eigenvalue conjecture and the Siegel zeros for Hecke L-series / Erik Balslev ; Alexei Venkov
Proprietes asymptotiques des groupes lineaires (II) / Yves Benoist
Matrix coefficients of the principal P[subscript J]-series and the middle discrete series of SU (2, 2) / Takahiro Hayata ; Harutaka Koseki ; Takayuki Oda
K-type sturucture in the principal series of GL[subscript 3], I / Roger Howe
Discretely decomposable restrictions of unitary representations of reductive Lie groups--examples and conjectures / Toshiyuki Kobayashi
On [Lambda]g for a semisimple Lie algebra g, as an equivariant module over the symmetric algebra S(g) / Bertram Kostant
Tilting modules and their applications / Olivier Mathieu
On the theta lift for the trivial representation / Eng-Chye Tan
Hypergeometric systems and Radon transforms for Hermitian symmetric spaces / Toshiyuki Tanisaki
Orbits on homogeneous spaces of arithmetic origin and approximations / George Tomanov
A Langlands classification for unitary representations / David A. Vogan, Jr.
Modular transformation of twisted characters of admissible representations and fusion algebras associated to non-symmetric transformation matrices / Minoru Wakimoto
Symposia
Preface
Characters of non-linear groups / Jeffrey Adams
Selberg's eigenvalue conjecture and the Siegel zeros for Hecke L-series / Erik Balslev ; Alexei Venkov
23.
図書
Irena Lasiecka, Roberto Triggiani
24.
図書
Michael E. Tarter
出版情報:
Natick, Mass. : A K Peters, c2000 xiii, 386 p. ; 24 cm
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Preface
Introduction / 1：
Background / 1.1：
A fictional example / 1.2：
Curves and statistical history / 1.3：
Model and Distribution Terminology / 2：
Modeling background / 2.1：
Representative number / 2.2：
Curve types / 2.3：
Distribution and data terminology / 2.4：
Parameter validity and property existence / 2.5：
Estimator terminology / 2.6：
Degenerate curves / 2.7：
Variability and Related Curve Properties / 3：
Uncertainty and variability / 3.1：
The absolute deviation curve property / 3.2：
The general AD and the ADM curve properties / 3.3：
Curve property selection / 3.4：
The history of variability appreciation / 3.5：
Simplistic approaches and the history of probability / 3.6：
Moments and Curve Uncertainty / 4：
E and Var Geometry / 4.1：
Higher order moments and the indicator function / 4.2：
Early statistical models / 4.3：
Early statistical models and higher order moments / 4.4：
Curve sub-types and model choice / 4.5：
Goodness of fit / 5：
Neyman's and alternative criteria / 5.1：
Criteria, metrics and estimators / 5.2：
The Kolmogoroff-Smirnoff criteria / 5.3：
Bernoulli variation and the Cauchy density / 5.4：
Comparative goodness of fit / 5.5：
Variates, Variables and Regression / 6：
Variates and variables / 6.1：
Variates and subjects / 6.2：
Expressions, algorithms and life tables / 6.3：
Distinctions between curve types / 6.4：
Curve properties and symbols / 6.5：
Variates, variables, and E[subscript f](Y|x) regression / 6.6：
[mu](x), E[subscript f] (Y|x) and regression alternatives / 6.7：
Mixing Parameters and Data-generation models / 7：
An introduction to data-generation models / 7.1：
Error, regression, and probit, models / 7.2：
Regression and data-generation models / 7.3：
Probability, proportion, and data-generation models / 7.4：
The generation of contagious model and mixture model data / 7.5：
The Association Parameter [rho] / 8：
Response, key, and nuisance, variates / 8.1：
The association parameter [rho] / 8.2：
Conditional, joint and marginal, notation / 8.3：
The sample and the population correlation coefficient / 8.4：
Correlation geometry / 8.5：
Regression and Association Parameters / 9：
The curse of dimensionality / 9.1：
Multiple variable interdependence / 9.2：
Logit and linear models / 9.3：
Dual regression functions / 9.4：
Parameters, Confounding, and Least Squares / 10：
Ideal objects / 10.1：
Linear data-generation models and mixture models / 10.2：
Parameter distinctiveness / 10.3：
Representational uniqueness and model fitting / 10.4：
Model-fitting considerations / 10.5：
The variance curve property and bathtub functions / 10.6：
Regression and least squares / 10.7：
Nonparametric Adjustment / 11：
Age-adjustment and logistic regression / 11.1：
Crude and specific rates / 11.2：
Age-adjustment; marginal, joint, and conditional curves / 11.3：
Age-adjustment and partial correlation / 11.4：
Direct and indirect adjustment / 11.5：
The computation of adjusted rates / 11.6：
Continuous Variate Adjustment / 12：
Observed and expected rates / 12.1：
Trivariate data-generation and additive regression models / 12.2：
Regression and data generation / 12.3：
Correlation, regression, and nuisance variables / 12.4：
Trivariate Normality graphics / 12.5：
Procedural Road Maps / 13：
The organization of statistical data and statistical methods / 13.1：
Log and log(-log) transformations / 13.2：
Methodological alternatives / 13.3：
Conditional and joint density models / 13.4：
Model-based and Generalized Representation / 14：
Multiple properties and parameters / 14.1：
Specification and generalized representation / 14.2：
Identifiability of generalized versus extended model representation / 14.3：
The E(X) curve property's relationship to location and scale / 14.4：
Parameters, Transformations, and Quantiles / 15：
Location and scale parameter representation of continuous variates / 15.1：
[rho]-focused transformations and [sigma]-focused transformations / 15.2：
Quantiles, quartiles, and box-and-whisker plots / 15.3：
Normal ranges and box sizes / 15.4：
Confidence bands and prediction bands / 15.5：
Notches, stems, and leaves / 15.6：
The log transformation and skewness / 15.7：
Noncentrality Parameters and Degress of Freedom / 16：
The (C[subscript 1]|A[subscript 2]) case and variate-variable relationships / 16.1：
Invariance and confounding / 16.2：
ANOVA tables and confounding / 16.3：
Contingency tables and the parameter v / 16.4：
Student-t and Cauchy densities / 16.5：
Parameter-Based Estimation / 17：
Likelihood and BLU estimation / 17.1：
Censoring and incompleteness / 17.2：
Outliers and errors / 17.3：
Ordered variates and subscripts / 17.4：
BLU estimators / 17.5：
BLU estimation and censoring / 17.6：
BLU estimators and alternatives / 17.7：
Inference and Composite Variates / 18：
Curves and composite variates / 18.1：
Specific sampling distributions / 18.2：
The mean's variance formula and mixtures / 18.3：
Inference and a two-valued metric / 18.4：
The one tail z-test / 18.5：
Parameters and Test Statistics / 19：
The parameter [Delta] / 19.1：
Power and efficiency / 19.2：
Power and test considerations / 19.3：
The sample mean and the sample median / 19.4：
Tables and the details of test construction / 19.5：
Power, efficiency and BLU estimators / 19.6：
Curve Truncation and the Curve e(x) / 20：
Expectation as a limit and the effects of truncation / 20.1：
Truncation symmetry / 20.2：
Truncation and bias / 20.3：
Truncation and the curve e(x) / 20.4：
When are curve properties relevant and when are model parameters relevant / 20.5：
Models and Notation / I：
Notation historical background / I.1：
Specific models, the Normal / I.2：
Specific models, lognormals and related curves / I.3：
Model families / I.4：
Mixtures and Bayesian statistics / I.5：
Notational conventions about moments and variates / I.6：
Variate Independence and Curve Identity / II：
Independence and identical distribution / II.1：
Regression notation / II.2：
General Statistical and Mathematical Notation / III：
References
Index
Preface
Introduction / 1：
Background / 1.1：
25.
図書
Dieter A. Wolf-Gladrow
目次情報:
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Introduction
Preface / 1.1：
Overview / 1.2：
The basic idea of lattice-gas cellular automata and lattice Boltzmann models / 1.3：
Cellular Automata / 2：
What are cellular automata? / 2.1：
A short history of cellular automata / 2.2：
One-dimensional cellular automata / 2.3：
Two-dimensional cellular automata / 2.4：
Lattice-gas cellular automata / 3：
The HPP lattice-gas cellular automata / 3.1：
The FHP lattice-gas cellular automata / 3.2：
Lattice tensors and isotropy in the macroscopic limit / 3.3：
Desperately seeking a lattice for simulations in three dimensions / 3.4：
FCHC / 3.5：
The pair interaction (PI) lattice-gas cellular automata / 3.6：
Multi-speed and thermal lattice-gas cellular automata / 3.7：
Zanetti ("staggered") invariants / 3.8：
Lattice-gas cellular automata: What else? / 3.9：
Some statistical mechanics / 4：
The Boltzmann equation / 4.1：
Chapman-Enskog: From Boltzmann to Navier-Stokes / 4.2：
The maximum entropy principle / 4.3：
Lattice Boltzmann Models / 5：
From lattice-gas cellular automata to lattice Boltzmann models / 5.1：
BGK lattice Boltzmann model in 2D / 5.2：
Hydrodynamic lattice Boltzmann models in 3D / 5.3：
Equilibrium distributions: the ansatz method / 5.4：
Hydrodynamic LBM with energy equation / 5.5：
Stability of lattice Boltzmann models / 5.6：
Simulating ocean circulation with LBM / 5.7：
A lattice Boltzmann equation for diffusion / 5.8：
Lattice Boltzmann model: What else? / 5.9：
Summary and outlook / 5.10：
Appendix / 6：
Boolean algebra / 6.1：
FHP: After some algebra one finds ... / 6.2：
Coding of the collision operator of FHP-II and FHP-III in C / 6.3：
Thermal LBM: derivation of the coefficients / 6.4：
SchlA[$$$]fli symbols / 6.5：
Notation, symbols and abbreviations / 6.6：
Introduction
Preface / 1.1：
Overview / 1.2：
26.
図書
edited by B. Brent Gordon ... [et al.]
27.
図書
edited by C. Corduneanu and I.W. Sandberg
28.
図書
Saber N. Elaydi
出版情報:
Boca Raton, Fla. : Chapman & Hall/CRC, c2000 xiii, 355 p. ; 25 cm
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List of Symbols
Preface
The Stability of One-Dimensional Maps / 1：
Maps vs. Difference Equations / 1.1：
Maps vs. Differential Equations / 1.2：
Linear Maps/Difference Equations / 1.3：
Fixed (Equilibrium) Points / 1.4：
Graphical Iteration and Stability / 1.5：
Criteria for Stability / 1.6：
Hyperbolic Fixed Points / 1.6.1：
Nonhyperbolic Fixed Points / 1.6.2：
Periodic Points and their Stability / 1.7：
The Period-Doubling Route to Chaos / 1.8：
Fixed Points / 1.8.1：
2-Cycles / 1.8.2：
2[superscript 2]-Cycles / 1.8.3：
Beyond [mu][characters not reproducible] / 1.8.4：
Applications / 1.9：
A Genotype Selection Model / 1.9.1：
Sharkovsky's Theorem and Bifurcation / 2：
The Mystery of Period 3 / 2.1：
Converse of Sharkovsky's Theorem / 2.2：
Basin of Attraction / 2.3：
The Schwarzian Derivative / 2.4：
Bifurcation / 2.5：
The Lorenz Map / 2.6：
Appendix
Chaos in One Dimension / 3：
Introduction / 3.1：
Metric Spaces / 3.2：
Transitivity / 3.3：
Sensitive Dependence and Liapunov Exponents / 3.4：
Definition of Chaos / 3.5：
Symbolic Dynamics / 3.6：
Conjugacy / 3.7：
Stability of Two-Dimensional Maps / 4：
Linear Maps vs. Linear Systems / 4.1：
Computing A[superscript n] / 4.2：
Fundamental Set of Solutions / 4.3：
Second-Order Difference Equations / 4.4：
Phase Space Diagrams / 4.5：
Stability Notions / 4.6：
Stability of Linear Systems / 4.7：
Liapunov Functions for Nonlinear Maps / 4.8：
Linear Systems Revisited / 4.9：
Stability via Linearization / 4.10：
The Hartman-Grobman Theorem / 4.10.1：
The Stable Manifold Theorem / 4.10.2：
The Kicked Rotator and the Henon Map / 4.11：
The Henon Map / 4.11.2：
Discrete Epidemic Model for Gonorrhea / 4.11.3：
Perennial Grass / 4.11.4：
Chaos in Two Dimensions / 5：
Hyperbolic Anosov Toral Automorphism / 5.1：
Subshifts of Finite Type / 5.2：
The Horseshoe and Henon Maps / 5.3：
The Henon Map Revisited / 5.3.1：
Center Manifolds / 5.4：
Neimark-Sacker (Hopf) Bifurcation / 5.5：
Fractals / 6：
Examples of Fractals / 6.1：
The Dimension of a Fractal / 6.2：
Iterated Function System / 6.3：
Mathematical Foundation of Fractals / 6.4：
The Collage Theorem and Image Compression / 6.5：
The Julia and Mandelbrot Sets / 7：
Mapping by Functions on the Complex Domain / 7.1：
The Riemann Sphere / 7.2：
The Julia Set / 7.3：
Topological Properties of the Julia Set / 7.4：
Newton's Method in the Complex Plane / 7.5：
The Mandelbrot Set / 7.6：
Bibliography
Answers to Selected Problems
Index
List of Symbols
Preface
The Stability of One-Dimensional Maps / 1：
29.
