1.
図書
Joachim Kock, Israel Vainsencher
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Preface
Introduction
Prologue: Warming up with Cross Ratios, and the Definition of Moduli Space / 0：
Cross ratios / 0.1：
Definition of moduli space / 0.2：
Stable n-pointed Curves / 1：
n-pointed smooth rational curves / 1.1：
Stable n-pointed rational curves / 1.2：
Stabilization, forgetting marks, contraction / 1.3：
Sketch of the construction of [Characters not reproducible subscript 0,n] / 1.4：
The boundary / 1.5：
Generalizations and references / 1.6：
Stable Maps / 2：
Maps P[superscript 1 Characters not reproducible] P[superscript r] / 2.1：
1-parameter families / 2.2：
Kontsevich stable maps / 2.3：
Idea of the construction of [Characters not reproducible subscript 0,n] (P[superscript r], d) / 2.4：
Evaluation maps / 2.5：
Forgetful maps / 2.6：
Easy properties and examples / 2.7：
Complete conics / 2.9：
Enumerative Geometry via Stable Maps / 2.10：
Classical enumerative geometry / 3.1：
Counting conics and rational cubics via stable maps / 3.2：
Kontsevich's formula / 3.3：
Transversality and enumerative significance / 3.4：
Stable maps versus rational curves / 3.5：
Gromov-Witten Invariants / 3.6：
Definition and enumerative interpretation / 4.1：
Properties of Gromov-Witten invariants / 4.2：
Recursion / 4.3：
The reconstruction theorem / 4.4：
Quantum Cohomology / 4.5：
Quick primer on generating functions / 5.1：
The Gromov-Witten potential and the quantum product / 5.2：
Associativity / 5.3：
Kontsevich's formula via quantum cohomology / 5.4：
Bibliography / 5.5：
Index
Preface
Introduction
Prologue: Warming up with Cross Ratios, and the Definition of Moduli Space / 0：
2.
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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3.
図書
Yu.L. Pavlov
出版情報:
Utrecht : VSP, 2000 122 p. ; 26 cm
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4.
図書
Grigor A. Barsegian
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Preface
Tangent Variation Principle
Satellite Principles
Modification of Length-area Principle
Estimates for collections of Gamma-Lines
Estimates of lengths of Gamma-Lines for angular-quasiconformal mappings
Remarks on applying of estimates of L (D, Gamma)
Nevanlinna and Ahilfors Theories
Additions
Basic concepts and outcomes of Nevanlinna Value Distribution theory and Ahlfors theory of covering surfaces
Geometric deficient values
On some
Preface
Tangent Variation Principle
Satellite Principles
5.
図書
Abdul-Majid Wazwaz
出版情報:
Lisse ; Tokyo : A.A. Balkema, c2002 xi, 459 p. ; 25 cm
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6.
図書
M.S. Howe
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Preface
Introduction / 1：
Lighthill's theory / 2：
The compact Green's function / 3：
Vorticity / 4：
Vortex sound / 5：
Vortex-surface interaction noise in two-dimensions / 6：
Problems in three-dimensions / 7：
Further worked examples / 8：
Bibliography
Preface
Introduction / 1：
Lighthill's theory / 2：
7.
図書
Giuliana Davidoff, Peter Sarnak, Alain Valette
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An overview
Graph theory / 1：
Number theory / 2：
PSL2(q) / 3：
The graphs Xp, q / 4：
4-regular graphs with large girth / Appendix A：
Index
Bibliography
An overview
Graph theory / 1：
Number theory / 2：
8.
図書
Robert Botet, Marek Płoszajczak
9.
図書
Andrew Majda
出版情報:
New York : Courant Institute of Mathematical Sciences, New York University , Providence, R.I : American Mathematical Society, 2003 ix, 234 p. ; 26 cm
シリーズ名:
Courant lecture notes in mathematics ; 9
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Preface
Introduction / Chapter 1.：
Basic Properties of the Equations with Rotation and Stratification / 1.1.：
Two-Dimensional Exact Solutions / 1.2.：
Buoyancy and Stratification / 1.3.：
Jet Flows with Rotation and Stratification / 1.4.：
From Vertical Stratification to Shallow Water / 1.5.：
Some Remarkable Features of Stratified Flow / Chapter 2.：
Energy Principle / 2.1.：
Vorticity in Stratified Fluids and Exact Solutions Motivated by Local Analysis / 2.2.：
Use of Theorem 2.4: Exact Two-Dimensional Solutions / 2.3.：
Nonlinear Plane Waves in Stratified Flow: Internal Gravity Waves / 2.4.：
Exact Solutions with Large-Scale Motion and Nonlinear Plane Waves / 2.5.：
More Details for Theorem 2.7 on Special Exact Solutions for the Boussinesq Equations Including Plane Waves / 2.6.：
Linear and Nonlinear Instability of Stratified Flows with Strong Stratification / Chapter 3.：
Boussinesq Equations and Vorticity Stream Formulation / 3.1.：
Nonlinear Instability of Stratified Flows / 3.2.：
Shear Flows / 3.3.：
Some Background Facts on ODEs / 3.4.：
Rotating Shallow Water Theory / Chapter 4.：
Rotating Shallow Water Equations / 4.1.：
Conservation of Potential Vorticity / 4.2.：
Nonlinear Conservation of Energy / 4.3.：
Linear Theory for the Rotating Shallow Water Equations / 4.4.：
Nondimensional Form of the Rotating Shallow Water Equations / 4.5.：
Derivation of the Quasi-Geostrophic Equations / 4.6.：
The Quasi-Geostrophic Equations as a Singular PDE Limit / 4.7.：
The Model Rotating Shallow Water Equations / 4.8.：
Preliminary Mathematical Considerations / 4.9.：
Regorous Convergence of the Model Rotating Shallow Water Equations to the Quasi-Geostrophic Equations / 4.10.：
Proof of the Convergence Theorem / 4.11.：
Linear and Weakly Nonlinear Theory of Dispersive Waves with Geophysical Examples / Chapter 5.：
Linear Wave Midlatitude Planetary Equations / 5.1.：
Dispersive Waves: General Properties / 5.2.：
Interpretation of Group Velocity / 5.3.：
Distant Propagation from a Localized Source / 5.4.：
WKB Methods for Linear Dispersive Waves / 5.5.：
Beyond Caustics: Eikonal Equation Revisited / 5.6.：
Weakly Nonlinear WKB for Perturbations Around a Constant State / 5.7.：
Nonlinear WKB and the Boussinesq Equations / 5.8.：
Simplified Equations for the Dynamics of Strongly Stratified Flow / Chapter 6.：
Nondimensionalization of the Boussinesq Equations for Stably Stratified Flow / 6.1.：
The Vorticity Stream Formulation and Elementary Properties of the Limit Equations for Strongly Stratified Flow / 6.2.：
Solutions of the Limit Dynamics with Strong Stratification as Models for Laboratory Experiments / 6.3.：
The Stratified Quasi-Geostrophic Equations as a Singular Limit of the Rotating Boussinesq Equations / Chapter 7.：
The Rotating Boussinesq Equations / 7.1.：
The Nondimensional Rotating Boussinesq Equations / 7.3.：
Formal Asymptotic Derivation of the Quasi-Geostrophic Equations as a Distinguished Asymptotic Limit of Small Rossby and Froude Numbers / 7.4.：
Rigorous Convergence of the Rotating Boussinesq Equations to the Quasi-Geostrophic Equations / 7.5.：
Introduction to Averaging over Fast Waves for Geophysical Flows / 7.6.：
Motivation for Fast-Wave Averaging / 8.1.：
A General Framework for Averaging over Fast Waves / 8.3.：
Elementary Analytic Models for Comparing Instabilities at Low Froude Numbers with the Low Froude Number Limit Dynamics / 8.4.：
The Rapidly Rotating Shallow Water Equations with Unbalanced Initial Data in the Quasi-Geostrophic Limit / 8.5.：
The Interaction of Fast Waves and Slow Dynamics in the Rotating Stratified Boussinesq Equations / 8.6.：
Waves and PDEs for the Equatorial Atmosphere and Ocean / Chapter 9.：
Introduction to Equatorial Waves for Rotating Shallow Water / 9.1.：
The Equatorial Primitive Equations / 9.2.：
The Nonlinear Equatorial Long-Wave Equations / 9.3.：
A Simple Model for the Steady Circulation of the Equatorial Atmosphere / 9.4.：
Bibliography
Preface
Introduction / Chapter 1.：
Basic Properties of the Equations with Rotation and Stratification / 1.1.：
10.
図書
Christopher Parker, Peter Rowley
11.