図書
Editors, Thomas Peternell, Frank-Olaf Schreyer
出版情報:
Berlin : Walter de Gruyter, 2000 x, 406 p. ; 25 cm
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Almost-lines and quasi-lines on projective manifolds / Lucian Badescu ; Mauro C. Beltrametti ; Paltin Ionescu
Transfert de metrique / Daniel Barlet ; Jon Magnusson
On the classification of K3 surfaces with nine cusps / Wolf P. Barth
Complex manifolds with split tangent bundle / Arnaud Beauville
Projections from subvarieties / Alan Howard ; Michael Schneider ; Andrew J. Sommese
Generalized Petersson-Weil metric on the Douady space of embedded manifolds / Indranil Biswas ; Georg Schumacher
On simply connected Godeaux surfaces / Fabrizio Catanese ; Roberto Pignatelli
On the Wahl map of plane nodal curves / Ciro Ciliberto ; Angelo Felice Lopez ; Rick Miranda
A remark on projective embeddings of varieties with non-negative cotangent bundles / Lawrence Ein ; Bo Ilic ; Robert Lazarsfeld
The fundamental group's structure of the complement of some configurations of real line arrangements / David Garber ; Mina Teicher
Kahlerian structures on symplectic reductions / Peter Heinzner ; Alan Huckleberry
Nef divisors on moduli spaces of abelian varieties / Klaus Hulek
Abelian surfaces with two plane cubic curve fibrations and Calabi-Yau threefolds / Kristian Ranestad
Real algebraic threefolds IV. Del Pezzo fibrations / Janos Kollar
Seiberg-Witten invariants for 4-manifolds with b+ = 0 / Christian Okonek ; Andrei Teleman
A geometric proof of Ax' theorem / Jeroen G. Spandaw
A note on the Cayley-Bacharach property for vector bundles / Sheng-Li Tan ; Eckart Viehweg
The scientific work of Michael Schneider / Thomas Peternell
Michael Schneider-an alpine vita / Ulf Persson
Lectures of the Symposium
List of Authors and Participants
Almost-lines and quasi-lines on projective manifolds / Lucian Badescu ; Mauro C. Beltrametti ; Paltin Ionescu
Transfert de metrique / Daniel Barlet ; Jon Magnusson
On the classification of K3 surfaces with nine cusps / Wolf P. Barth
30.
図書
Jürgen M. Appell, Anatolij S. Kalitvin, Petr P. Zabrejko
目次情報:
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Preface
Introduction
Equations of Barbashin Type / Chapter I.：
Differential equations in Banach spaces / 1.：
Integro-differential equations of Barbashin type / 1.1.：
The evolution operator / 1.2.：
Special cases and examples / 1.3.：
Some auxiliary results / 1.4.：
Degenerate kernels / 1.5.：
Symmetric kernels / 1.6.：
Barbashin equations in the space C / 2.：
Linear operators in the space C / 2.1.：
The spaces [characters not reproducible] / 2.2.：
Compact and weakly compact operators / 2.3.：
Strongly continuous operator functions / 2.4.：
Norm-continuous operator functions / 2.5.：
Representation of the evolution operator / 2.6.：
Stamping and infra-stamping operators / 2.7.：
Barbashin equations in Lebesgue spaces / 3.：
Linear operators in the space L[subscript p] / 3.1.：
The space [characters not reproducible characters not reproducible](L[subscript p]) / 3.2.：
Sufficient conditions for regularity / 3.3.：
Barbashin equations in ideal spaces / 3.4.：
Ideal spaces / 4.1.：
Functions of two variables and vector functions / 4.2.：
Barbashin operators in ideal spaces / 4.3.：
The space [characters not reproducible characters not reproducible](X) / 4.4.：
Some spectral theory for Barbashin operators / 4.5.：
Theory of Linear Barbashin Equations / Chapter II.：
Stability of solutions / 5.：
Ljapunov and Ljapunov-Bohl exponents / 5.1.：
Perturbation of the Ljapunov-Bohl exponent / 5.2.：
Application to Barbashin operators / 5.3.：
Ljapunov functions / 5.4.：
Continuous dependence on parameters / 6.：
Continuous dependence of the evolution operator / 6.1.：
The first Bogoljubov theorem / 6.2.：
Smooth dependence / 6.4.：
Bounded and periodic solutions / 7.：
A fixed point principle / 7.1.：
The use of majorant functions / 7.2.：
The Green function / 7.4.：
Comparison of Green functions / 7.5.：
The second Bogoljubov theorem / 7.6.：
Application of Darbo's fixed point principle / 7.7.：
Application of the Fredholm alternative / 7.8.：
A general approach / 8.：
Explicit solution for a particular class / 8.2.：
An abstract degeneration result / 8.3.：
Stationary boundary value problems / 9.：
The abstract problem / 9.1.：
Equivalent operator equations / 9.2.：
Reduction to a two-dimensional integral equation / 9.3.：
Application of K-normed spaces / 9.4.：
Unbounded multipliers / 9.5.：
Non-stationary boundary value problems / 10.：
Equations with variable operators / 10.1.：
Partial Integral Operators / 10.2.：
General properties / 11.：
Continuity properties / 11.1.：
Regularity properties / 11.2.：
The associate operator / 11.3.：
Algebras of partial integral operators / 11.4.：
Operators in spaces with mixed norm / 12.：
Ideal spaces with mixed norm / 12.1.：
Lebesgue spaces with mixed norm / 12.2.：
Orlicz spaces with mixed norm / 12.3.：
Operator functions with values in [characters not reproducible][subscript p](L[subscript [infinity]]) and [characters not reproducible][subscript p](L[subscript 1]) / 12.4.：
Operator functions with values in [characters not reproducible][subscript p](L[subscript p]) / 12.5.：
Partial integral operators in the space C / 13.：
Weakly continuous functions / 13.1.：
Acting and boundedness conditions / 13.2.：
Operator functions with values in [characters not reproducible][subscript p](C) / 13.3.：
Spectral properties / 14.：
Essential spectra of bounded linear operators / 14.1.：
Application to partial integral operators in L[subscript 2] / 14.2.：
Application to other partial integral operators / 14.3.：
An index formula for partial integral operators / 14.4.：
The case of positive kernels / 14.5.：
Linear partial integral equations / 15.：
Fredholm equations / 15.1.：
Volterra equations / 15.2.：
Bounded and continuous solutions / 15.3.：
Using tensor products / 15.4.：
Using eigenfunction expansions / 15.5.：
Generalizations and Applications / Chapter IV.：
Generalized equations of Barbashin type / 16.：
Reduction to partial integral equations / 16.1.：
Volterra operators and Barbashin equations / 16.2.：
Generalized Barbashin equations / 16.3.：
Nonlinear equations and operators / 16.4.：
Barbashin equations with Uryson operators / 17.1.：
Equations with Hammerstein operators / 17.2.：
Surjectivity results for monotone operators / 17.4.：
Equations with monotone operators / 17.5.：
Variational methods / 17.6.：
The Newton-Kantorovich method / 18.：
The abstract Newton-Kantorovich method / 18.1.：
Lipschitz conditions for derivatives / 18.2.：
Lipschitz conditions for partial Uryson operators / 18.3.：
The case X = C(T [times] S) / 18.4.：
The case X = L[subscript infinity] (T [times] S) / 18.5.：
The case X = L[subscript p](T [times] S) (1 [less than or equal] p [ [infinity]) / 18.6.：
Applications of Barbashin equations / 19.：
Applications to probability theory / 19.1.：
Applications to evolution equations / 19.2.：
Systems with substantially distributed parameters / 19.3.：
The Kimura continuum-of-alleles model / 19.4.：
An application to a radiation problem / 19.5.：
Applications to astrophysics / 19.6.：
Plane-parallel transport problems / 19.7.：
Applications of partial integral equations / 20.：
Applications to elasticity theory / 20.1.：
Applications to mechanics of continuous media / 20.2.：
Mixed problems of evolutionary type / 20.3.：
Axially symmetric contact problems / 20.4.：
Creeping of non-uniformly aging bodies / 20.5.：
A unified approach to some equations of mechanics / 20.6.：
Other applications / 20.7.：
References
List of symbols
Index
Preface
Introduction
Equations of Barbashin Type / Chapter I.：
31.
図書
Fong Yuen, Wang Yuan
出版情報:
Singapore : Springer-Verlag, c2000 xi, 797 p. ; 24 cm
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32.
図書
edited by Yuriy M. Bunkov and Henri Godfrin
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Preface
Dictionary: Condensed matter - High energy physics & cosmology / G.E. Volovik
Classification of topological defects and their relevance to cosmology and elsewhere / T.W.B. Kibble
The Normal and Superfluid States of Liquid 3He / A.J. Leggett
Formation, interaction and observation of topological defects / T. Vachaspati
Shards of broken symmetry: topological defects as traces of the phase transition dynamics / W.H. Zurek, et al
'Grenoble' cosmological experiment: The Kibble-Zurek scenario in superfluid 3He / C. Bauerle, et al
'Aurore de Venise' - Cosmological scenario of the A-B phase transition in superfluid 3He / Y.M. Bunkov
Non-equilibrium phase transitions in condensed matter and cosmology: spinodal decomposition, condensates and defects / D. Boyanovsky, et al.
formation through boson condensation in quantum field theory / G. Vitiello
Magnetic monopoles and vortices in the standard model of electroweak interactions / A. Achucarro
Time-dependent Ginzburg-Landau theory and duality / A.M.J. Schakel
Broken Symmetry and Nonequilibrium Superfluid 3He: Circular Birefringence of Propagating Transverse Currents / J.A. Sauls
Relativistic dynamics of vortex defects in superfluids / B. Carter
Nucleation and pinning of vortices in 4He / E. Varoquaux
Topolotical defects in 3He superfluids / V.B. Eltsov ; M. Krusius
Regular vortex production by a moving wire in superfluid 3He-B / D.I. Bradley ; G.R. Pickett
3He and Universe parallelism
Authors Index
Subject Index
The `Grenoble' cosmological experiment: The Kibble-Zurek scenario in superfluid 3He / W.H. Zurek, et al. ; C. BSuerle, et al.
`Aurore de Venise' - Cosmological scenario of the A-B phase transition in superfluid 3He
Defect formation through boson condensation in quantum field theory
Preface
Dictionary: Condensed matter - High energy physics & cosmology / G.E. Volovik
Classification of topological defects and their relevance to cosmology and elsewhere / T.W.B. Kibble
33.
図書
editor Yuri Bahturin
出版情報:
Berlin ; New York : Walter de Gruyter, 2000 xx, 410 p. ; 25 cm
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Schedule of Talks
A word about Kurosh / A. I. Kostrikin
Two methods for solving the linear problem of elimination / A. A. Abramov ; V. O. Belash ; L. F. Yukhno
Strictly stratified algebras / I. Agoston ; V. Dlab ; E. Lukacs
Randomness: algebraic, statistical and complexity theory aspects / N. Yu. Anisimov ; E. E. Demidov
General quantum polynomials / V. A. Artamonov
Grobner bases and involutive bases / A. V. Astrelin ; O. D. Golubitsky ; E. V. Pankratiev
Codimension growth and graded identities / Y. Bahturin ; A. Giambruno ; M. Zaicev
On certain non-finitely based varieties of groups / R. M. Bryant ; A. N. Krasil'nikov
G-connectedness of compact Kahler manifolds, II. Solvable quotients of Kahler groups / F. Campana
Finite groups with the same character tables, Drinfel'd algebras and Galois algebras / A. A. Davydov
The profinite completion of certain torsion p-groups / R. I. Grigorchuk ; W. N. Herfort ; P. A. Zalesskii
Birational correspondences of a double cone / M. Grinenko
Groups with neighborhood conditions for certain lattices / H. Heineken
Subalgebra membership problem and subalgebra standard basis / N. K. Iyudu
Graded algebras generated by Eulerian derivatives / D. A. Jordan
Characterizations of projective spaces and hyperquadrics / Y. Kachi ; E. Sato
Non additive Morita theory. A survey / U. Knauer
Modular Lie algebras: new trends / A. S. Dzhumadil'daev
On generic coverings of the plane / V. S. Kulikov
General version of standard bases in linear structures / V. N. Latyshev
Division rings generated by group rings and enveloping algebras / A. I. Lichtman
Some notes on universal algebraic geometry / D. B. Nikolova ; B. I. Plotkin
Groups with all irreducible modules of finite degree / D. S. Passman ; W. V. Temple
Schreier's formulae for free Lie algebras, their applications and asymptotics / V. M. Petrogradsky
Conditional terms and their applications / A. G. Pinus
Blow-ups of canonical singularities / Yu. G. Prokhorov
On the growth of identities / A. Regev ; A. Gouterman
Radical and residual classes of finite groups / L. A. Shemetkov
Speciality and deformations of algebras / I. P. Shestakov
Infinite torsion groups arising as generalizations of the second Grigorchuk groups / T. Vovkivsky
Brauer groups of curves and reciprocity law in Brauer groups of their function fields / V. I. Yanchevskii
Mathematical systems / V. K. Zakharov ; A. V. Mikhalev
Schedule of Talks
A word about Kurosh / A. I. Kostrikin
Two methods for solving the linear problem of elimination / A. A. Abramov ; V. O. Belash ; L. F. Yukhno
34.
図書
Donal J. Hurley, Michael A. Vandyck
出版情報:
London : Springer , Chichester, UK : Published in association with Praxis Pub., 2000 xvii, 369 p. ; 25 cm
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35.
図書
Hardeo Sahai, Mohammed I. Ageel
出版情報:
Boston : Birkhäuser Boston, c2000 xxxv, 742 p. ; 24 cm
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36.
図書
Bryan P. Rynne and Martin A. Youngson
37.
図書
A.L. Bukhgeim
38.
図書
室井和男著
出版情報:
東京 : 東京大学出版会, 2000.3 xi, 187p ; 22cm
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39.
図書
Irena Lasiecka, Roberto Triggiani
目次情報:
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Categories / 1：
Categories and exact sequences / 2：
Change of rings / 3：
The Morita theory / 4：
Limits in categories / 5：
Localization / 6：
Local-global methods / 7：
Categories / 1：
Categories and exact sequences / 2：
Change of rings / 3：
40.
図書
Ernst Kleinert
41.
図書
Nicola Bellomo, Luigi Preziosi, Antonio Romano
42.
図書
砂田利一著
出版情報:
東京 : 日本評論社, 2000.4 v, 169p ; 21cm
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43.
図書
R.A. Minlos, Senya Shlosman, Yu. M. Suhov, editors
44.
図書
Gerald W. Johnson, Michel L. Lapidus
出版情報:
Oxford : Clarendon Press , New York : Oxford University Press, 2000 xviii, 771 p. ; 25 cm
シリーズ名:
Oxford mathematical monographs
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Introduction / 1：
The physical phenomena of Brownian motion / 2：
Wiener measure / 3：
Scaling in Wiener space and the analytic Feynman integral / 4：
Stochastic processes and the Wiener process / 5：
Quantum dynamics and the Schrodinger equation / 6：
The Feynman integral: heuristic ideas and mathematical difficulties / 7：
Semigroups of operators: an informal introduction / 8：
Linear semigroups of operators / 9：
Unbounded self-adjoint operators and quadratic forms / 10：
Product formulas with applications to the Feynman integral / 11：
The Feynman-Kac formula / 12：
Analytic-in-time or -mass operator-valued Feynman integrals / 13：
Feynman's operational calculus for noncommuting operaors: an introduction / 14：
Generalized Dyson series, the Feynman integral and Feynman's operational calculus / 15：
Stability results / 16：
The Feynman-Kac formula with a Lebesgue-Stieltjes measure and Feynman's operational calculus / 17：
Noncommutative operations on Wiener functionals, disentangling algebras and Feynman's operational calculus / 18：
Feynman's operational calculus and evolution equations / 19：
Further work on or related to the Feynman integral / 20：
References
Index of Symbols
Author index
Subject index
Introduction / 1：
The physical phenomena of Brownian motion / 2：
Wiener measure / 3：
45.
図書
L.E. Fraenkel
目次情報:
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Preface
Some notation, terminology and basic calculus / 0：
Introduction / 1：
Some maximum principles for elliptic equations / 2：
Symmetry for a non-linear Poisson equation / 3：
Symmetry for the non-linear Poisson equation in RN / 4：
Monotonicity of positive solutions in a bounded set W / 5：
On the Newtonian potential / Appendix A：
Rudimentary facts about harmonic functions and the Poisson equation / Appendix B：
Construction of the primary function of Siegel type / Appendix C：
On the divergence theorem and related matters / Appendix D：
The edge-point lemma / Appendix E：
Notes on sources
References
Index
Preface
Some notation, terminology and basic calculus / 0：
Introduction / 1：
46.
図書
Kjeld B. Laursen and Michael M. Neumann
47.
図書
Luigi Ambrosio, Nicola Fusco, Diego Pallara
48.
図書
P.J. Hunt, J.E. Kennedy
49.
図書
Theodore J. Rivlin, Edward B. Saff, editors
出版情報:
New York : Springer, c2000 xliv, 682 p. ; 25 cm
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50.
図書
Jürgen Appell, editor
51.
図書
堤正義著
出版情報:
東京 : 共立出版, 2000.3 vi, 262p ; 22cm
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52.
図書
by Edgar E. Enochs, Overtoun M.G. Jenda
目次情報:
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Preface
Basic Concepts / 1：
Zorn's lemma, ordinal and cardinal numbers / 1.1：
Modules / 1.2：
Categories and functors / 1.3：
Complexes of modules and homology / 1.4：
Direct and inverse limits / 1.5：
I-adic topology and completions / 1.6：
Flat Modules, Chain Conditions and Prime Ideals / 2：
Flat modules / 2.1：
Localization / 2.2：
Chain conditions / 2.3：
Prime ideals and primary decomposition / 2.4：
Artin-Rees lemma and Zariski rings / 2.5：
Injective and Flat Modules / 3：
Injective modules / 3.1：
Natural identities, flat modules, and injective modules / 3.2：
Injective modules over commutative noetherian rings / 3.3：
Matlis duality / 3.4：
Torsion Free Covering Modules / 4：
Existence of torsion free precovers / 4.1：
Existence of torsion free covers / 4.2：
Examples / 4.3：
Direct sums and products / 4.4：
Covers / 5：
F-precovers and covers / 5.1：
Existence of precovers and covers / 5.2：
Projective and flat covers / 5.3：
Injective covers / 5.4：
Direct sums and T-nilpotency / 5.5：
Envelopes / 6：
F-preenvelopes and envelopes / 6.1：
Existence of preenvelopes / 6.2：
Existence of envelopes / 6.3：
Direct sums of envelopes / 6.4：
Flat envelopes / 6.5：
Existence of envelopes for injective structures / 6.6：
Pure injective envelopes / 6.7：
Covers, Envelopes, and Cotorsion Theories / 7：
Definitions and basic results / 7.1：
Fibrations, cofibrations and Wakamatsu lemmas / 7.2：
Set theoretic homological algebra / 7.3：
Cotorsion theories with enough injectives and projectives / 7.4：
Relative Homological Algebra and Balance / 8：
Left and right F-resolutions / 8.1：
Derived functors and balance / 8.2：
Applications to modules / 8.3：
F-dimensions / 8.4：
Minimal pure injective resolutions of flat modules / 8.5：
[lambda] and [mu]-dimensions / 8.6：
Iwanaga-Gorenstein and Cohen-Macaulay Rings and Their Modules / 9：
Iwanaga-Gorenstein rings / 9.1：
The minimal injective resolution of R / 9.2：
More on flat and injective modules / 9.3：
Torsion products of injective modules / 9.4：
Local cohomology and the dualizing module / 9.5：
Gorenstein Modules / 10：
Gorenstein injective modules / 10.1：
Gorenstein projective modules / 10.2：
Gorenstein flat modules / 10.3：
Foxby classes / 10.4：
Gorenstein Covers and Envelopes / 11：
Gorenstein injective precovers and covers / 11.1：
Gorenstein injective preenvelopes / 11.2：
Gorenstein injective envelopes / 11.3：
Gorenstein essential extensions / 11.4：
Gorenstein projective precovers and covers / 11.5：
Auslander's last theorem (Gorenstein projective covers) / 11.6：
Gorenstein flat covers / 11.7：
Gorenstein flat and projective preenvelopes / 11.8：
Balance over Gorenstein and Cohen-Macaulay Rings / 12：
Balance of Hom (--, --) / 12.1：
Balance of--[characters not reproducible]-- / 12.2：
Dimensions over n-Gorenstein rings / 12.3：
Dimensions over Cohen-Macaulay rings / 12.4：
[Omega]-Gorenstein modules / 12.5：
Bibliographical Notes
Bibliography
Index
Preface
Basic Concepts / 1：
Zorn's lemma, ordinal and cardinal numbers / 1.1：
53.
図書
by Mati Kilp, Ulrich Knauer, Alexander V. Mikhalev
目次情報:
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Foreword
Introduction
Elementary properties of monoids, acts and categories / I：
Sets and relations / 1：
Groupoids, semigroups and monoids / 2：
Some classes of semigroups / 3：
Acts over monoids (monoid automata) / 4：
Decompositions and components / 5：
Categories / 6：
Functors / 7：
Constructions / II：
Products and coproducts
Pullbacks and pushouts
Free objects and generators
Cofree objects and cogenerators
Tensor products
Wreath products of monoids and acts
The wreath product of a monoid with a small category
Classes of acts / III：
Injective acts
Divisible acts
Principally weakly injective acts
fg-weakly injective acts
Weakly injective acts
Absolutely pure acts
Cogenerators and overview
Torsion free acts / 8：
Flatness of acts and related properties / 9：
Principally weakly flat acts / 10：
Weakly flat acts / 11：
Flat acts / 12：
Acts satisfying Condition (P) / 13：
Acts satisfying Condition (E) / 14：
Equalizer flat acts / 15：
Pullback flat acts and overview / 16：
Projective acts / 17：
Generators / 18：
Regular acts and overview / 19：
Homological classification of monoids / IV：
Principal weak injectivity
On fg-weak injectivity
Weak injectivity
Absolute purity
Injectivity and overview
Torsion freeness and principal weak flatness
Weak flatness
Flatness
Condition (P)
Strong flatness
Projectivity
Projective generators
Freeness and overview
Regularity of acts
Equivalence and Duality / V：
Adjoint functors
Categories equivalent to Act -- S
Morita equivalence of monoids
Endomorphism monoids of generators
On Morita duality
Bibliography
Index of symbols
Index
Foreword
Introduction
Elementary properties of monoids, acts and categories / I：
54.
図書
edited by Tan Lei
目次情報:
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Introduction / L. Tan
Preface / J. Hubbard
The Mandelbrot set is universal / C. McMullen
Baby Mandelbrot sets are born in cauliflowers / A. Douady ; X. Buff ; R. Devaney ; P. Sentenac
Modulation dans l'ensemble de Mandelbrot / P. Haissinsky
Local connectivity of Julia sets: expository lectures / J. Milnor
Holomorphic motions and puzzles (following M. Shishikura) / P. Roesch
Local properties of the Mandelbrot set at parabolic points
Convergence of rational rays in parameter spaces / C. Petersen ; G. Ryd
Bounded recurrence of critical points and Jakobson's Theorem / S. Luzzatto
The Herman-Swiatek Theorems with applications
Perturbation d'une fonction linearisable / H. Jellouli
Indice holomorphe et multiplicateur
An alternative proof of Mane's theorem on non-expanding Julia sets / M. Shishikura
Geometry and dimension of Julia sets / Y.-C. Yin
On a theorem of M. Rees for the matings of polynomials
Le theoreme d'integrabilite des structures presque complexes
Bifurcation of parabolic fixed points
References
Introduction / L. Tan
Preface / J. Hubbard
The Mandelbrot set is universal / C. McMullen
55.
図書
Vassili N. Kolokoltsov
目次情報:
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Introduction
Gaussian diffusions / Chapter 1：
Gaussian diffusion. Probabilistic and analytic approaches / 1：
Classification of Gaussian diffusions by the Young schemes / 2：
Longtime behaviourofthe Greenfunctions ofGaussiandiffusions / 3：
Complex stochastic Gaussian diffusion / 4：
The rate of escape for Gaussian diffusions and scattering for its perturbations / 5：
Boundary value problem for Hamiltonian systems / Chapter 2：
Rapid course in calculus of variations
Boundary value problem for non-degenerate Hamiltonians
RegulardegenerateHamiltoniansofthe firstrank
General regular Hamiltonians depending quadratically on momenta
Hamiltonians of exponential growth in momenta
Complex Hamiltonians and calculus of variations of saddle-points / 6：
Stochastic Hamiltonians / 7：
Semiclassical approximation for regular diffusion / Chapter 3：
Main ideas of the WKB-method with imaginary phase
Calculation of the two-point function for regular Hamiltonians
Asymptotic solutionsofthe transportequation
Local asymptotics of the Green function for regular Hamiltonians
Global small diffusion asymptotics and large deviations
Asymptotics for non-regular diffusion: an example
Analytic solutions to some linear PDE
Invariant degenerate diffusion on cotangent bundles / Chapter 4：
Curvilinear Ornstein-Uhlenbeck process and stochastic geodesic flow
Small time asymptotics for stochastic geodesic flow
The traceofthe Greenfunctionandgeometricinvariants
Transition probability densities for stable jump-diffusion / Chapter 5：
Asymptotic properties of one-dimensional stable laws
Asymptotic properties of finite-dimensional stable laws
Stable jump-diffusions combined with compound Poisson processes
Stable-like processes
Applications to the sample path properties of stable jump-diffusions
Semiclassical asymptotics for the localised Feller-Courrege processes / Chapter 6：
Maslov's tunnel equations and the Feller-Courrege processes
Rough local asymptotics and local large deviations
Refinementandglobalisation
Complex stochastic diffusions or stochastic Schrodinger equations / Chapter 7：
Semiclassical approximation: formal asymptotics
Semiclassical approximation: justification and globalisation
Applications: two-sided estimates to complex heat kernels, large deviation principle, well-posedness of the Cauchy problem
Path integration and infinite-dimensional saddle-point method
Some topics in Semiclassical spectral analysis / Chapter 8：
Double-well splitting
Low lying eigenvalues of diffusion operators and the life-times of diffusion processes
Quasi-modes of diffusion operators around a closed orbit of the corresponding classical system
Path integration for the Schrodinger, heat and complex stochastic diffusion equations / Chapter 9：
Path integral for the Schrodinger equation in p-representation
Path integral for the Schrodinger equation in x-representation
Singular potentials
Semiclassical asymptotics
Fock space representation
Appendices
Main equation of the theory of continuous quantum measurements / A：
Asymptotics of Laplace integrals with complex phase / B：
Characteristic functions of stable laws / C：
Levy-Khintchine ?DO and Feller-Courrege processes / D：
Equivalence of convex functions / E：
Unimodality of symmetric stable laws / F：
Infinite divisible complex distributions and complex Markov processes / G：
A review of main approaches to the rigorous construction of path integral / H：
Perspectives and problems / I：
References
Main notations
Subject Index
Introduction
Gaussian diffusions / Chapter 1：
Gaussian diffusion. Probabilistic and analytic approaches / 1：
56.