図書
Ken A. Brown, Ken R. Goodearl
12.
図書
Michael Frame and Benoit B. Mandelbrot, editors ; foreword by Lynn Arthur Steen
出版情報:
[Washington, D.C.] : Mathematical Association of America, c2002 xiii, 206 p., [4] p. of plates ; 28 cm
シリーズ名:
MAA notes ; 58
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Foreword / Lynn Arthur Steen
Preface
Introductory Essays
Some Reasons for the Effectiveness of Fractals in Mathematics Education / Benoit B. Mandelbrot ; Michael Frame1.：
Unsolved Problems and Still-Emerging Concepts in Fractal Geometry / 2.：
Fractals, Graphics, and Mathematics Education / 3.：
Mathematics and Society in the 20th Century / 4.：
Classroom Experiences
Teaching Fractals and Dynamical Systems at The Hotchkiss School / Melkana Brakalova ; David Coughlin5.：
Reflecting on Wada Basins: Some Fractals with a Twist / Dane Camp6.：
Learning and Teaching about Fractals / Donald M. Davis7.：
The Fractal Geometry of the Mandelbrot Set: Periods of the Bulbs / Robert L. Devaney8.：
Fractals--Energizing the Mathematics Classroom / Vicki Fegers ; Mary Beth Johnson9.：
Other Chaos Games / Sandy Fillebrown10.：
Creating and Teaching Undergraduate Courses and Seminars in Fractal Geometry: a Personal Experience / Michel Lapidus11.：
Exploring Fractal Dimensions by Experiment / Ron Lewis12.：
Fractal Themes at Every Level / Kenneth G. Monks13.：
Art and Fractals: Artistic Explorations of Natural Self-Similarity / Brianna Murratti14.：
Order and Chaos, Art and Magic: a First College Course in Quantitative Reasoning Based on Fractals and Chaos / David Peak15.：
A Software Driven Undergraduate Fractals Course / Douglas C. Ravenel16.：
A Final Word
The Fractal Ring from Art to Art through Mathematics, Finance, and the Sciences / 17.：
Appendices
Panorama of Fractals and Their Uses. An Alphabetic Wordbook-Index / 18.：
Reports of Some Field Experiences / 19.：
Guide to Topics
References
About the Editors and Other Contributors
Index
Foreword / Lynn Arthur Steen
Preface
Introductory Essays
13.
図書
A. Galves, J.K. Hale, C. Rocha, editors
14.
図書
M. O. Deville, P. F. Fischer, E. H. Mund
目次情報:
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Preface
Fluid mechanics and computation: an introduction / 1：
Approximation methods for elliptic problems / 2：
Parabolic and hyperbolic problems / 3：
Mutidimensional problems / 4：
Steady Stokes and Navier-Stokes equations / 5：
Unsteady Stokes and Navier-Stokes equations / 6：
Domain decomposition / 7：
Vector and parallel implementations / 8：
Preliminary mathematical concepts / Appendix A：
Orthogonal polynomials and discrete transforms / Appendix B：
Preface
Fluid mechanics and computation: an introduction / 1：
Approximation methods for elliptic problems / 2：
15.
図書
Prem K. Kythe, Pratap Puri
出版情報:
Boston : Birkhäuser, c2002 xviii, 508 p. ; 25 cm
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16.
図書
by Nikolay Sidorov ... [et al.]
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Preface
On Regularization of Linear Equations on the Basis of Perturbation Theory / 1.：
Generalised Jordan chains, sets and root numbers of linear operators
Regularization of linear equations with Fredholm operators / 2.：
Principal theorem on regularization of linear equations by the perturbation method / 3.：
Regularization of linear equations on the basis of perturbation theory in Hilbert spaces / 4.：
Computation of eigenvalues and eigenvectors of linear operators by pseudo-perturbation method / 5.：
Notes / 6.：
Investigation of Bifurcation Points of a Nonlinear Equations
Lyapunov-Schmidt BEq in the problem of a bifurcation point
General existence theorems for the bifurcation points
Construction of asymptotics in a neighborhood of a bifurcation point
Asymptotic bifurcation points
On perturbation of the branch points of nonlinear equations
Notes and generalization
Regularization of Computation of Solutions in a Neighborhood of the Branch Point
Construction of the regularizing equation in the problem at a branch point
Definition and properties of simple solutions
Regularization of calculations of simple solutions of nonlinear equations
Regularization of method for continuation along parameter in a neighborhood of a branch point
Notes and remarks
Iterations, Interlaced Equations and Lyapunov Convex Majorants in Nonlinear Analysis
Iterations and uniformization of branching solutions in nonlinear analysis
BEq and the selection of the initial approximation / 1.1：
On the role of supporting lines and Newton diagrams in the construction of the initial approximation / 1.2：
A one-step iteration method / 1.3：
An N-step iteration method / 1.4：
On regularization in the sense of Tikhonov, modifications and possible generalizations of an N-step method / 1.5：
Remarks / 1.6：
Interlaced and potential BEq
The property of (S, K)-interlacing of an equation and its inheritance by the BEq / 2.1：
(T, M)-interlaced and (T[superscript 2], M)-interlaced BEq / 2.2：
[alpha]-parametric interlaced BEq / 2.3：
Interlaced BEq of potential type / 2.4：
Surface bundle of a domain of free parameters / 2.5：
Parametrization of solutions and the method of successive approximations / 2.6：
On the role of Lyapunov convex majorants in the nonlocal existence theorems of implicit functions
Majorants independent of parameters / 3.1：
Majorants depending on a parameter / 3.2：
Investigation of the existence domain of the solution of equation F(u, [varepsilon]) = 0. / 3.3：
Methods of Representation Theory and Group Analysis in Bifurcation Theory
Nonlinear equations invariant under transformation groups
Lyapounov-Schmidt BEq and some methods of their reduction
Some applications
Hereditary symmetry of branching equations and resolving systems
Invariance properties of BEq
Resolving systems for differential equations with Fredholm operator at the derivative and their symmetry
On the Grobman-Hartman theorem for equations with degenerate operator at the derivative
Construction and investigation of the branching equation by group analysis methods
BEq of solutions invariant relative to subgroups of the original equation group symmetry
Potential BEq
Direct methods of BEq group invariance usage for its general form construction by admitted group symmetry
Applications of Lie--Ovsyannikov theorem about invariant manifolds for the construction of BEq general form by allowing group symmetry / 4.1：
Non-linearly perturbed Helmholtz equations
Domain symmetry and bifurcational solutions asymptotics / 5.1：
Periodic solutions / 5.2：
Capillary--gravity waves in fluid layers
Capillary--gravity waves in a floating fluid spatial layer / 6.1：
Capillary--gravity waves at the interface of two fluids flow / 6.2：
Capillary--gravity waves on a cylindrical surface / 6.3：
Ferrofluid layer in a magnetic field / 6.4：
Fluid phase state crystallization problem in statistical crystal theory / 7.：
The statement of the problem / 7.1：
Subspaces N(B[subscript s]). Their expansions on irreducible subspaces relative to O[subscript h] / 7.2：
The BEq construction / 7.3：
Asymptotics of small solutions families for n[subscript s] = 1, 3 / 7.4：
Solutions invariant relative to normal divisors O[subscript h] / 7.5：
Andronov--Hopf bifurcation under group symmetry conditions / 8.：
BEq derivation in non-stationary bifurcation / 8.1：
Symmetry inheritance theorem / 8.2：
BEq construction by group analysis methods / 8.3：
On the asymptotics of small solutions / 8.4：
Stability of the bifurcating solutions / 9.：
Singular Differential Equations in Banach Spaces
Fundamental operator functions
Generalized functions in Banach spaces
Fundamental operator functions of singular differential operators
Fundamental operator functions of singular integral and integro-differential operators
The initial value problem for a differential equation having a Noetherian operator at the derivative. Periodic solutions and the property of convergence
Auxiliary information on Jordan sets of Noetherian operators
The initial value problem for a linear differential equation
The initial value problem for a nonlinear differential equation
Integral pseudo-solutions
Non-stationary differential equations with singularities
The initial value problem for a non-stationary linear equation and systems of 1st kind integral Volterra equations
The initial value problem for a non-stationary linear differential equation and a system of integral Volterra equations with a singularity
Branching differential equations of the initial value problem with singularity
The initial value problem for a nonlinear differential equation and equations with a singular point / 3.4：
Partial differential equations with the Fredholm operator in the main part
The theory of semigroups and groups of operators with kernels
Relative resolvents. Relatively adjoint elements
Relatively spectrally bounded operators and analytical groups of operators with kernells
Relatively sectorial operators and analytical semigroups of operators with kernels / 5.3：
Steady-State Solutions of the Vlasov--Maxwell System
Introduction
Stationary solutions of a VM system
The reduction of VM system to the resolving elliptic system (2.28), (2.29)
The reduction of the resolving system to the unique resolving equation
Existence of solutions of the boundary value problem (2.40)-(2.42)
Applications of the reduction theorems
Normalized solutions for a one-component distribution function
Non-stationary problem
Bifurcation points and nontrivial solutions of the stationary VM system
Statement of the boundary value problem and the problem at a bifurcation point / 4.2：
Resolution of the bifurcation equation / 4.3：
The existence theorem for bifurcation points and the construction of asymptotic solutions / 4.4：
Appendices
Positive solutions of the nonlinear singular boundary value problem of magnetic insulation / A：
References
Preface
On Regularization of Linear Equations on the Basis of Perturbation Theory / 1.：
Generalised Jordan chains, sets and root numbers of linear operators
17.