図書
Vojislav Marić
目次情報:
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Introduction
Linear Equations / Part 1：
Existence of regular solutions / Chapter 1：
Preliminaries / 1.1：
The case f(x) < 0 / 1.2：
?- and G- varying solutions / 1.3：
The case of f(x) of arbitrary sign / 1.4：
Regular boundedness of solutions / 1.5：
Generalizations / 1.6：
Examples / 1.7：
Comments / 1.8：
Asymptotic behavior of regular solutions / Chapter 2：
Slowly varying solutions / 2.1：
a)The case of f(x) of arbitrary sign
Regularly varying solutions / 2.2：
On zeros of oscillating solutions / 2.3：
Nonlinear Equations / 2.4：
Equations of Thomas-Fermi type / Chapter 3：
Introduction and preliminaries / 3.1：
The case of regularly varying f and f / 3.2：
The case of rapidly varying f or φ / 3.3：
A more general case / 3.5：
An equation arising in boundary-layer Theory / Chapter 4：
Existence and uniqueness / 4.1：
Estimates and asymptotic behavior of solutions / 4.3：
Appendix. Properties of RegularlyVarying and Related Functions / 4.4：
References
Index
Introduction
Linear Equations / Part 1：
Existence of regular solutions / Chapter 1：
57.
図書
Hermann Thorisson
目次情報:
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Random Variables
Markov Chains and Random Walks
Random Elements
Stochastic Processes
Shift-Coupling
Markov Processes
Transformation Coupling
Stationarity, the Palm Dualities
The Palm Dualities in Higher Dimensions
Regeneration
Random Variables
Markov Chains and Random Walks
Random Elements
58.
図書
Victor P. Havin, Nikolai K. Nikolski, editors
59.
図書
William McLean
出版情報:
Cambridge ; New York : Cambridge University Press, 2000 xiv, 357 p. ; 24 cm
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60.
図書
Karin Gatermann
61.
図書
Gregory L. Naber
目次情報:
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Preface
Acknowledgements
Geometrical Background
Physical Motivation
Frame Bundles and Spacetime
Differential Forms and Integration Introduction
de Rham Cohomology Introduction
Characteristic Classes
Appendix
References
Symbols
Index
Preface
Acknowledgements
Geometrical Background
62.
図書
V.V. Buldygin, Yu.V. Kozachenko ; [translated from the Russian by V. Zaiats]
目次情報:
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Sub-Gaussian and pre-Gaussian random variables
Orlicz spaces of random variables
Regularity of sample paths of a stochastic process
Pre-Gaussian processes
Shot noise processes and their properties Correlograms of stationary
Gaussian processes Jointly sub-Gaussian, super-Gaussian, and pseudo-Gaussian stochastic processes
Appendices
Comments
References
Basic notation
Index
Sub-Gaussian and pre-Gaussian random variables
Orlicz spaces of random variables
Regularity of sample paths of a stochastic process
63.
図書
Patrice Le Calvez ; translated by Philippe Mazaud
目次情報:
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Presentation and comparison of the different approaches to the theory of monotone twist diffeomorphisms of the annulus
Generating phases of the diffeomorphisms of the torus and the annulus
Index
Bibliography
Presentation and comparison of the different approaches to the theory of monotone twist diffeomorphisms of the annulus
Generating phases of the diffeomorphisms of the torus and the annulus
Index
64.
図書
Luis G. Gorostiza, B. Gail Ivanoff, editors
65.
図書
Hermann Grassmann ; translated by Lloyd C. Kannenberg
出版情報:
Providence, R.I. : American Mathematical Society, c2000 xviii, 411 p. ; 27 cm
シリーズ名:
History of mathematics ; v. 19
子書誌情報:
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The elementary conjunctions of extensive magnitudes: Addition, subtraction, multiples and fractions of extensive magnitudes
The product structure in general Combinatorial product
Inner product Applications to geometry
The theory of functions: Functions in general
Differential calculus Infinite series
Integral calculus Index of technical terms
Editorial notes Supplementary notes
Subject index
The elementary conjunctions of extensive magnitudes: Addition, subtraction, multiples and fractions of extensive magnitudes
The product structure in general Combinatorial product
Inner product Applications to geometry
66.
図書
Georges-Henri Cottet, Petros D. Koumoutsakos
出版情報:
New York : Cambridge University Press, 2000 xiii, 313 p.
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Definitions and governing equations / 1：
Vortex methods for incompressible two-dimensional flows / 2：
Three-dimensional vortex methods for inviscid flows / 3：
Inviscid boundary conditions / 4：
Viscous vortex methods / 5：
Vorticity boundary conditions for the Navier-Stokes equations / 6：
Lagrangian grid distortions: problems and solutions / 7：
Hybrid methods / 8：
Mathematical tools for the numerical analysis of vortex methods / Appendix A：
Fast multipole methods for three-dimensional N-body problems. / Appendix B：
Definitions and governing equations / 1：
Vortex methods for incompressible two-dimensional flows / 2：
Three-dimensional vortex methods for inviscid flows / 3：
67.
図書
Aleksey I. Prilepko, Dmitry G. Orlovsky, Igor A. Vasin
目次情報:
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Inverse problems for equations of parabolic type
inverse problems for equations of hyperbolic type
inverse problems for equations of elliptic type
inverse problems in dynamics of viscous incompressible fluid
some topics from functional analysis and operator theory
abstract inverse problems for first order equations and their applications in mathematical physics
two-point inverse problems for first order equations
inverse problems for equations of second order
applications of
Inverse problems for equations of parabolic type
inverse problems for equations of hyperbolic type
inverse problems for equations of elliptic type
68.
図書
Robert S. Doran, V.S. Varadarajan, editors
目次情報:
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Harish-Chandra, his work, and its legacy / V. S. Varadarajan
Some recollections of Harish-Chandra / A. Borel
Harish-Chandra memorial talk / S. Helgason
An elementary Introduction to Harish-Chandra's work / R. P. Langlands ; G. D. Mostow ; R. A. Herb
Stabilization of a family of differential equations / J. Arthur
Orbital integrals of nilpotent orbits / D. Barbasch
Representation theory of $p$-adic groups: A view from operator algebras / P. F. Baum ; N. Higson ; R. J. Plymen
Bruhat filtrations and Whittaker vectors for real groups / W. Casselman ; H. Hecht ; D. Milicic
Germs, characters, and the Fourier transforms of nilpotent orbits / S. DeBacker ; P. J. Sally
Bessel functions on boundary orbits and singular holomorphic representations / H. Ding ; K. I. Gross ; R. A. Kunze ; D. St. P. Richards
Restriction of small discrete series representations to symmetric subgroups / B. Gross ; N. Wallach
Harish-Chandra's c-function. A mathematical jewel
Two-structures and discrete series character formulas
Harish-Chandra homomorphisms / R. E. Howe
Unitary representations and Osterwalder-Schrader duality / P. E. T. Jorgensen ; G. Olafsson
Intertwining operators and small unitary representations / A. W. Knapp
On some problems in analysis suggested by representation theory
Distributional reciprocity and generalized Gelfand pairs / R. L. Lipsman
Displacement functions on the Bruhat-Tits building / A. Moy
Germs of characters of admissible representations / F. Murnaghan
Seiberg-Witten equations on locally symmetric spaces / B. Speh
Holomorphic double fibration transforms / J. A. Wolf ; R. Zierau
Harish-Chandra, his work, and its legacy / V. S. Varadarajan
Some recollections of Harish-Chandra / A. Borel
Harish-Chandra memorial talk / S. Helgason
69.
図書
Fumio Hiai, Dénes Petz
目次情報:
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Overview
Probability laws and noncommutative random variables
The free relation Analytic function theory and infinitely divisible laws
Random matrices and asymptotically free relation
Large deviations for random matrices
Free entropy of noncommutative random variables
Relation to operator algebras
Bibliography
Index
Overview
Probability laws and noncommutative random variables
The free relation Analytic function theory and infinitely divisible laws
70.
図書
Peter Kravanja, Marc Van Barel
目次情報:
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Zeros of analytic functions / 1：
Introduction / 1.1：
Computing the total number of zeros with certainty / 1.1.1：
An overview of other approaches / 1.1.2：
Formal orthogonal polynomials / 1.2：
An accurate algorithm to compute zeros of FOPs / 1.3：
The software package ZEAL / 1.5：
The approach taken by ZEAL / 1.5.1：
The structure of ZEAL / 1.5.2：
ZEAL'S user interface / 1.5.3：
A few examples of how to use ZEAL / 1.5.4：
Concluding remarks / 1.5.5：
A derivative-free approach / 1.6：
Clusters of zeros of analytic functions / 2：
How to obtain the centre of a cluster and its weight / 2.1：
A numerical example / 2.2：
Rational interpolation at roots of unity / 2.3：
More numerical examples / 2.4：
Zeros and poles of meromorphic functions / 3：
Theoretical considerations and numerical algorithm / 3.1：
Systems of analytic equations / 3.3：
A multidimensional logarithmic residue formula / 4.1：
The algorithm / 4.3：
Numerical examples / 4.4：
References
Zeros of analytic functions / 1：
Introduction / 1.1：
Computing the total number of zeros with certainty / 1.1.1：
71.
図書
Geir Ellingsrud, William Fulton, Angelo Vistoli, editors
出版情報:
Boston ; Basel : Birkhäuser, c2000 viii, 327 p. ; 25 cm
シリーズ名:
Trends in mathematics
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72.
図書
河添健著
73.
図書
V.M. Adamyan ... [et al.], editors
74.
図書
V.M. Adamyan ... [et al.], editors
75.
図書
Alexander N. Starkov ; [translated from the Russian by the author]
目次情報:
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Preliminaries Ergodicity and mixing of homogeneous flows
Dynamics of unipotent flows
Dynamics of nonunipotent flows
Applications to number theory
References
Index
Preliminaries Ergodicity and mixing of homogeneous flows
Dynamics of unipotent flows
Dynamics of nonunipotent flows
76.