図書
edited by Ugo Bruzzo, Vittorio Gorini and Ugo Moschella
目次情報:
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Preface
An elementary introduction to branes in string theory / Alberto LerdaPart 1：
Introduction / 1：
Branes in string theory / 2：
The superstring effective actions of type II / 2.1：
Type IIA / 2.1.1：
Type IIB / 2.1.2：
General construction / 2.2：
Explicit solutions / 2.3：
Fundamental string / 2.3.1：
NS 5-brane / 2.3.2：
D p-branes / 2.3.3：
The geometry of the D3-brane of type IIB / 2.3.4：
The boundary state description of D-branes / 3：
The boundary state with an external field / 3.1：
The effective action of D-branes / 4：
Classical D-branes from the boundary state / 5：
References
Physical aspects / Yassen Stanev ; Cesar Gomez ; Pedro RescoPart 2：
Two-dimensional conformal field theory on open and unoriented surfaces / 6：
General properties of two-dimensional CFT / 6.1：
The stress-energy tensor in two dimensions / 6.2.1：
Rational conformal field theories / 6.2.2：
Non-Abelian conformal current algebras / 6.2.3：
Partition function, modular invariance / 6.2.4：
Correlation functions in current algebra models / 6.3：
Properties of the chiral conformal blocks / 6.3.1：
Regular basis of 4-point functions in the SU (2) model / 6.3.2：
Matrix representation of the exchange algebra / 6.3.3：
Two-dimensional braid invariant Green functions / 6.3.4：
CFT on surfaces with holes and crosscaps / 6.4：
Open sector, sewing constraints / 6.4.1：
Closed unoriented sector, crosscap constraint / 6.4.2：
Partition functions / 6.5：
Klein bottle projection / 6.5.1：
Annulus partition function / 6.5.2：
Mobius strip projection / 6.5.3：
Solutions for the partition functions / 6.5.4：
Acknowledgments
Topics in string tachyon dynamics / 7：
Why tachyons? / 7.1：
Tachyons in AdS: The c = 1 barrier / 7.3：
Tachyon [sigma]-model beta-functions / 7.4：
Open strings and cosmological constant: the Fischler-Susskind mechanism / 7.5：
Fischler-Susskind mechanism: closed-string case / 7.5.1：
Open-string contribution to the cosmological constant: the filling brane / 7.5.2：
The effective action / 7.6：
A warming-up exercise / 7.6.1：
Non-critical dimension and tachyon condensation / 7.6.2：
D-branes, tachyon condensation and K-theory / 7.7：
Extended objects and topological stability / 7.7.1：
A gauge theory analogue for D-branes in type II strings / 7.7.2：
K-theory version of Sen's conjecture / 7.7.3：
Type IIA strings / 7.7.4：
Some final comments on gauge theories / 7.8：
Mathematical developments / Kenji Fukaya ; Antonella Grassi ; Michele RossiPart 3：
Deformation theory, homological algebra and mirror symmetry / 8：
Classical deformation theory / 8.1：
Holomorphic structure on vector bundles / 8.2.1：
Families of holomorphic structures on vector bundles / 8.2.2：
Cohomology and deformations / 8.2.3：
Bundle valued harmonic forms / 8.2.4：
Construction of a versal family and Feynman diagrams / 8.2.5：
The Kuranishi family / 8.2.6：
Formal deformations / 8.2.7：
Homological algebra and deformation theory / 8.3：
Homotopy theory of A[subscript infinity] and L[subscript infinity] algebras / 8.3.1：
Maurer-Cartan equation and moduli functors / 8.3.2：
Canonical model, Kuranishi map and moduli space / 8.3.3：
Superspace and odd vector fields--an alternative formulation of L[subscript infinity] algebras / 8.3.4：
Application to mirror symmetry / 8.4：
Novikov rings and filtered A[subscript infinity], L[subscript infinity] algebras / 8.4.1：
Review of a part of global symplectic geometry / 8.4.2：
From Lagrangian submanifold to A[subscript infinity] algebra / 8.4.3：
Maurer-Cartan equation for filtered A[subscript infinity] algebras / 8.4.4：
Homological mirror symmetry / 8.4.5：
Large N dualities and transitions in geometry / 9：
Geometry and topology of transitions / 9.1：
The local topology of a conifold transition / 9.1.1：
Transitions of Calabi-Yau threefolds / 9.1.2：
Transitions and mirror symmetry / 9.1.3：
Transitions, black holes etc / 9.1.4：
Chern-Simons theory / 9.2：
Chern-Simons' form and action / 9.2.1：
The Hamiltonian formulation of the Chern-Simons QFT (following Witten's canonical quantization) / 9.2.2：
Computability and link invariants / 9.2.3：
The Gopakumar-Vafa conjecture / 9.3：
Matching the free energies / 9.3.1：
The matching of expectation values / 9.3.2：
Lifting to M-theory / 9.4：
Riemannian Holonomy, G[subscript 2] manifolds and Calabi-Yau, revisited / 9.4.1：
The geometry / 9.4.2：
Branes and M-theory lifts / 9.4.3：
M-theory lift and M-theory flop / 9.4.4：
Appendix: Some notation on singularities and their resolutions / 9.5：
Appendix: More on the Greene-Plesser construction / 9.6：
Appendix: More on transitions in superstring theory / 9.7：
Appendix: Principal bundles, connections etc / 9.8：
Appendix: More on Witten's open-string theory interpretation of QFT / 9.9：
Index
Preface
An elementary introduction to branes in string theory / Alberto LerdaPart 1：
Introduction / 1：
18.
図書
edited by S. Müller-Stach and C. Peters
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Introductory Material / Part I：
Chow varieties, the Euler-Chow series and the total coordinate ring / J. Elizondo1：
Introduction to Lawson homology / C. Peters ; S. Kosarew2：
Lawson (Co)homology / Part II：
Topological properties of the algebraic cycles functor / P. Lima-Filho3：
Motives and Motivic Cohomology / Part III：
Lectures on motives / J. P. Murre4：
A short introduction to higher Chow groups / P. Elbaz-Vincent5：
Hodge Theoretic Invariants of Cycles / Part IV：
Three lectures on the Hodge conjecture / J. D. Lewis6：
Lectures on Nori's connectivity theorem / J. Nagel7：
Beilinson's Hodge and Tate conjectures / S. Saito8：
Introductory Material / Part I：
Chow varieties, the Euler-Chow series and the total coordinate ring / J. Elizondo1：
Introduction to Lawson homology / C. Peters ; S. Kosarew2：
19.
図書
Ayalvadi Ganesh, Neil O'Connell, Damon Wischik
20.
図書
Rolf Gohm
21.
図書
Simon Tavaré, Ofer Zeitouni ; editor, Jean Picard
目次情報:
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Simon Tavare: Ancestral Inference in Population Genetics Contents / Part I：
Introduction / 1：
The Wright-Fisher model / 2：
The Ewens Sampling Formula / 3：
The Coalescent / 4：
The Infinitely-many-sites Model / 5：
Estimation in the Infinitely-many-sites Model / 6：
Ancestral Inference in the Infinitely-many-sites Model / 7：
The Age of a Unique Event Polymorphism / 8：
Markov Chain Monte Carlo Methods / 9：
Recombination / 10：
ABC: Approximate Bayesian Computation / 11：
Afterwords / 12：
References
Ofer Zeitouni: Random Walks in Random Environment Contents / Part II：
RWRE - d=1
RWRE - d > 1
List of Participants
List of Short Lectures
Simon Tavare: Ancestral Inference in Population Genetics Contents / Part I：
Introduction / 1：
The Wright-Fisher model / 2：
22.
図書
A. D. Alexandrov ; [english translation by N.S. Dairbekov, S.S. Kutateladze and A.B. Sossinsky]
目次情報:
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Introduction
Basic Concepts and Simplest Properties of Convex Polyhedra
Methods and Results
Uniqueness of Polyhedra with Prescribed Development
Existence of Polyhedra with Prescribed Development
Gluing and Flexing Polyhedra with Boundary
Conditions for Congruence of Polyhedra with Parallel Faces
Existence Theorems for Polyhedra with Prescribed Face Directions
Relationship Between the Congruence Condition for Polyhedra with Parallel Faces and Other Problems
Polyhedra with Vertices on Prescribed Rays
Infinitesimal Rigidity of Convex Polyhedra with Stationary Development
Infinitesimal Rigidity Conditions for Polyhedra with Prescribed Face Directions
Supplements
References
Subject Index
Introduction
Basic Concepts and Simplest Properties of Convex Polyhedra
Methods and Results
23.
図書
上野健爾 [ほか] 著
出版情報:
東京 : 岩波書店, 2005.5-2005.11 2冊 ; 22cm
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24.
図書
Donald E. Knuth
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Combinatorial Analysis and Computers / 1：
Two Notes on Notation / 2：
Bracket Notation for the 'Coefficient of' Operator / 3：
Johann Faulhaber and Sums of Powers / 4：
Notes on Thomas Harriot / 5：
A Permanent Inequality / 6：
Overlapping Pfaffians / 7：
The Sandwich Theorem / 8：
Combinatorial Matrices / 9：
Aztec Diamonds, Checkerboard Graphs, and Spanning Trees / 10：
Partitioned Tensor Products and Their Spectra / 11：
Oriented Subtrees of an Arc Digraph / 12：
Another Enumeration of Trees / 13：
Abel Identities and Inverse Relations / 14：
Convolution Polynomials / 15：
Polynomials Involving the Floor Function / 16：
Construction of a Random Sequence / 17：
An Imaginary Number System / 18：
Tables of Finite Fields
Finite Semifields and Projective Planes / 20：
A Class of Projective Planes / 21：
Notes on Central Groupoids / 22：
Huffman's Algorithm via Algebra / 23：
Wheels Within Wheels / 24：
Complements and Transitive Closures / 25：
Random Matroids / 26：
The Asymptotic Number of Geometries / 27：
Permutations with Nonnegative Partial Sums / 28：
Efficient Balanced Codes / 29：
The Knowlton - Graham Partition Problem / 30：
Permutations, Matrices, and Generalized Young Tableaux / 31：
Enumeration of Plane Partitions / 32：
A Note on Solid Partitions / 33：
Identities from Partition Involutions / 34：
Subspaces, Subsets, and Partitions / 35：
The Power of a Prime That Divides a Generalized Coefficient / 36：
An Almost Linear Recurrence / 37：
Recurrence Relations Based on Minimization / 38：
A Recurrence Related to Trees / 39：
The First Cycles in an Evolving Graph / 40：
The Birth of the Giant Component / 41：
Index
Combinatorial Analysis and Computers / 1：
Two Notes on Notation / 2：
Bracket Notation for the 'Coefficient of' Operator / 3：
25.
図書
Harry Kesten (editor)
目次情報:
続きを見る
The Random-Cluster Model / Geoffrey Grimmett
Models of First-Passage Percolation / C. Douglas Howard
Relaxation Times of Markov Chains in Statistical Mechanics and Combinatorial Structures / Fabio Martinelli
Random Walks on Finite Groups / Laurent Saloff-Coste
Index
Introduction / 1：
A Motivating Example: the Assignment Problem / 1.1：
A Stalking Horse: the Partial Matching Problem / 1.2：
Organization of the Survey / 1.3：
Geometric Graphs and Local Weak Convergence / 2：
Geometric Graphs / 2.1：
<$>{\cal G}^\ast<$> as a Metric Space / 2.2：
Local Weak Convergence / 2.3：
The Standard Construction / 2.4：
A Prototype: The Limit of Uniform Random Trees / 2.5：
Maximal Weight Partial Matching on Random Trees / 3：
Weighted Matchings of Graphs in General / 3.1：
Our Case: Random Trees with Random Edge Weights / 3.2：
Two Obvious Guesses: One Right, One Wrong / 3.3：
Not Your Grandfather's Recursion / 3.4：
A Direct and Intuitive Plan / 3.5：
Characterization of the Limit of <$>B(T_n^{small})<$> / 3.6：
Characterization of the Limit of <$>B(T_n^{big})<$> / 3.7：
The Limit Theorem for Maximum Weight Partial Matchings / 3.8：
Closing the Loop: Another Probabilistic Solution of a Fixed-Point Equation / 3.9：
From Coupling to Stability - Thence to Convergence / 3.10：
Looking Back: Perspective on a Case Study / 3.11：
The Mean-Field Model of Distance / 4：
From Poisson Points in <$>{\op R}^{d}<$> to a Simple Distance Model / 4.1：
The Poisson Weighted Infinite Tree - or, the PWIT / 4.2：
The Cut-off Components of a Weighted Graph and a PWIT / 4.3：
The Minimum Spanning Forests of an Infinite Graph / 4.4：
The Average Length Per Vertex of the MSF of a PWIT / 4.5：
The Connection to Frieze's ζ(3) Theorem / 4.6：
Minimal Cost Perfect Matchings / 5：
A Natural Heuristic - Which Fails for a Good Reason / 5.1：
Involution Invariance and the Standard Construction / 5.2：
Involution Invariance and the Convergence of MSTs / 5.3：
A Heuristic That Works by Focusing on the Unknown / 5.4：
A Distributional Identity with a Logistic Solution / 5.5：
A Stochastic Process that Constructs a Matching / 5.6：
Calculation of a Limiting Constant: <$>\pi^{2}/6<$> / 5.7：
Passage from a PWIT Matching to a Kn Matching / 5.8：
Finally - Living Beyond One's Means / 5.9：
Problems in Euclidean Space / 6：
A Motivating Problem / 6.1：
Far Away Places and Their Influence / 6.2：
Euclidean Methods and Some Observations in Passing / 6.3：
Recurrence of Random Walks in Limits of Planar Graphs / 6.4：
Limitations, Challenges, and Perspectives / 7：
References
Potts and random-cluster processes
Random-cluster measures
Ising and Potts models
Random-cluster and Ising-Potts coupled
The limit as <$>q \downarrow 0<$>
Rank-generating functions
Infinite-volume random-cluster measures
Stochastic ordering
A differential formula
Conditional probabilities
Infinite-volume weak limits
Random-cluster measures on infinite graphs
The case q < 1
Phase transition, the big picture
Infinite open clusters
First- and second-order phase transition
General results in d (≥ 2) dimensions
The subcritical phase, p < pc (q)
The supercritical phase, p > pc (q)
Near the critical point, p ≃ pc (q)
In two dimensions
Graphical duality
Value of the critical point
First-order phase transition
SLE limit when q ≤ 4
On complete graphs and trees
On complete graphs / 7.1：
On trees and non-amenable graphs / 7.2：
Time-evolutions of random-cluster models / 8：
Reversible dynamics / 8.1：
Coupling from the past / 8.2：
Swendsen-Wang dynamics / 8.3：
The Basic Model and Some Fundamental Questions
Notation
The Time Constant
The Fundamental Processes of Hammersley and Welsh
About μ
Minimizing Paths
Asymptotic Shape and Shape Fluctuations
Shape Theorems for Standard FPP
About the Asymptotic Shape for Lattice FPP
FPP Based on Poisson Point Processes
Upper Bounds on Shape Fluctuations
Some Related Longitudinal Fluctuation Exponents
Monotonicity
Transversal Fluctuations and the Divergence of Shape Fluctuations
Transversal Fluctuation Exponents
Upper Bounds on <$>\xi<$>
Lower Bounds on <$>\chi<$>
Lower Bounds on <$>\xi<$>
Fluctuations for Other Related Models
Infinite Geodesics and Spanning Trees
Semi-Infinite Geodesics and Spanning Trees
Coalescence and Another Spanning Tree in 2 Dimensions
Doubly-Infinite Geodesics
Summary of Some Open Problems
Mixing times for reversible, continuous-time Markov chains