図書
L.A. Bunimovich ... [et al.] ; edited by Ya.G. Sinai
目次情報:
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General Ergodic Theory of Groupsof Measure Preserving Transformations / I：
Ergodic Theory of Smooth Dynamical Systems / II：
Dynamical Systems on Homogeneous Spaces / III：
The Dynamics of Billiard Flowsin Rational Polygons / IV：
Dynamical Systemsof Statistical Mechanics and Kinetic Equations / V：
Subject Index
Basic Notions of Ergodic Theory and Examples of Dynamical Systems / I.P. Kornfeld ; Ya.G. SinaiChapter 1：
Dynamical Systems with Invariant Measures / 1：
First Corollaries of the Existence of Invariant Measures. Ergodic Theorems / 2：
Ergodicity. Decomposition into Ergodic Components. Various Mixing Conditions / 3：
General Constructions / 4：
Direct Products of Dynamical Systems / 4.1：
Skew Products of Dynamical Systems / 4.2：
Factor-Systems / 4.3：
Integral and Induced Automorphisms / 4.4：
Special Flows and Special Representations of Flows / 4.5：
Natural Extensions of Endomorphisms / 4.6：
Spectral Theory of Dynamical Systems / Chapter 2：
Groups of Unitary Operators and Semigroups of Isometric Operators Adjoint to Dynamical Systems
The Structure of the Dynamical Systems with Pure Point and Quasidiscrete Spectra
Examples of Spectral Analysis of Dynamical Systems
Spectral Analysis of Gauss Dynamical Systems
Entropy Theory of Dynamical Systems / Chapter 3：
Entropy and Conditional Entropy of a Partition
Entropy of a Dynamical System
The Structure of Dynamical Systems of Positive Entropy
The Isomorphy Problem for Bernoulli Automorphisms and K-Systems
Equivalence of Dynamical Systems in the Sense of Kakutani / 5：
Shifts in the Spaces of Sequences and Gibbs Measures / 6：
Periodic Approximations and Their Applications. Ergodic Theorems, Spectral and Entropy Theory for the General Group Actions / A.M. VershikChapter 4：
Approximation Theory of Dynamical Systems by Periodic Ones. Flows on the Two-Dimensional Torus
Flows on the Surfaces of Genus p ≥ 1 and Interval Exchange Transformations
General Group Actions
Introduction / 3.1：
General Definition of the Actions of Locally Compact Groups on Lebesgue Spaces / 3.2：
Ergodic Theorems / 3.3：
Spectral Theory / 3.4：
Entropy Theory for the Actions of General Groups
Trajectory Theory / Chapter 5：
Statements of Main Results
Sketch of the Proof. Tame Partitions
Trajectory Theory for Amenable Groups
Trajectory Theory for Non-Amenable Groups. Rigidity
Concluding Remarks. Relationship Between Trajectory Theory and Operator Algebras
Bibliography
Additional Bibliography
Ergodic Theory of SmoothDynamical Systems
Stochasticity of Smooth Dynamical Systems. The Elements of KAM-Theory / Chapter 6：
Integrable and Nonintegrable Smooth Dynamical Systems. The Hierarchy of Stochastic Properties of Deterministic Dynamics
The Kolmogorov-Arnold-Moser Theory (KAM-Theory)
General Theory of Smooth Hyperbolic Dynamical Systems / Ya.B.PesinChapter 7：
Hyperbolicity of Individual Trajectories
Introductory Remarks / 1.1：
Uniform Hyperbolicity / 1.2：
Nonuniform Hyperbolicity / 1.3：
Local Manifolds / 1.4：
Global Manifolds / 1.5：
Basic Classes of Smooth Hyperbolic Dynamical Systems. Definitions and Examples
Anosov Systems / 2.1：
Hyperbolic Sets / 2.2：
Locally Maximal Hyperbolic Sets / 2.3：
Axiom A-Diffeomorphisms / 2.4：
Hyperbolic Attractors. Repellers / 2.5：
Partially Hyperbolic Dynamical Systems / 2.6：
Mather Theory / 2.7：
Nonuniformely Hyperbolic Dynamical Systems. Lyapunov Exponents / 2.8：
Ergodic Properties of Smooth Hyperbolic Dynamical Systems
u-Gibbs Measures
Symbolic Dynamics
Measures of Maximal Entropy
Construction of u-Gibbs Measures
Topological Pressure and Topological Entropy / 3.5：
Properties of u-Gibbs Measures / 3.6：
Small Stochastic Perturbations / 3.7：
Equilibrium States and Their Ergodic Properties / 3.8：
Ergodic Properties of Dynamical Systems with Nonzero Lyapunov Exponents / 3.9：
Ergodic Properties of Anosov Systems and of UPH-Systems / 3.10：
Continuous Time Dynamical Systems / 3.11：
Hyperbolic Geodesic Flows
Manifolds with Negative Curvature
Riemannian Metrics Without Conjugate (or Focal) Points
Entropy of Geodesic Flows
Riemannian Metrics of Nonpositive Curvature
Geodesic Flows on Manifolds with Constant Negative Curvature
Dimension-like Characteristics of Invariant Sets for Dynamical Systems
Hausdorff Dimension / 6.1：
Other Dimension Characteristics / 6.3：
Carathéodory Dimension Structure. Carathéodory Dimension Characteristics / 6.4：
Examples of C-structures and Carathéodory Dimension Characteristics / 6.5：
Multifractal Formalism / 6.6：
Coupled Map Lattices / 7：
Additional References
Billiards and Other Hyperbolic Systems / L.A. BunimovichChapter 8：
Billiards
The General Definition of a Billiard
Billiards in Polygons and Polyhedrons
Billiards in Domains with Smooth Convex Boundary
Dispersing or Sinai Billiards
The Lorentz Gas and Hard Spheres Gas
Semi-dispersing Billiards and Boltzmann Hypotheses / 1.6：
Billiards in Domains with Boundary Possessing Focusing Components / 1.7：
Hyperbolic Dynamical Systems with Singularities (a General Approach) / 1.8：
Markov Approximations and Symbolic Dynamics for Hyperbolic Billiards / 1.9：
Statistical Properties of Dispersing Billiards and of the Lorentz Gas / 1.10：
Transport Coefficients for the Simplest Mechanical Models / 1.11：
Strange Attractors
Definition of a Strange Attractor
The Lorenz Attractor
Some Other Examples of Hyperbolic Strange Attractors
Ergodic Theory of One-Dimensional Mappings / M.V. JakobsonChapter 9：
Expanding Maps
Definitions, Examples, the Entropy Formula
Walters Theorem
Absolutely Continuous Invariant Measures for Nonexpanding Maps
Some Examples
Intermittency of Stochastic and Stable Systems
Ergodic Properties of Absolutely Continuous Invariant Measures
Feigenbaum Universality Law
The Phenomenon of Universality
Doubling Transformation
Neighborhood of the Fixed Point
Properties of Maps Belonging to the Stable Manifold of Φ
Rational Endomorphisms of the Riemann Sphere
The Julia Set and Its Complement
The Stability Properties of Rational Endomorphisms
Ergodic and Dimensional Properties of Julia Sets
Dynamical Systemson Homogeneous Spaces
Measures on homogeneous spaces / S.G. DaniChapter 10：
Examples of lattices
Ergodicity and its consequences
Isomorphisms and factors of affine automorphisms
Affine automorphisms of tori and nilmanifolds
Ergodic properties; the case of tori
Ergodic properties on nilmanifolds
Unipotent affine automorphisms
Quasi-unipotent affine automorphisms
Closed invariant sets of automorphisms
Dynamics of hyperbolic automorphisms
More on invariant sets of hyperbolic toral automorphisms
Distribution of orbits of hyperbolic automorphisms
Dynamics of ergodic toral automorphisms / 2.9：
Actions of groups of affine automorphisms / 2.10：
Group-induced translation flows; special cases
Flows on solvmanifolds
Homogeneous spaces of semisimple groups
Flows on low-dimensional homogeneous spaces
Ergodic properties of flows on general homogeneous spaces
Horospherical subgroups and Mautner phenomenon
Ergodicity of one-parameter flows
Invariant functions and ergodic decomposition
Actions of subgroups
Duality
Spectrum and mixing of group-induced flows
Mixing of higher orders / 4.7：
Entropy / 4.8：
K-mixing, Bernoullicity / 4.9：
Group-induced flows with hyperbolic structure
Anosov automorphisms / 5.1：
Affine automorphisms with a hyperbolic fixed point / 5.2：
Anosov flows / 5.3：
Invariant measures of group-induced flows
Invariant measures of Ad-unipotent flows
Invariant measures and epimorphic subgroups
Invariant measures of actions of diagonalisable groups
A weak recurrence property and infinite invariant measures
Distribution of orbits and polynomial trajectories
A uniform version of uniform distribution
Distribution of translates of closed orbits / 6.7：
Orbit closures of group-induced flows
Homogeneity of orbit closures / 7.1：
Orbit closures of horospherical subgroups / 7.2：
Orbits of reductive subgroups / 7.3：
Orbit closures of one-parameter flows / 7.4：
Dense orbits and minimal sets of flows / 7.5：
Divergent trajectories of flows / 7.6：
Bounded orbits and escapable sets / 7.7：
Duality and lattice-actions on vector spaces / 8：
Duality between orbits / 8.1：
Duality of invariant measures / 8.2：
Applications to Diophantine approximation / 9：
Polynomials in one variable / 9.1：
Values of linear forms / 9.2：
Diophantine approximation with dependent quantities / 9.3：
Values of quadratic forms / 9.4：
Forms of higher degree / 9.5：
Integral points on algebraic varieties / 9.6：
Classification and related questions / 10：
Metric isomorphisms and factors / 10.1：
Metric rigidity / 10.2：
Topological conjugacy / 10.3：
Topological equivalence / 10.4：
The Dynamics of Billiard Flows in Rational Polygons of Dynamical Systems / J. SmillieChapter 11：
Two Examples
Formal Properties of the Billiard Flow
The Flow in a Fixed Direction
Billiard Techniques: Minimality and Closed Orbits
Billiard Techniques: Unique Ergodicity
Dynamics on Moduli Spaces
The Lattice Examples of Veech
Dynamical Systems of Statistical Mechanicsand Kinetic Equations
Dynamical Systems of Statistical Mechanics / R.L. Dobrushin ; Yu.M. SukhovChapter 12：
Phase Space of Systems of Statistical Mechanics and Gibbs Measures
The Configuration Space
Poisson Measures
The Gibbs Configuration Probability Distribution
Potential of the Pair Interaction. Existence and Uniqueness of a Gibbs Configuration Probability Distribution
The Phase Space. The Gibbs Probability Distribution
Gibbs Measures with a General Potential
The Moment Measure and Moment Function
Dynamics of a System of Interacting Particles
Statement of the Problem
Construction of the Dynamics and Time Evolution
Hierarchy of the Bogolyubov Equations
Equilibrium Dynamics
Definition and Construction of Equilibrium Dynamics
The Gibbs Postulate
Degenerate Models
Asymptotic Properties of the Measures Pt
Ideal Gas and Related Systems
The Poisson Superstructure
Asymptotic Behaviour of the Probability Distribution Pt as t → ∞
The Dynamical System of One-Dimensional Hard Rods
Kinetic Equations
The Boltzmann Equation
The Vlasov Equation
The Landau Equation
Hydrodynamic Equations
Existence and Uniqueness Theorems for the Boltzmann Equation / N.B. MaslovaChapter 13：
Formulation of Boundary Problems. Properties of Integral Operators
Formulation of Boundary Problems
Properties of the Collision Integral
Linear Stationary Problems
Asymptotics
Internal Problems
External Problems
Kramers' Problem
Nonlinear Stationary Problems
Non-Stationary Problems
General Ergodic Theory of Groupsof Measure Preserving Transformations / I：
Ergodic Theory of Smooth Dynamical Systems / II：
Dynamical Systems on Homogeneous Spaces / III：
77.
図書
Boris A. Kupershmidt
78.
図書
W.Y. Hsiang
79.
図書
A.J. Berrick & M.E. Keating
目次情報:
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Basics / 1：
Direct sums and their short exact sequences / 2：
Noetherian rings and polynomial rings / 3：
Artinian rings and modules / 4：
Dedekind domains / 5：
Modules over Dedekind domains / 6：
Basics / 1：
Direct sums and their short exact sequences / 2：
Noetherian rings and polynomial rings / 3：
80.
図書
edited by Stefaan Caenepeel, Freddy Van Oystaeyen
目次情報:
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Preface
Contributors
Conference Participants
Lifting of Nichols Algebras of Type A[subscript 2] and Pointed Hopf Algebras of Order p[superscript 4] / Nicolas Andruskiewitsch ; Hans-Jurgen Schneider1.：
Survey of Cross Product Bialgebras / Yuri Bespalov ; Bernhard Drabant2.：
A Morita-Takeuchi Context for Graded Coalgebras / Crina Boboc3.：
Coalgebra-Galois Extensions from the Extension Theory Point of View / Tomasz Brzezinski4.：
Separable Functors for the Category of Doi-Hopf Modules II / Stefaan Caenepeel ; Bogdan Ion ; Gigel Militaru ; Shenglin Zhu5.：
Cyclic Cohomology of Coalgebras, Coderivations and De Rham Cohomology / Marco A. Farinati ; Andrea Solotar6.：
Schur-Weyl Categories and Non-Quasiclassical Weyl Type Formula / Dimitri Gurevich ; Zakaria Mriss7.：
A Generalized Power Map for Hopf Algebras / Yevgenia Kashina8.：
Associated Varieties for Classical Lie Superalgebras / Ian M. Musson9.：
Algebraic Versions of a Finite-Dimensional Quantum Groupoid / Dmitri Nikshych ; Leonid Vainerman10.：
Quasi-Hopf Algebras and the Centre of a Tensor Category / Florin Panaite ; Freddy van Oystaeyen11.：
An Easy Proof for the Uniqueness of Integrals / Serban Raianu12.：
The Coquasitriangular Hopf Algebra Associated to a Rigid Yang-Baxter Coalgebra / Mitsuhiro Takeuchi13.：
On Regularity of the Algebra of Covariants for Actions of Pointed Hopf Algebras on Regular Commutative Algebras / Andrzej Tyc14.：
A Survey on Multiplier Hopf Algebras / Alfons van Daele ; Yinhuo Zhang15.：
Preface
Contributors
Conference Participants
81.