Analytic methods
Tensorization of the Poincaré and logarithmic Sobolev inequalities
Geometric tools
Comparison methods
Coupling methods and block dynamics
Statistical mechanics models in <$>{\op Z}^d<$>
Grand canonical Gibbs measures
Mixing conditions and absence of long-range order
Canonical Gibbs measures for lattice gases
The ferromagnetic Ising and Potts models
FK representation of Potts models
Antiferromagnetic models on an arbitrary graph: Potts and hard-core models
Model with random interactions
Unbounded spin systems
Ground states of certain quantum Heisenberg models as classical Gibbs measures
Glauber dynamics in <$>{\op Z}^d<$>
The dynamics in a finite volume
The dynamics in an infinite volume
Graphical construction
Uniform ergodicity and logarithmic Sobolev constant
Mixing property versus logarithmic Sobolev constant in <$>{\op Z}^d<$>
The auxiliary chain and sweeping out relations method
The renormalization group approach
The martingale method
The recursive analysis
Rapid mixing for unbounded spin systems
Torpid mixing in the phase coexistence region
Torpid mixing for the Ising model in <$>\Lambda \subset {\op Z}^{d}<$> with free boundary conditions
Interface driven mixing inside one phase
Torpid mixing for Potts model in <$>{\op Z}^d<$>
Glauber dynamics for certain random systems in <$>{\op Z}^d<$>
Combination of torpid and rapid mixing: the dilute Ising model
Relaxation to equilibrium for spin glasses
Glauber dynamics for more general structures
Glauber dynamics on trees and hyperbolic graphs
Glauber dynamics for the hard-core model
Cluster algorithms: the Swendsen-Wang dynamics for Potts models
Mixing time for conservative dynamics / 9：
Random transposition, Bernoulli-Laplace and symmetric simple exclusion / 9.1：
The asymmetric simple exclusion / 9.2：
The Kac model for the Boltzmann equation / 9.3：
Adsorbing staircase walks / 9.4：
Kawasaki dynamics for lattice gases / 10：
Diffusive scaling of the mixing time in the one-phase region / 10.1：
Background and Notation / 10.2：
Finite Markov Chains
Invariant Markov Chains on Finite Groups
Shuffling Cards and the Cut-off Phenomenon
Three Examples of Card Shuffling
Exact Computations
The Cut-off Phenomenon
Probabilistic Methods
Coupling
Strong Stationary Times
Spectrum and Singular Values
General Finite Markov Chains
The Random Walk Case
Lower Bounds
Eigenvalue Bounds Using Paths
Cayley Graphs
The Second Largest Eigenvalue
The Lowest Eigenvalue
Diameter Bounds, Isoperimetry and Expanders
Results Involving Volume Growth Conditions
Moderate Growth
Nilpotent Groups
Nilpotent Groups with many Generators / 7.3：
Representation Theory for Finite Groups
The General Set-up
Abelian Examples
Random Random Walks
Central Measures and Bi-invariant Walks
Characters and Bi-invariance
Random Transposition on the Symmetric Group
Walks Based on Conjugacy Classes of the Symmetric Group
Finite Classical Groups
Fourier Analysis for Non-central Measures / 9.5：
Comparison Techniques
The min-max Characterization of Eigenvalues
Comparing Dirichlet Forms Using Paths
Comparison for Non-symmetric Walks / 10.3：
The Random-Cluster Model / Geoffrey Grimmett
Models of First-Passage Percolation / C. Douglas Howard
Relaxation Times of Markov Chains in Statistical Mechanics and Combinatorial Structures / Fabio Martinelli
26.
図書
Jean-Philippe Anker, Bent Orsted, editors
目次情報:
続きを見る
Preface / Ji
Introduction to Symmetric Spaces and Their Compactifications / Borel/Ji
Compactifications of Symmetric and Locally Symmetric Spaces / Kobayashi
Restrictions of Unitary Representations of Real Reductive Groups
Preface / Ji
Introduction to Symmetric Spaces and Their Compactifications / Borel/Ji
Compactifications of Symmetric and Locally Symmetric Spaces / Kobayashi
27.
図書
S. Ramanan
目次情報:
続きを見る
Preface
Sheaves and Differential Manifolds: Definitions and Examples / Chapter 1：
Sheaves and Presheaves / 1：
Basic Constructions / 2：
Differential Manifolds / 3：
Lie Groups; Action on a Manifold / 4：
Exercises
Differential Operators / Chapter 2：
First Order Differential Operators
Locally Free Sheaves and Vector Bundles
Flow of a Vector Field
Theorem of Frobenius
Tensor Fields; Lie Derivative / 5：
The Exterior Derivative; de Rham Complex / 6：
Differential Operators of Higher Order / 7：
Integration on Differential Manifolds / Chapter 3：
Integration on a Manifold
Sheaf of Densities
Adjoints of Differential Operators
Cohomology of Sheaves and Applications / Chapter 4：
Injective Sheaves
Sheaf Cohomology
Cohomology through Other Resolutions
Singular and Sheaf Cohomologies
Cech and Sheaf Cohomologies
Differentiable Simplices; de Rham's Theorem
Connections on Principal and Vector Bundles; Lifting of Symbols / Chapter 5：
Connections in a Vector Bundle
The Space of All Connections on a Bundle
Principal Bundles
Connections on Principal Bundles
Curvature
Chern-Weil Theory
Holonomy Group; Ambrose-Singer Theorem
Linear Connections / Chapter 6：
Lifting of Symbols and Torsion
Manifolds with Additional Structures / Chapter 7：
Reduction of the Structure Group
Torsion Free G-Connections
Complex Manifolds
The Outer Gauge Group
Riemannian Geometry
Riemannian Curvature Tensor
Ricci, Scalar and Weyl Curvature Tensors
Clifford Structures and the Dirac Operator / 8：
Local Analysis of Elliptic Operators / Chapter 8：
Regularisation
A Characterisation of Densities
Schwartz Space of Functions and Densities
Fourier Transforms
Distributions
Theorem of Sobolev
Interior Regularity of Elliptic Solutions
Vanishing Theorems and Applications / Chapter 9：
Elliptic Operators on Differential Manifolds
Elliptic Complexes
Composition Formula
A Vanishing Theorem
Hodge Decomposition
Lefschetz Decomposition
Kodaira's Vanishing Theorem
The Imbedding Theorem
Appendix
Algebra
Topology
Analysis
Bibliography
Index
Preface
Sheaves and Differential Manifolds: Definitions and Examples / Chapter 1：
Sheaves and Presheaves / 1：
28.
図書
谷口雅彦著
出版情報:
東京 : 培風館, 2004.12 v, 224p ; 21cm
子書誌情報:
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所蔵情報:
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29.
図書
Burak Ozbagci, András I. Stipsicz
目次情報:
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Preface
Introduction
Topological Surgeries
Symplectic 4-Manifolds
Contact 3-Manifolds
Convex Surfaces in Contact 3-Manifolds
Spinc Structures on 3- and 4-Manifolds
Symplectic Surgery
Stein Manifolds
Open Books and Contact Structures
Lefschetz Fibrations on 4-Manifolds
Contact Dehn Surgery
Fillings of Contact 3-Manifolds
Appendix: Seiberg-Witten Invariants
Appendix: Heegaard Floer Theory
Appendix: Mapping Class Groups
Bibliography
Index
Preface
Introduction
Topological Surgeries
30.
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
31.
図書
J. Frédéric Bonnans, Alexander Shapiro
32.
図書
Masaki Kashiwara, Tetsuji Miwa, editors
33.
図書
Luis Ribes, Pavel Zalesskii
目次情報:
続きを見る
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：
34.
図書
M. Rørdam, F. Larsen, N. Laustsen
目次情報:
続きを見る
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：
35.
図書
Nicolae Dinculeanu
目次情報:
続きを見る
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.：
36.
図書
edited by N. Kenmochi
37.
図書
D. Bao, S.-S. Chern, Z. Shen
目次情報:
続きを見る
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：
38.