図書
edited by Freddy Van Oystaeyen, Manuel Saorin
目次情報:
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Preface
Contributors
Global Krull Dimension / Toma Albu ; Patrick F. Smith1.：
Derivations de la n-ieme algebre de Weyl quantique multiparametree / L'Moufadal Ben Yakoub2.：
Tensor Hochschild Homology and Cohomology / Claude Cibils3.：
Generalized Path Algebras / Flavio Ulhoa Coelho ; Shao-Xue Liu4.：
Representations and Corepresentations of Hopf Algebras / Miriam Cohen5.：
Cotilting Bimodules and Their Dualities / Riccardo Colpi6.：
Finding Splitting Elements and Maximal Tori in Matrix Algebras / Willem A. de Graaf ; Gabor Ivanyos7.：
Cohen-Macaulay Modules and Vector Bundles / Yuri A. Drozd8.：
A Note on Filtrations and Valuations for Ordered Groups / Maha Helmy Ibrahim El Baroudy ; Freddy van Oystaeyen9.：
A Survey of Covers and Envelopes / Edgar E. Enochs ; Overtoun M. G. Jenda10.：
On D-Gorenstein Modules / 11.：
Skew Polynomial Rings with Wide Family of Prime Ideals / Miguel Ferrero ; Jerzy Matczuk12.：
On Auslander-Reiten Systems via Tensor Product / Odile Garotta13.：
On a Projective Version of Maranda's Theorem / Yuval Ginosar ; Uri Onn14.：
Chain Conditions on Direct Summands and Pure Quotient Modules / Jose L. Gomez Pardo ; Pedro A. Guil Asensio15.：
Prime Spectra of Quantized Coordinate Rings / K. R. Goodearl16.：
Prime Ideals in Certain Quantum Determinantal Rings / T. H. Lenagan17.：
Noetherian Semigroup Algebras: A Survey / Eric Jespers ; Jan Okninski18.：
On the Recognition Problem of the Irreducibility for A[subscript 1](k)-Modules nd Their Characteristic Varieties / Huishi Li ; Lu Chen19.：
The Construction of a Generator for R-DMod / Leandro Marin20.：
A Lattice Invariant for Modules / Barbara L. Osofsky21.：
Unit Groups of Lie Centre-by-Metabelian Group Algebras / Richard Rossmanith22.：
Covers and Envelopes in Functor Categories / Manuel Saorin ; Alberto Del Valle23.：
Faithful Flatness over Hopf Subalgebras: Counterexamples / Peter Schauenburg24.：
Cohen-Macaulay Modules over Classical Orders / Daniel Simson25.：
On Associated Primes and Weakly Associated Primes / Boris Sirola26.：
On Kaplansky's Conjectures / Yorck Sommerhauser27.：
The Duality Theorem for Coactions of Multiplier Hopf Algebras / Alfons van Daele ; Yinhuo Zhang28.：
Static Modules and Equivalences / Robert Wisbauer29.：
Preface
Contributors
Global Krull Dimension / Toma Albu ; Patrick F. Smith1.：
82.
図書
M. Bachir Bekka, Matthias Mayer
目次情報:
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Preface
Ergodic Systems / I.：
Examples and Basic Results / 1：
Ergodic Theory and Unitary Representations / 2：
Invariant Measures and Unique Ergodicity / 3：
The Geodesic Flow of Riemannian Locally Symmetric Spaces / II.：
Some Hyperbolic Geometry
Lattices and Fundamental Domains
The Geodesic Flow of Compact Riemann Surfaces
The Geodesic Flow on Riemannian Locally Symmetric Spaces / 4：
The Vanishing Theorem of Howe and Moore / III.：
Howe--Moore's Theorem
Moore's Ergodicity Theorems
Counting Lattice Points in the Hyperbolic Plane
Mixing of All Orders
The Horocycle Flow / IV.：
The Horocycle Flow of a Riemann Surface
Proof of Hedlund's Theorem--Cocompact Case
Classification of Invariant Measures
Equidistribution of Horocycle Orbits
Siegel Sets, Mahler's Criterion and Margulis' Lemma / V.：
Siegel Sets in SL(n, R)
SL(n, Z) is a lattice in SL(n, R)
Mahler's Criterion
Reduction of Positive Definite Quadratic Forms
Margulis' Lemma / 5：
An Application to Number Theory: Oppenheim's Conjecture / VI.：
Oppenheim's Conjecture
Proof of the Theorem--Preliminaries
Existence of Minimal Closed Subsets
Orbits of One-Parameter Groups of Unipotent Linear Transformations
Proof of the Theorem--Conclusion
Ratner's Results on the Conjectures of Raghunathan, Dani and Margulis / 6：
Bibliography
Index
Preface
Ergodic Systems / I.：
Examples and Basic Results / 1：
83.
図書
James T. Smith
目次情報:
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Preface
About the author
Introduction / 1：
Episodes / 1.1：
Advanced geometry / 1.2：
This book / 1.3：
Reading about geometry / 1.4：
Projects / 1.5：
Foundations / 2：
Geometry as applied mathematics / 2.1：
Need for rigor / 2.2：
Axiomatic method / 2.3：
Euclid's Elements / 2.4：
Coordinate geometry / 2.5：
Foundation problem / 2.6：
Parallel axiom / 2.7：
Firm foundations / 2.8：
Geometry as pure mathematics / 2.9：
Exercises and projects / 2.10：
Elementary Euclidean geometry / 3：
Incidence geometry / 3.1：
Ruler axiom and its consequences / 3.2：
Pasch's axiom and the separation theorems / 3.3：
Angles and the protractor axioms / 3.4：
Congruence / 3.5：
Perpendicularity / 3.6：
Parallel axiom and related theorems / 3.7：
Area and Pythagoras' theorem / 3.8：
Similarity / 3.9：
Polyhedral volume / 3.10：
Circles and spheres / 3.11：
Arcs and trigonometric functions / 3.13：
[pi] / 3.14：
Exercises on elementary geometry / 4：
Exercises on the incidence and ruler axioms / 4.1：
Exercises related to Pasch's axiom / 4.2：
Exercises on congruence and perpendicularity / 4.3：
Exercises involving the parallel axiom / 4.4：
Exercises on similarity and Pythagoras' theorem / 4.5：
Exercises on circles and spheres, part 1 / 4.6：
Exercises on area / 4.7：
Exercises on volume / 4.8：
Exercises on circles and spheres, part 2 / 4.9：
Exercises on coordinate geometry / 4.10：
Some triangle and circle geometry / 5：
Four concurrence theorems / 5.1：
Menelaus' theorem / 5.2：
Desargues' theorem / 5.3：
Ceva's theorem / 5.4：
Trigonometry / 5.5：
Vector products / 5.6：
Centroid / 5.7：
Orthocenter / 5.8：
Incenter and excenters / 5.9：
Euler line and Feuerbach circle / 5.10：
Exercises / 5.11：
Plane isometries and similarities / 6：
Transformations / 6.1：
Isometries / 6.2：
Reflections / 6.3：
Translations / 6.4：
Rotations / 6.5：
Structure theorem / 6.6：
Glide reflections / 6.7：
Isometries and orthogonal matrices / 6.8：
Classifying isometries / 6.9：
Similarities / 6.10：
Three dimensional isometries and similarities / 6.11：
Translations and rotations / 7.1：
Glide and rotary reflections / 7.4：
Symmetry / 7.5：
Polygonal symmetry / 8.1：
Friezes / 8.2：
Wallpaper ornaments / 8.3：
Polyhedra / 8.4：
Equivalence relations / 8.5：
Least upper bound principle / Appendix B：
Vector and matrix algebra / Appendix C：
Bibliography
Index
Preface
About the author
Introduction / 1：
84.
図書
by Michael B. Mensky
85.
図書
Reinhard Diestel
目次情報:
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Preface
The Basics / 1：
Graphs / 1.1：
The degree of a vertex / 1.2：
Paths and cycles / 1.3：
Connectivity / 1.4：
Trees and forests / 1.5：
Bipartite graphs / 1.6：
Contraction and minors / 1 7：
Euler tours / 1.8：
Some linear algebra / 1.9：
Other notions of graphs / 1.10：
Exercises
Notes
Matching, Covering and Packing / 2：
Matching in bipartite graphs / 2.1：
Matching in general graphs(*) / 2.2：
Packing and covering / 2.3：
Tree-packing and arboricity / 2.4：
Path covers / 2.5：
2-Connected graphs and subgraphs / 3：
The structure of 3-connected graphs / 3.2：
Menger's theorem / 3.3：
Mader's theorem / 3.4：
Linking pairs of vertices / 3.5：
Planar Graphs / 4：
Topological prerequisites / 4.1：
Plane graphs / 4.2：
Drawings / 4.3：
Planar graphs: Kuratowski's theorem / 4.4：
Algebraic planarity criteria / 4.5：
Plane duality / 4.6：
Colouring / 5：
Colouring maps and planar graphs / 5.1：
Colouring vertices / 5.2：
Colouring edges / 5.3：
List colouring / 5.4：
Perfect graphs / 5.5：
Flows / 6：
Circulations(*) / 6.1：
Flows in networks / 6.2：
Group-valued flows / 6.3：
k-Flows for small k / 6.4：
Flow-colouring duality / 6.5：
Tutte's flow conjectures / 6.6：
Extremal Graph Theory / 7：
Subgraphs / 7.1：
Minors / 7.2：
Hadwiger's conjecture / 7.3：
Szemerèdi's regularity lemma / 7.4：
Applying the regularity lemma / 7.5：
Infinite Graphs / 8：
Basic notions, facts and techniques / 8.1：
Paths, trees, and ends(*) / 8.2：
Homogeneous and universal graphs / 8.3：
Connectivity and matching / 8.4：
The topological end space / 8.5：
Ramsey Theory for Graphs / 9：
Ramsey's original theorems / 9.1：
Ramsey numbers(*) / 9.2：
Induced Ramsey theorems / 9.3：
Ramsey properties and connectivity / 9.4：
Hamilton Cycles / 10：
Simple sufficient conditions / 10.1：
Hamilton cycles and degree sequences / 10.2：
Hamilton cycles in the square of a graph / 10.3：
Random Graphs / 11：
The notion of a random graph / 11.1：
The probabilistic method / 11.2：
Properties of almost all graphs / 11.3：
Threshold functions and second moments / 11.4：
Minors, Trees and WQO / 12：
Well-quasi-ordering / 12.1：
The graph minor theorem for trees / 12.2：
Tree-decompositions / 12.3：
Tree-width and forbidden minors / 12.4：
The graph minor theorem / 12.5：
A. Infinite sets
B. Surfaces Hints for all the exercises
Index
Symbol index
Sections marked by an asterisk are recommended for a first course
Of sections marked (*), the beginning is recommended for a first course
Preface
The Basics / 1：
Graphs / 1.1：
86.
図書
Stephen A. Fulling with Michael N. Sinyakov, Sergei V. Tischchenko
出版情報:
Singapore : World Scientific, 2000 x, 445 p. ; 23 cm
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87.
図書
Svante Janson, Tomasz Łuczak, Andrzej Rucinski
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Preliminaries
Exponentially Small Probabilities
Small Subgraphs
Matchings
The Phase Transition
Asymptotic Distributions
The Chromatic Number
Extremal and Ramsey Properties
Random Regular Graphs
Zero-One Laws
References
Indexes
Preliminaries
Exponentially Small Probabilities
Small Subgraphs
88.
図書
editors, Young Gheel Baik, David L. Johnson, Ann Chi Kim
出版情報:
Berlin ; New York : W. de Gruyter, 2000 viii, 383 p. ; 25 cm
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89.
図書
Shahn Majid
出版情報:
Cambridge : Cambridge University Press, 2000 xix, 640 p. ; 25 cm
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Introduction
Definition of Hopf algebras / 1：
Quasitriangular Hopf algebras / 2：
Quantum enveloping algebras / 3：
Matrix quantum groups / 4：
Quantum random walks and combinatorics / 5：
Bicrossproduct Hopf algebras / 6：
Quantum double and double cross products / 7：
Lie algebras and Poisson brackets / 8：
Representation theory / 9：
Braided groups and q-deformation / 10：
References
Index
Introduction
Definition of Hopf algebras / 1：
Quasitriangular Hopf algebras / 2：
90.
図書
Marc Hindry, Joseph H. Silverman
目次情報:
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Preface
Acknowledgments
Contents
Detailed Contents for Part A
Introduction
The Geometry of Curves and Abelian Varieties / Part A：
Algebraic Varieties / A.1：
Divisors / A.2：
Linear Systems / A.3：
Algebraic Curves / A.4：
Abelian Varieties over C / A.5：
Jacobians over C / A.6：
Abelian Varieties over Arbitrary Fields / A.7：
Jacobians over Arbitrary Fields / A.8：
Schemes / A.9：
Height Functions / Part B：
Absolute Values / B.1：
Heights on Projective Space / B.2：
Heights on Varieties / B.3：
Canonical Height Functions / B.4：
Canonical Heights on Abelian Varieties / B.5：
Counting Rational Points on Varieties / B.6：
Heights and Polynomials / B.7：
Local Height Functions / B.8：
Canonical Local Heights on Abelian Varieties / B.9：
Introduction to Arakelov Theory / B.10：
Exercises
Rational Points on Abelian Varieties / Part C：
The Weak Mordell-Weil Theorem / C.1：
The Kernel of Reduction Modulo p / C.2：
Finiteness Theorems in Algebraic Number Theory / C.3 Appendix：
The Selmer and Tate-Shafarevich Groups / C.4 Appendix：
Galois Cohomology and Homogeneous Spaces / C.5 Appendix：
Diophantine Approximation and Integral Points on Curves / Part D：
Two Elementary Results on Diophantine Approximation / D.1：
Roth's Theorem / D.2：
Preliminary Results / D.3：
Construction of the Auxiliary Polynomial / D.4：
The Index Is Large / D.5：
The Index Is Small (Roth's Lemma) / D.6：
Completion of the Proof of Roth's Theorem / D.7：
Application: The Unit Equation U + V = 1 / D.8：
Application: Integer Points on Curves / D.9：
Rational Points on Curves of Genus at Least 2 / Part E：
Vojta's Geometric Inequality and Faltings' Theorem / E.1：
Pinning Down Some Height Functions / E.2：
An Outline of the Proof of Vojta's Inequality / E.3：
An Upper Bound for h[subscript Omega](z, w) / E.4：
A Lower Bound for h[subscript Omega](z, w) for Nonvanishing Sections / E.5：
Constructing Sections of Small Height I: Applying Riemann-Roch / E.6：
Constructing Sections of Small Height II: Applying Siegel's Lemma / E.7：
Lower Bound for h[subscript Omega](z, w) at Admissible (i*[subscript 1], i*[subscript 2]): Version I / E.8：
Eisenstein's Estimate for the Derivatives of an Algebraic Function / E.9：
Lower Bound for h[subscript Omega](z, w) at Admissible (i*[subscript 1], i*[subscript 2]): Version II / E.10：
A Nonvanishing Derivative of Small Order / E.11：
Completion of the Proof of Vojta's Inequality / E.12：
Further Results and Open Problems / Part F：
Curves and Abelian Varieties / F.1：
Rational Points on Subvarieties of Abelian Varieties / F.1.1：
Application to Points of Bounded Degree on Curves / F.1.2：
Discreteness of Algebraic Points / F.2：
Bogomolov's Conjecture / F.2.1：
The Height of a Variety / F.2.2：
Height Bounds and Height Conjectures / F.3：
The Search for Effectivity / F.4：
Effective Computation of the Mordell-Weil Group A([kappa]) / F.4.1：
Effective Computation of Rational Points on Curves / F.4.2：
Quantitative Bounds for Rational Points / F.4.3：
Geometry Governs Arithmetic / F.5：
Kodaira Dimension / F.5.1：
The Bombieri-Lang Conjecture / F.5.2：
Vojta's Conjecture / F.5.3：
Varieties Whose Rational Points Are Dense / F.5.4：
References
List of Notation
Index
Affine and Projective Varieties / A.1.1：
Algebraic Maps and Local Rings / A.1.2：
Dimension / A.1.3：
Tangent Spaces and Differentials / A.1.4：
Weil Divisors / A.2.1：
Cartier Divisors / A.2.2：
Intersection Numbers / A.2.3：
Linear Systems and Maps / A.3.1：
Ampleness and the Enriques-Severi-Zariski Lemma / A.3.2：
Line Bundles and Sheaves / A.3.3：
Birational Models of Curves / A.4.1：
Genus of a Curve and the Riemann-Roch Theorem / A.4.2：
Curves of Genus 0 / A.4.3：
Curves of Genus 1 / A.4.4：
Curves of Genus at Least 2 / A.4.5：
Algebraic Surfaces / A.4.6：
Complex Tori / A.5.1：
Divisors, Theta Functions, and Riemann Forms / A.5.2：
Riemann-Roch for Abelian Varieties / A.5.3：
Abelian Integrals / A.6.1：
Periods of Riemann Surfaces / A.6.2：
The Jacobian of a Riemann Surface / A.6.3：
Albanese Varieties / A.6.4：
Generalities / A.7.1：
Divisors and the Theorem of the Cube / A.7.2：
Dual Abelian Varieties and Poincare Divisors / A.7.3：
Construction and Properties / A.8.1：
The Divisor [Theta] / A.8.2：
Families of Subvarieties / A.8.3 Appendix：
Varieties over Z / A.9.1：
Analogies Between Number Fields and Function Fields / A.9.2：
Minimal Model of a Curve / A.9.3：
Neron Model of an Abelian Variety / A.9.4：
Preface
Acknowledgments
Contents
91.
図書
R.A. Minlos
92.
図書
Salma Kuhlmann
目次情報:
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Preliminaries on valued and ordered modules
Non-archimedean exponential fields
Valuation theoretic interpretation of the growth and Taylor axioms
The exponential rank
Construction of exponential fields
Models for the elementary theory of the reals with restricted analytic functions and exponentiation
Exponential Hardy fields
The model theory of contraction groups
Bibliography
Index
List of notation
Preliminaries on valued and ordered modules
Non-archimedean exponential fields
Valuation theoretic interpretation of the growth and Taylor axioms
93.
図書
Werner Balser
出版情報:
New York ; Tokyo : Springer, c2000 xviii, 299 p. ; 25 cm
シリーズ名:
Universitext
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Basic Properties of Solutions
Singularities of First Kind
Highest Level Simplifications
Asymptotic Power Series
Integral Transforms
Summable Power Series
Cauchy-Heine Transform
Solutions of Highest Level
Acceleration Operators
Multisummable Power Series
Some Equivalent Definitions of Multisummability
Matrices and Vector Spaces
Functions with Values in Banach Spaces
Functions of a Matrix
Basic Properties of Solutions
Singularities of First Kind
Highest Level Simplifications
94.
図書
A. Süleyman Üstünel, Moshe Zakai
目次情報:
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Introduction
Some Background Material and Preliminary Results / 1：
The Radon-Nikodym Theorem / 1.1：
Uniform Integrability / 1.2：
Two Measures Associated with a Point Transformation / 1.3：
Kakutani's Dichotomy Theorem / 1.4：
The Structure of Non-negative Continuous Martingales / 1.5：
Notes and References
Transformation of Measure Induced by Adapted Shifts / 2：
The Girsanov Theorem / 2.1：
Integrability Conditions on λt / 2.2：
Transformation of Measure Induced on C0 ([0, 1]) by Direct Shifts / 2.3：
Transformations of Measure Induced on C0 ([0, 1]) by Indirect Shifts / 2.4：
The Innovation Theorem / 2.5：
A Dimension-free Extension of Results of the Previous Sections / 2.6：
The Representability of Measures by Shifts / 2.7：
Transformation of Measure Induced by General Shifts / 3：
The Change of Variables Formula for a Small Perturbation of the Identity / 3.1：
H-Regularity of Random Variables / 3.3：
Some Preliminaries / 3.4：
The Change of Variables Formula / 3.5：
A Comparison Between the Formulas Associated with Adapted and Non Adapted Cases / 3.6：
The Sard Inequality / 4：
Introduction and Preliminaries / 4.1：
The Measurability of the Forward Image / 4.2：
The Sard Inequality I / 4.3：
The Sard Inequality II / 4.4：
Some Applications to Absolute Continuity / 4.5：
Transformation of Measure Under Anticipative Flows / 5：
Introduction and Finite Dimensional Flows / 5.1：
Cylindrical Flows / 5.2：
Infinite Dimensional Flows / 5.3：
A Singular Flow on the Classical Wiener Space / 5.4：
Monotone Shifts / 6：
Absolute Continuity of Monotone Shifts-I / 6.1：
Absolute Continuity of Monotone Shifts-II / 6.4：
Shifts of Hammerstein Type / 6.5：
Generalized Radon-Nikodym Derivatives / 7：
The Gλ Class of Wiener functionals and its Composition with Shifts / 7.1：
The Gλ -class of Wiener Functionals / 7.2.1：
The Extendibility of Gλ Functionals / 7.2.2：
A Generahzed R-N Derivative for Gλ Functionals / 7.3：
The Conditioning of Gλ Functionals with Respect to Certain Sub-sigma-fields / 7.4：
Composition of the Rademacher Class of Wiener Functionals with Shifts / 7.5：
The Composition Rules / 7.6：
The Cyhndrical Case / 7.6.1：
Extensions of the Composition Rules / 7.6.2：
Random Rotations / 8：
A Partial Converse to Theorem 8.2.1 / 8.1：
The Invertibility of Tw = w + R{w)h and that of &Rcirc; / 8.4：
Stochastic Calculus of Rotations / 8.5：
A New Derivation and Calculation of E[<$>\delta\eta|{\cal B}<$>] / 8.5.1：
Case of Deterministic R / 8.5.2：
Transformations of Measure Induced by Euclidean Motions of the Wiener Path / 8.6：
The Degree Theorem on Wiener Space / 9：
Measure Theoretic Degree / 9.1：
Applications to Absolute Continuity / 9.3：
Relations with Leray-Schauder Degree / 9.4：
Some Inequalities / A：
Gronwall and Young Inequalities / A.1：
Gronwall Inequality / A.1.1：
Young Inequality / A.1.2：
Some Inequalities for det2 (IH + A) / A.2：
An Introduction to Malliavin Calculus / B：
Introduction to Abstract Wiener Space / B.1：
An Introduction to Analysis on Wiener Space / B.2：
Construction of Sobolev Derivatives / B.3：
The Divergence / B.4：
Ornstein-Uhlenbeck Operator and Meyer Inequalities / B.5：
Some Useful Lemmas / B.6：
Local Versus Global Differentiability of Wiener Functionals / B.7：
Exponential Integrability of Wiener Functionals and Poincaré Inequality / B.8：
References
Index
Notations
Introduction
Some Background Material and Preliminary Results / 1：
The Radon-Nikodym Theorem / 1.1：
95.
図書
Sibe Mardešić
目次情報:
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Preface
Introduction
Coherent Homotopy / I：
Coherent mappings / 1：
Mappings of inverse systems / 1.1：
Coherent mappings of inverse systems / 1.2：
Composition of coherent mappings / 1.3：
The coherence operator C / 1.4：
Coherent homotopy / 2：
The coherent homotopy category CH(pro-Top) / 2.1：
Associativity of the composition / 2.2：
The identity morphism / 2.3：
Coherent homotopy of sequences / 3：
Coherent homotopy of finite height / 3.1：
Coherent homotopy of inverse sequences / 3.2：
Coherent homotopy and localization / 4：
An isomorphism theorem in CH(pro-Top) / 4.1：
Cotelescopes (homotopy limits) / 4.2：
Localizing pro-Top at level homotopy equivalences / 4.3：
Coherent homotopy as a Kleisli category / 5：
The Kleisli category of a monad / 5.1：
CH(pro-Top) is the Kleisli category of a monad / 5.2：
Strong Shape / II：
Resolutions / 6：
Resolutions of spaces and mappings / 6.1：
Characterization of resolutions / 6.2：
Resolutions versus limits / 6.3：
Existence of polyhedral and ANR - resolutions / 6.4：
Resolutions of direct products and pairs / 6.5：
Strong expansions / 7：
Strong expansions of spaces / 7.1：
Resolutions are strong expansions / 7.2：
Invariance under coherent domination / 7.3：
Strong shape / 8：
Coherent expansions of spaces / 8.1：
The strong shape category / 8.2：
Strong shape equivalences / 8.3：
Strong shape of metric compacta / 9：
The Quigley strong shape category / 9.1：
Complement theorems / 9.2：
Selected results on strong shape / 10：
Normal pairs of spaces / 10.1：
Normal triads of spaces / 10.2：
Strong shape using the Vietoris system / 10.3：
The Bauer - Günther description of strong shape / 10.4：
Strong shape of compacta via multi-valued maps / 10.5：
Strong shape using approximate systems / 10.6：
Strong shape and localization / 10.7：
Stable strong shape / 10.8：
Higher Derived Limits / III：
The derived functors of lim / 11：
Inverse systems of modules / 11.1：
Projective and injective systems / 11.2：
lim and its right derived functors / 11.3：
Axiomatic characterization of the functors limn / 11.4：
Explicit formulae for limn / 11.5：
limn for sequences / 11.6：
limn and the extension functors Extn / 12：
The bifunctors Extn / 12.1：
Expressing limn in terms of Extn / 12.2：
The vanishing theorems / 13：
Homological dimension / 13.1：
Goblot's vanishing theorem / 13.2：
Systems with non-vanishing limn / 13.3：
The cofinality theorem / 14：
Colimits and tensor products / 14.1：
The cofinality theorem for limn / 14.2：
Higher limits on the category pro-Mod / 15：
limn as a functor on pro - Mod / 15.1：
Properties of limn on pro - Mod / 15.2：
Homology Groups / IV：
Homology pro-groups / 16：
Homology pro-groups and Čech homology / 16.1：
Higher limits of homology pro-groups / 16.2：
Strong homology groups of systems / 17：
Strong homology of pro-chain complexes / 17.1：
The first Miminoshvili sequence / 17.2：
The second Miminoshvili sequence / 17.3：
Isomorphism theorems for strong homology / 17.4：
Strong homology on CH(pro-Top) / 18：
Chain mappings induced by coherent mappings / 18.1：
Chain mappings induced by congruence classes / 18.2：
Chain mappings induced by homotopy classes / 18.3：
Chain mappings induced by composition / 18.4：
Induced chain mappings and the coherence functor / 18.5：
Strong homology of spaces / 19：
Strong homology groups of spaces / 19.1：
Strong excision property / 19.2：
Strong homology of clusters / 19.3：
Strong homology and dimension / 19.4：
Strong homology of polyhedra / 19.5：
Strong homology of metric compacta / 19.6：
Spectral sequences. Abelian groups / 20：
The spectral sequence of a filtered complex / 20.1：
The spectral sequences of a bicomplex / 20.2：
The Roos spectral sequence / 20.3：
Pure extension functors Pextn / 20.4：
Some theorems on abelian groups / 20.5：
Strong homology of compact spaces / 21：
Universal coefficients for compact polyhedra / 21.1：
Homology of compact spaces / 21.2：
Universal coefficients for compact spaces / 21.3：
A filtration of the strong homology group / 21.4：
Strong homology with compact supports / 21.5：
Generalized strong homology / 22：
References
List of Special Symbols
Author Index
Subject Index
Preface
Introduction
Coherent Homotopy / I：
96.