図書
Franco Vivaldi
目次情報:
続きを見る
What is Maple? / 1：
Integers and rationals / 2：
Integers / 2.1：
Arithmetical expressions / 2.2：
Some Maple / 2.3：
Divisibility / 2.4：
Rationals / 2.5：
Primes / 2.6：
Standard library functions / 2.7：
Sets and functions / 3：
Sets / 3.1：
Sets with Maple / 3.2：
Functions / 3.3：
User-defined functions / 3.4：
Sequences / 4：
Basics / 4.1：
Sequences with Maple / 4.2：
Plotting the elements of a sequence / 4.3：
Periodic and eventually periodic sequences / 4.4：
Some non-periodic sequences / 4.5：
Basic counting sequences / 4.6：
Sequences defined recursively / 4.7：
Real and complex numbers / 5：
Digits of rationals / 5.1：
Real numbers / 5.2：
Random and pseudo-random digits* / 5.3：
Complex numbers / 5.4：
Structure of expressions / 5.5：
Analysis of an expression / 6.1：
More on substitutions / 6.2：
Functions acting on operands of expressions / 6.3：
Polynomials and rational functions / 7：
Polynomials / 7.1：
Polynomial arithmetic / 7.2：
Rational functions / 7.3：
Basic manipulations / 7.4：
Partial fractions decomposition* / 7.5：
Finite sums and products / 8：
Sums and products with Maple / 8.1：
Symbolic evaluation of sums and products / 8.3：
Double sums and products / 8.4：
Sums and products as recursive sequences / 8.5：
Elements of programming / 9：
Iteration / 9.1：
Study of an eventually periodic sequence / 9.2：
Conditional execution* / 9.3：
Procedures* / 9.4：
Vector spaces / 10：
Cartesian product of sets / 10.1：
Vectors with Maple / 10.2：
Matrices / 10.4：
Matrices with Maple / 10.5：
Modular arithmetic* / 11：
A modular system / 11.1：
Arithmetic of equivalence classes / 11.2：
Some arithmetical constructions in F[subscript p] / 11.3：
Some abstract structures* / 12：
The axioms of arithmetic / 12.1：
Metric spaces / 12.2：
Rings and fields / 12.3：
What is Maple? / 1：
Integers and rationals / 2：
Integers / 2.1：
39.
図書
Kai-Seng Chou, Xi-Ping Zhu
出版情報:
Boca Raton, Flo. : Chapman & Hall/CRC, c2001 ix, 255 p. ; 24 cm
子書誌情報:
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Preface
Basic Results / 1：
Short time existence / 1.1：
Facts from the parabolic theory / 1.2：
The evolution of geometric quantities / 1.3：
Invariant Solutions for the Curve Shortening Flow / 2：
Travelling waves / 2.1：
Spirals / 2.2：
The support function of a convex curve / 2.3：
Self-similar solutions / 2.4：
The Curvature-Eikonal Flow for Convex Curves / 3：
Blaschke Selection Theorem / 3.1：
Preserving convexity and shrinking to a point / 3.2：
Gage-Hamilton Theorem / 3.3：
The contracting case of the ACEF / 3.4：
The stationary case of the ACEF / 3.5：
The expanding case of the ACEF / 3.6：
The Convex Generalized Curve Shortening Flow / 4：
Results from the Brunn-Minkowski Theory / 4.1：
The AGCSF for [sigma] in (1/3, 1) / 4.2：
The affine curve shortening flow / 4.3：
Uniqueness of self-similar solutions / 4.4：
The Non-convex Curve Shortening Flow / 5：
An isoperimetric ratio / 5.1：
Limits of the rescaled flow / 5.2：
Classification of singularities / 5.3：
A Class of Non-convex Anisotropic Flows / 6：
The decrease in total absolute curvature / 6.1：
The existence of a limit curve / 6.2：
Shrinking to a point / 6.3：
A whisker lemma / 6.4：
The convexity theorem / 6.5：
Embedded Closed Geodesics on Surfaces / 7：
Basic results / 7.1：
The limit curve / 7.2：
Convergence to a geodesic / 7.3：
The Non-convex Generalized Curve Shortening Flow / 8：
The number of convex arcs / 8.1：
Removal of interior singularities / 8.3：
The almost convexity theorem / 8.5：
Bibliography
Index
Preface
Basic Results / 1：
Short time existence / 1.1：
40.
図書
Mohamed A. Khamsi, William A. Kirk
目次情報:
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Preface
Metric Spaces
Introduction
Metric Contraction Principles
Hyperconvex Spaces
"Normal" Structures in Metric Spaces
Banach Spaces
Banach Spaces: Introduction
Continuous Mappings in Banach Spaces
Metric Fixed Point Theory
Banach Space Ultrapowers
Appendix: Set Theory
Bibliography
Index
Preface
Metric Spaces
Introduction
41.
図書
Dietrich Braess ; translated by Larry L. Schumaker
出版情報:
Cambridge : Cambridge University Press, 2001 xvii, 352 p. ; 23 cm
子書誌情報:
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Preface to the Third English Edition page
Preface to the First English Edition
Preface to the German Edition
Notation
Introduction / Chapter I：
Examples and Classification of PDE's / 1：
Examples
Classification of PDE's
Well-posed Problems
Problems
The Maximum Principle / 2：
Corollaries
Problem
Finite Difference Methods / 3：
Discretization
Discrete maximum principle
A Convergence Theory for Difference Methods / 4：
Consistency
Local and global error
Limits of the convergence theory
Conforming Finite Elements / Chapter II：
Sobolev Spaces
Introduction to Sobolev spaces
Friedrichs' inequality
Possible singularities of H1 functions
Compact imbeddings
Variational Formulation of Elliptic Boundary-Value Problems of Second Order
Variational formulation
Reduction to homogeneous boundary conditions
Existence of solutions
Inhomogeneous boundary conditions
The Neumann Boundary-Value Problem. A Trace Theorem
Ellipticity in H1
Boundary-value problems with natural boundary conditions
Neumann boundary conditions
Mixed boundary conditions
Proof of the trace theorem
Practical consequences of the trace theorem
The Ritz-Galerkin Method and Some Finite Elements
Model Problem
Some Standard Finite Elements / 5：
Requirements on the meshes
Significance of the differentiability properties
Triangular elements with complete polynomials
Remarks on C1 elements
Bilinear elements
Quadratic rectangular elements
Affine families
Choice of an element
Approximation Properties / 6：
The Bramble-Hilbert lemma
Bilinear quadrilateral elements
Inverse estimates
Clément's interpolation
Appendix: On the optimality of the estimates
Error Bounds for Elliptic Problems of Second Order / 7：
Remarks on regularity
Error bounds in the energy norm
L2 estimates
A simple L? estimate
The L2-projector
Computational Considerations / 8：
Assembling the stiffness matrix
Static condensation
Complexity of setting up the matrix
Effect on the choice of a grid
Local mesh refinement
Implementation of the Neumann boundary-value Problem
Nonconforming and Other Methods / Chapter III：
Abstract Lemmas and a Simple Boundary Approximation
Generalizations of Céa's lemma
Duality methods
The Crouzeix-Raviart element
A Simple approximation to curved boundaries
Modifications of the duality argument
Isoparametric Elements
Isoparametric triangular elements
Isoparametric quadrilateral elements
Further Tools from Functional Analysis
Negative norms
Adjoint operators
An abstract existence theorem
An abstract convergence theorem
Proof of Theorem 3.4
Saddle Point Problems
Saddle points and minima
The inf-sup condition
Mixed finite element methods
Fortin interpolation
Saddle point problems with penalty term
Typical applications
Mixed Methods for the Poisson Equation
The Poisson equation as a mixed problem
The Raviart - Thomas element
Interpolation by Raviart-Thomas elements
Implementation and postprocessing
Mesh-dependent norms for the Raviart-Thomas element
The Softening behaviour of mixed methods
The Stokes Equation
Nearly incompressible flows
Finite Elements for the Stokes Problems
An instable element
The Taylor-Hood element
The MINI element
The divergence-free nonconforming P1 element
A Posteriori Error Estimates
Residual estimators
Lower estimates
Remark on other estimators
Local mesh refinement and convergence
A Posteriori Error Estimates via the Hypercircle Method / 9：
The Conjugate Gradient Method / Chapter IV：
Classical Iterative Methods for Solving Linear Systems
Stationary linear processes
The Jacobi and Gauss-Seidel methods
The model problem
Overrelaxation
Gradient Methods
The general gradient method
Gradient methods and quadratic functions
Convergence behavior in the case of large condition numbers
Conjugate Gradient and the Minimal Residual Method
The CG algorithm
Analysis of the CG method as an optimal method
The minimal residual method
Indefinite and unsymmetric matrices
Preconditioning
Preconditioning by SSOR
Preconditioning by ILU
Remarks on parallelization
Nonlinear Problems
The Uzawa algorithm and its variants
An alternative
Multigrid Methods / Chapter V：
Multigrid Methods for Variational Problems
Smoothing properties of classical iterative methods
The multigrid idea
The algorithm
Transfer between grids
Convergence of Multigrid Methods
Discrete norms
Connection with the Sobolev norm
Approximation property
Convergence proof for the two-grid method
An alternative short proof
Some variants
Convergence for Several Levels
A recurrence formula for the W-cycle
An improvement for the energy norm
The convergence proof for the V-cycle
Nested Iteration
Computation of starting values
Complexity
Multigrid methods with a small number of levels
The CASCADE algorithm
Multigrid Analysis via Space Decomposition
Schwarz alternating method
Assumptions
Direct consequences
Convergence of multiplicative methods
Verification of A1
Local mesh refinements
The multigrid-Newton method
The nonlinear multigrid method
Starting values
Finite Elements in Solid Mechanics / Chapter VI：
Introduction to Elasticity Theory
Kinematics
The equilibrium equations
The Piola transform
Constitutive Equations
Linear material laws
Hyperelastic Materials
Linear Elasticity Theory
The variational problem
The displacement formulation
The mixed method of Hellinger and Reissner
The mixed method of Hu and Washizu
Nearly incompressible material
Locking
Locking of the Timoshenko beam and typical remedies
Membranes
Plane stress states
Plane strain states
Membrane elements
The PEERS element
Beams and Plates: The Kirchhoff Plate
The hypotheses
Note on beam models
Mixed methods for the Kirchoff plate
DKT elements
The Mindlin-Reissner Plate
The Helmholtz decomposition
The mixed formulation with the Helmholtz decomposition
MITC elements
The Model without a Helmboltz decomposition
References
Index
Preface to the Third English Edition page
Preface to the First English Edition
Preface to the German Edition
42.
図書
Günter Scharf
目次情報:
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Preface
Free fields / 1：
Bosonic scalar fields / 1.1：
Ferminoic scalar (ghost) fields / 1.2：
Massless vector fields / 1.3：
Operator gauge transformations / 1.4：
Massive vector fields / 1.5：
Fermionic vector (ghost) fields / 1.6：
Tensor fields / 1.7：
Spinor fields / 1.8：
Normally ordered products in free fields / 1.9：
Problems / 1.10：
Causal perturbation theory / 2：
The S-matrix in quantum mechanics / 2.1：
The method of Epstein and Glaser / 2.2：
Splitting of causal distributions in x-space / 2.3：
Splitting in momentum space / 2.4：
Calculation of tree graphs / 2.5：
Calculation of loop graphs / 2.6：
Normalizability / 2.7：
Spin-1 gauge theories: massless gauge fields / 2.8：
Perturbative gauge invariance / 3.1：
Self-coupling of gauge fields / 3.2：
Divergence and coboundary couplings / 3.3：
Yang-Mills theory to second order / 3.4：
Reductive Lie algebras / 3.5：
Coupling to matter fields / 3.6：
Gauge invariance to all orders / 3.7：
Unitarity / 3.8：
Other gauges / 3.9：
Gauge independence / 3.10：
Appendix A: Cauchy problem for the iterated wave equation / 3.11：
Spin-1 gauge theories: massive gauge fields / 3.12：
Massive QED and Abelian Higgs model / 4.1：
General massive gauge theory / 4.2：
First-order gauge invariance / 4.3：
Second-order gauge invariance / 4.4：
Third-order gauge invariance / 4.5：
Derivation of the electroweak gauge theory / 4.6：
Coupling to leptons / 4.7：
More fermionic families / 4.8：
Gauge invariance to third order: axial anomalies / 4.9：
Spin-2 gauge theory / 4.10：
Perturbative gauge invariance with tensor fields / 5.1：
The general spin-2 theory / 5.2：
Classification of spin-2 quantum gauge theories / 5.3：
Expansion of the Einstein-Hilbert Lagrangian / 5.5：
Q-vertex / 5.6：
Second-order gauge invariance: graviton sector / 5.7：
Second-order gauge invariance: ghost sector / 5.8：
Coupling to matter / 5.9：
Radiative corrections / 5.10：
Appendix B: Divergence couplings for gravity / 5.11：
Appendix C: General Q-vertex for quantum gravity / 5.12：
Bibliographical Notes / 5.13：
Index
Preface
Free fields / 1：
Bosonic scalar fields / 1.1：
43.
図書
Alexander M. Samsonov
目次情報:
続きを見る
Nonlinear waves in elastic solids / 1：
Basic definitions / 1.1：
Wave terminology / 1.1.1：
Deformation and strains / 1.1.2：
Stresses / 1.1.3：
Physical and geometrical sources of nonlinearity / 1.2：
Elastic potentials and moduli / 1.2.1：
Compressibility, dispersion and dissipation in wave guides / 1.3：
A mathematical description of the general deformation wave problem / 2：
Action functional and the Lagrange formalism / 2.1：
Coupled equations of long wave propagation / 2.2：
One-dimensional quasi-hyperbolic equation / 2.3：
Derivation of the Doubly Dispersive Equation (DDE) / 2.3.1：
Refinement of the derivation of the DDE / 2.3.2：
Equations for wave in non-uniform highly nonlinear wave guide / 2.3.3：
Main assumptions and 2-D coupled equations / 2.4：
Waves in a wave guide embedded in an external medium / 2.5：
Direct methods and formal solutions / 3：
Nonlinear hyperbolic and evolution equations / 3.1：
Travelling wave solutions to the KdV and the DDE equations / 3.1.1：
Conservation laws / 3.2：
The Hamiltonian structure / 3.2.1：
Some notices in critical points analysis for an o.d.e. / 3.3：
New approach to a solution for an autonomous dissipative nonlinear equation / 3.4：
A general theorem of reduction / 3.5：
Dissipative equations with polynomial nonlinearity / 3.6：
Square and cubic polynomial nonlinearities / 3.6.1：
Physical interpretation of additional conditions for the travelling wave existence / 3.6.2：
Elliptic function solutions to higher order problems / 3.7：
Example of a nonlinear reaction-diffusion problem / 3.8：
Discontinuous solutions / 3.8.1：
Bounded periodical and solitary wave solutions / 3.8.2：
Autosoliton solution / 3.8.3：
Periodic bounded solutions in case [Delta] ] 0 / 3.8.4：
Nonlinear strain waves in elastic wave guides / 4：
Features of longitudinal waves in a rod / 4.1：
Experiments in nonlinear waves in solids / 4.2：
Strain soliton observation / 4.2.1：
Why is it a soliton? / 4.2.2：
Reflection of a strain soliton / 4.2.3：
Solitons in inhomogeneous rods / 4.3：
Solitons in the non-uniform rod / 4.3.1：
Solitons in the inhomogeneous rod / 4.3.2：
Experiments in soliton propagation in the non-uniform rod / 4.4：
Nonlinear waves in complex wave guides / 5：
Longitudinal nonlinear waves in an elastic plate / 5.1：
Generation and observation of the strain soliton in a plate / 5.1.1：
Longitudinal waves in rods embedded in a surrounding medium / 5.2：
Kinks in a rod in full contact with a surrounding medium / 5.2.1：
Waves in a rod in sliding contact with a surrounding medium / 5.2.2：
Statement and the solution to the problem / 5.2.3：
External stresses on the rod lateral surface / 5.2.4：
Derivation of strain-displacement relationships inside the rod / 5.2.5：
A nonlinear evolution equation for longitudinal strain waves along the rod and its solution / 5.2.6：
The influence of the external medium on the propagation of the strain soliton along the rod / 5.2.7：
A numerical simulation of unsteady strain wave propagation / 5.2.8：
Applications of the theory / 5.2.9：
Conclusions / 5.2.10：
Nonlinear waves in the layer upon the elastic half space / 5.3：
Physical background / 5.3.1：
Basic equations / 5.3.2：
The layer and the half-space contact with slippage / 5.3.3：
The full contact of the layer and the half-space / 5.3.4：
On various mathematical models of nonlinear waves in a layered medium / 5.3.5：
On physical experiments in waves in a layered medium / 5.3.6：
Numerical simulation of the solitary waves in solids / 6：
Numerical simulation of non-stationary deformation waves / 6.1：
Parametrisation of the strain solitary wave / 6.1.1：
Solitary waves in a homogeneous rod / 6.2：
Solitary waves in a nonuniform rod / 6.3：
Solitary waves in complex rods / 6.4：
Strain solitions in a rod with the periodically varied cross section / 6.4.1：
An example of classification using soliton transformation / 6.4.2：
Conclusive remarks and tentative applications
Bibliography
Appendix
Index
Nonlinear waves in elastic solids / 1：
Basic definitions / 1.1：
Wave terminology / 1.1.1：
44.
図書
Tadeusz Iwaniec and Gaven Martin
出版情報:
Oxford : Clarendon Press , New York : Oxford University Press, 2001 xv, 552 p. ; 25 cm
シリーズ名:
Oxford mathematical monographs
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45.
図書
Larry C. Grove
46.
図書
H. Hauser ... [et al.], editors
47.