図書
by Karl-Hermann Neeb
目次情報:
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Preface
Introduction
Abstract Representation Theory / A.：
Reproducing Kernel Spaces / Chapter I.：
Operator-Valued Positive Definite Kernels / I.1.：
The Cone of Positive Definite Kernels / I.2.：
Representations of Involutive Semigroups / Chapter II.：
Involutive Semigroups / II.1.：
Bounded Representations / II.2.：
Hermitian Representations / II.3.：
Representations on Reproducing Kernel Spaces / II.4.：
Positive Definite Functions on Involutive Semigroups / Chapter III.：
Positive Definite Functions--the Discrete Case / III.1.：
Enveloping C*-algebras / III.2.：
Multiplicity Free Representations / III.3.：
Continuous and Holomorphic Representations / Chapter IV.：
Continuous Representations and Positive Definite Functions / IV.1.：
Holomorphic Representations of Involutive Semigroups / IV.2.：
Convex Geometry and Representations of Vector Spaces / B.：
Convex Sets and Convex Functions / Chapter V.：
Convex Sets and Cones / V.1.：
Finite Reflection Groups and Convex Sets / V.2.：
Convex Functions and Fenchel Duality / V.3.：
Laplace Transforms / V.4.：
The Characteristic Function of a Convex Set / V.5.：
Representations of Cones and Tubes / Chapter VI.：
Commutative Representation Theory / VI.1.：
Representations of Cones / VI.2.：
Holomorphic Representations of Tubes / VI.3.：
Realization of Cyclic Representations by Holomorphic Functions / VI.4.：
Holomorphic Extensions of Unitary Representations / VI.5.：
Convex Geometry of Lie Algebras / C.：
Convexity in Lie Algebras / Chapter VII.：
Compactly Embedded Cartan Subalgebras / VII.1.：
Root Decompositions / VII.2.：
Lie Algebras With Many Invariant Convex Sets / VII.3.：
Convexity Theorems and Their Applications / Chapter VIII.：
Admissible Coadjoint Orbits and Convexity Theorems / VIII.1.：
The Structure of Admissible Lie Algebras / VIII.2.：
Invariant Elliptic Cones in Lie Algebras / VIII.3.：
Highest Weight Representations of Lie Algebras, Lie Groups, and Semigroups / D.：
Unitary Highest Weight Representations: Algebraic Theory / Chapter IX.：
Generalized Highest Weight Representations / IX.1.：
Positive Complex Polarizations / IX.2.：
Highest Weight Modules of Finite-Dimensional Lie Algebras / IX.3.：
The Metaplectic Factorization / IX.4.：
Unitary Highest Weight Representations of Hermitian Lie Algebras / IX.5.：
Unitary Highest Weight Representations: Analytic Theory / Chapter X.：
The Convex Moment Set of a Unitary Representation / X.1.：
Irreducible Unitary Representations / X.2.：
The Metaplectic Representation and Its Applications / X.3.：
Special Properties of Unitary Highest Weight Representations / X.4.：
Moment Sets for C*-algebras / X.5.：
Moment Sets for Group Representations / X.6.：
Complex Ol'shanskii Semigroups and Their Representations / Chapter XI.：
Lawson's Theorem on Ol'shanskii Semigroups / XI.1.：
Holomorphic Extension of Unitary Representations / XI.2.：
Holomorphic Representations of Ol'shanskii Semigroups / XI.3.：
Irreducible Holomorphic Representations / XI.4.：
Gelfand-Raikov Theorems for Ol'shanskii Semigroups / XI.5.：
Decomposition and Characters of Holomorphic Representations / XI.6.：
Realization of Highest Weight Representations on Complex Domains / Chapter XII.：
The Structure of Groups of Harish-Chandra Type / XII.1.：
Representations of Groups of Harish-Chandra Type / XII.2.：
The Compression Semigroup and Its Representations / XII.3.：
Examples / XII.4.：
Hilbert Spaces of Square Integrable Holomorphic Functions / XII.5.：
Complex Geometry and Representation Theory / E.：
Complex and Convex Geometry of Complex Semigroups / Chapter XIII.：
Locally Convex Functions and Local Recession Cones / XIII.1.：
Invariant Convex Sets and Functions in Lie Algebras / XIII.2.：
Calculations in Low-Dimensional Cases / XIII.3.：
Biinvariant Plurisubharmonic Functions / XIII.4.：
Complex Semigroups and Stein Manifolds / XIII.5.：
Biinvariant Domains of Holomorphy / XIII.6.：
Biinvariant Hilbert Spaces and Hardy Spaces on Complex Semigroups / Chapter XIV.：
Biinvariant Hilbert Spaces / XIV.1.：
Hardy Spaces Defined by Sup-Norms / XIV.2.：
Hardy Spaces Defined by Square Integrability / XIV.3.：
The Fine Structure of Hardy Spaces / XIV.4.：
Coherent State Representations / Chapter XV.：
Complex Structures on Homogeneous Spaces / XV.1.：
Heisenberg's Uncertainty Principle and Coherent States / XV.2.：
Appendices
Bounded Operators on Hilbert Spaces / Appendix I.：
Spectral Measures and Unbounded Operators / Appendix II.：
Holomorphic Functions on Infinite-Dimensional Spaces / Appendix III.：
Symplectic Geometry / Appendix IV.：
Simple Modules of p-Length 2 / Appendix V.：
Symplectic Modules of Convex Type / Appendix VI.：
Square Integrable Representations of Locally Compact Groups / Appendix VII.：
The Stone-von Neumann-Mackey Theorem / Appendix VIII.：
Bibliography
List of Symbols
Index
Preface
Introduction
Abstract Representation Theory / A.：
97.
図書
Marcel Berger
98.
図書
Frederick P. Gardiner, Nikola Lakic
目次情報:
続きを見る
Quasiconformal mapping Riemann surfaces
Quadratic differentials
Part I Quadratic differentials
Part II Teichmuller equivalence
The Bers embedding Kobayashi's metric on Teichmuller space Isomorphisms and automorphisms
Teichmuller uniqueness
The mapping class group Jenkins-Strebel differentials
Measured foliations Obstacle problems
Asymptotic Teichmuller space
Asymptotically extremal maps Universal Teichmuller space
Substantial boundary points Earthquake mappings
Bibliography
Index
Quasiconformal mapping Riemann surfaces
Quadratic differentials
Part I Quadratic differentials
99.
図書
Michel Demazure ; translated from the French by David Chillingworth
出版情報:
Berlin ; Tokyo : Springer, c2000 viii, 301 p. ; 24 cm
シリーズ名:
Universitext
子書誌情報:
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所蔵情報:
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目次情報:
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Introduction
Notation
Local Inversion / 1：
A Preliminary Statement / 1.1：
Partial Derivatives. Strictly Differentiable Functions / 1.3：
The Local Inversion Theorem: General Statement / 1.4：
Functions of Class Cr / 1.5：
The Local Inversion Theorem for Cr maps / 1.6：
Generalizations of the Local Inversion Theorem / 1.8：
Submanifolds / 2：
Definitions of Submanifolds / 2.1：
First Examples / 2.3：
Tangent Spaces of a Submanifold / 2.4：
Transversality: Intersections / 2.5：
Transversality: Inverse Images / 2.6：
The Implicit Function Theorem / 2.7：
Diffeomorphisms of Submanifolds / 2.8：
Parametrizations, Immersions and Embeddings / 2.9：
Proper Maps: Proper Embeddings / 2.10：
From Submanifolds to Manifolds / 2.11：
Some History / 2.12：
Transversality Theorems / 3：
Countability Properties in Topology / 3.1：
Negligible Subsets / 3.3：
The Complement of the Image of a Submanifold / 3.4：
Sard''s Theorem / 3.5：
Critical Points, Submersions and the Geometrical Form of Sard''s Theorem / 3.6：
The Transversality Theorem: Weak Form / 3.7：
Jet Spaces / 3.8：
The Thom Transversality Theorem / 3.9：
Classification of Differentiable Functions / 3.10：
Taylor Formulae Without Remainder / 4.1：
The Problem of Classification of Maps / 4.3：
Critical Points: the Hessian Form / 4.4：
The Morse Lemma / 4.5：
Fiburcations of Critical Points / 4.6：
Apparent Contour of a Surface in R3 / 4.7：
Maps from R2 into R2 / 4.8：
Envelopes of Plane Curves / 4.9：
Caustics / 4.10：
Genericity and Stability / 4.11：
Catastrophe Theory / 5：
The Language of Germs / 5.1：
r-sufficient Jets; r-determined Germs / 5.3：
The Jacobian Ideal / 5.4：
The Theorem on Sufficiency of Jets / 5.5：
Deformations of a Singularity / 5.6：
The Principles of Catastrophe Theory / 5.7：
Catastrophes of Cusp Type / 5.8：
A Cusp Example / 5.9：
Liquid-Vapour Equilibrium / 5.10：
The Elementary Catastrophes / 5.11：
Catastrophes and Controversies / 5.12：
Vector Fields / 6：
Exemples of Vector Fields (Rn Case) / 6.1：
First Integrals / 6.3：
Vector Fields on Submanifolds / 6.4：
The Uniqueness Theorem and Maximal Integral Curves / 6.5：
One-parameter Groups of Diffeomorphisms / 6.6：
The Existence Theorem (Local Case) / 6.8：
The Existence Theorem (Global Case) / 6.9：
The Integral Flow of a Vector Field / 6.10：
The Main Features of a Phase Portrait / 6.11：
Discrete Flows and Continuous Flows / 6.12：
Linear Vector Fields / 7：
The Spectrum of an Endomorphism / 7.1：
Space Decomposition Corresponding to Partition of the Spectrum / 7.3：
Norm and Eigenvalues / 7.4：
Contracting, Expanding and Hyperbolic Endommorphisms / 7.5：
The Exponential of an Endomorphism / 7.6：
One-parameter Groups of Linear Transformations / 7.7：
The Image of the Exponential / 7.8：
Contracting, Expanding and Hyperbolic Exponential Flows / 7.9：
Topological Classification of Linear Vector Fields / 7.10：
Topological Classification of Automorphisms / 7.11：
Classification of Linear Flows in Dimension 2 / 7.12：
Singular Pints of Vector Fields / 8：
The Classification Problem / 8.1：
Linearization of a Vector Field in the Neighbourhodd of a Singular Point / 8.3：
Difficulties with Linearization / 8.4：
Singularities with Attracting Linearization / 8.5：
Liapunov Theory / 8.6：
The Theorems of Grobman and Hartman / 8.7：
Stable and Unstable Manifolds of a Hyperbolic Singularity / 8.8：
Differentiable Linearization: Statement of the Problem / 8.9：
Differentiable Linearization: Resonances / 8.10：
Differentiable Linearization: The Theorems of Sternberg and Hartman / 8.11：
Linearization in Dimenension 2 / 8.12：
Some Historical Landmarks / 8.13：
Closed Orbits - Structural Stability / 9：
The Poincarè Map / 9.1：
Characteristic Multipliers of a Closed Orbit / 9.3：
Attracting Closed Orbits / 9.4：
Classification of Closed Orbits and Classification of Diffeomorphisms / 9.5：
Hyperbolic Closed Orbits / 9.6：
Local Structural Stability / 9.7：
The Kupka-Smale Theorem / 9.8：
Morse-Smale Fields / 9.9：
Structural Stability Through the Ages / 9.10：
Bifurcations of Phase Portrait / 10：
What Do We Mean by a Bifurcation? / 10.1：
The Centre Manifold Theorem / 10.3：
The Saddle-Node Bifurcation / 10.4：
The Hopf Bifurcation / 10.5：
Local Bifurcations Carried by a Closed Orbit / 10.6：
Saddle / 10.7：
Introduction
Notation
Local Inversion / 1：
100.
図書
Alexander Reznikov, Norbert Schappacher, editors
図書