図書
Roland Hagen, Steffen Roch, Bernd Silbermann
目次情報:
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Preface
Introduction / 0：
Numerical analysis / 0.1：
Operator chemistry / 0.2：
The algebraic language of numerical analysis / 0.3：
Microscoping / 0.4：
A few remarks on economy / 0.5：
Brief description of the contents / 0.6：
Approximation methods / 1：
Basic definitions / 1.1.1：
Projection methods / 1.1.2：
Finite section method / 1.1.3：
Banach algebras and stability / 1.2：
Algebras, ideals and homomorphisms / 1.2.1：
Algebraization of stability / 1.2.2：
Small perturbations / 1.2.3：
Compact perturbations / 1.2.4：
Finite sections of Toeplitz operators with continuous generating function / 1.3：
Laurent, Toeplitz and Hankel operators / 1.3.1：
Invertibility and Fredholmness of Toeplitz operators / 1.3.2：
The finite section method / 1.3.3：
C*-algebras of approximation sequences / 1.4：
C*-algebras, their ideals and homomorphisms / 1.4.1：
The Toeplitz C*-algebra and the C*-algebra of the finite section method for Toeplitz operators / 1.4.2：
Stability of sequences in the C*-algebra of the finite section method for Toeplitz operators / 1.4.3：
Symbol of the finite section method for Toeplitz operators / 1.4.4：
Asymptotic behaviour of condition numbers / 1.5：
The condition of an operator / 1.5.1：
Convergence of norms / 1.5.2：
Condition numbers of finite sections of Toeplitz operators / 1.5.3：
Fractality of approximation methods / 1.6：
Fractal homomorphisms, fractal algebras, fractal sequences / 1.6.1：
Fractal algebras, and convergence of norms / 1.6.2：
Notes and references
Regularization of approximation methods / 2：
Stably regularizable sequences / 2.1：
Moore-Penrose inverses and regularizations of matrices / 2.1.1：
Moore-Penrose inverses and regularization of operators / 2.1.2：
Stably regularizable approximation sequences / 2.1.3：
Algebraic characterization of stably regularizable sequences / 2.2：
Moore-Penrose invertibility in C*-algebras / 2.2.1：
Stable regularizability, and Moore-Penrose invertibility in F/G / 2.2.2：
Finite sections of Toeplitz operators and their stable regularizability / 2.2.3：
Convergence of generalized condition numbers / 2.2.4：
Difficulties with Moore-Penrose stability / 2.2.5：
Approximation of spectra / 3：
Set sequences / 3.1：
Limiting sets of set functions / 3.1.1：
Coincidence of the partial and uniform limiting set / 3.1.2：
Spectra and their limiting sets / 3.2：
Limiting sets of spectra of norm convergent sequences / 3.2.1：
Limiting sets of spectra: the general case / 3.2.2：
The case of fractal sequences / 3.2.3：
Limiting sets of singular values / 3.2.4：
Pseudospectra and their limiting sets / 3.3：
[varepsilon]-invertibility / 3.3.1：
Limiting sets of pseudospectra / 3.3.2：
Pseudospectra of operator polynomials / 3.3.3：
Numerical ranges and their limiting sets / 3.4：
Spatial and algebraic numerical ranges / 3.4.1：
Limiting sets of numerical ranges / 3.4.2：
Stability analysis for concrete approximation methods / 3.4.3：
Local principles / 4.1：
Commutative C*-algebras / 4.1.1：
The local principle by Allan and Douglas / 4.1.2：
Fredholmness of Toeplitz operators with piecewise continuous generating function / 4.1.3：
Finite sections of Toeplitz operators generated by a piecewise continuous function / 4.2：
The lifting theorem / 4.2.1：
Application of the local principle / 4.2.2：
Galerkin methods with spline ansatz for singular integral equations / 4.2.3：
Finite sections of Toeplitz operators generated by a quasi-continuous function / 4.3：
Quasicontinuous functions / 4.3.1：
Stability of the finite section method / 4.3.2：
Some other classes of oscillating functions / 4.3.3：
Polynomial collocation methods for singular integral operators with piecewise continuous coefficients / 4.4：
Singular integral operators / 4.4.1：
Stability of the polynomial collocation method / 4.4.2：
Collocation versus Galerkin methods / 4.4.3：
Paired circulants and spline approximation methods / 4.5：
Circulants and paired circulants / 4.5.1：
The stability theorem / 4.5.2：
Finite sections of band-dominated operators / 4.6：
Multidimensional band dominated operators / 4.6.1：
Fredholmness of band dominated operators / 4.6.2：
Finite sections of band dominated operators / 4.6.3：
Representation theory / 5：
Representations / 5.1：
The spectrum of a C*-algebra / 5.1.1：
Primitive ideals / 5.1.2：
The spectrum of an ideal and of a quotient / 5.1.3：
Representations of some concrete algebras / 5.1.4：
Postliminal algebras / 5.2：
Liminal and postliminal algebras / 5.2.1：
Dual algebras / 5.2.2：
Finite sections of Wiener-Hopf operators with almost periodic generating function / 5.2.3：
Lifting theorems and representation theory / 5.3：
Lifting one ideal / 5.3.1：
Sufficient families of homomorphisms / 5.3.2：
Structure of fractal lifting homomorphisms / 5.3.4：
Fredholm sequences / 6：
Fredholm sequences in standard algebras / 6.1：
The standard model / 6.1.1：
Fredholm sequences and stable regularizability / 6.1.2：
Fredholm sequences and Moore-Penrose stability / 6.1.4：
Fredholm sequences and the asymptotic behavior of singular values / 6.2：
The main result / 6.2.1：
A distinguished element and its range dimension / 6.2.2：
Upper estimate of dim Im [Pi subscript n] / 6.2.3：
Lower estimate of dim Im [Pi subscript n] / 6.2.4：
Some examples / 6.2.5：
A general Fredholm theory / 6.3：
Centrally compact and Fredholm sequences / 6.3.1：
Fredholmness modulo compact elements / 6.3.2：
Weakly Fredholm sequences / 6.3.3：
Sequences with finite splitting property / 6.4.1：
Properties of weakly Fredholm sequences / 6.4.2：
Strong limits of weakly Fredholm sequences / 6.4.3：
Weakly Fredholm sequences of matrices / 6.4.4：
Some applications / 6.5：
Numerical determination of the kernel dimension / 6.5.1：
Around the finite section method for Toeplitz operators / 6.5.2：
Discretization of shift operators / 6.5.3：
Self-adjoint approximation sequences / 7：
The spectrum of a self-adjoint approximation sequence / 7.1：
Essential and transient points / 7.1.1：
Fractality of self-adjoint sequences / 7.1.2：
Arveson dichotomy: band operators / 7.1.3：
Arveson dichotomy: standard algebras / 7.1.4：
Szego-type theorems / 7.2：
Folner and Szego algebras / 7.2.1：
Szego's theorem revisited / 7.2.2：
A further generalization of Szego's theorem / 7.2.3：
Algebras with unique tracial state / 7.2.4：
Bibliography
Index
Preface
Introduction / 0：
Numerical analysis / 0.1：
48.
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：
49.
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.：
50.
図書
Hari Bercovici, Ciprian Foias, editors
51.
図書
Israel Gohberg, Seymour Goldberg, Nahum Krupnik
52.
図書
by Han-lin Chen
出版情報:
Dordrecht ; Boston : Kluwer Academic, c2000 xii, 226 p. ; 25 cm
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53.
図書
Tai-Ping Liu
目次情報:
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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：
54.
図書
R. MacKenzie, M.B. Paranjape, W.J. Zakrzewski, [editors]
55.
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
56.
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：
57.
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
58.
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
59.
図書
Irena Lasiecka, Roberto Triggiani
60.
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：
61.
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：
62.
図書
edited by B. Brent Gordon ... [et al.]
63.
図書
edited by C. Corduneanu and I.W. Sandberg
64.
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：
65.
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
66.
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.：
67.
図書
Fong Yuen, Wang Yuan
出版情報:
Singapore : Springer-Verlag, c2000 xi, 797 p. ; 24 cm
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68.
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
69.
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
70.
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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71.
図書
Hardeo Sahai, Mohammed I. Ageel
出版情報:
Boston : Birkhäuser Boston, c2000 xxxv, 742 p. ; 24 cm
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72.
図書
Bryan P. Rynne and Martin A. Youngson
73.
図書
A.L. Bukhgeim
74.
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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75.
図書
Irena Lasiecka, Roberto Triggiani
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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：
76.
図書
Ernst Kleinert
77.
図書
Nicola Bellomo, Luigi Preziosi, Antonio Romano
78.
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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79.
図書
R.A. Minlos, Senya Shlosman, Yu. M. Suhov, editors
80.
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：
81.
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：
82.
図書
Kjeld B. Laursen and Michael M. Neumann
83.
図書
Luigi Ambrosio, Nicola Fusco, Diego Pallara
84.
図書
P.J. Hunt, J.E. Kennedy
85.
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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86.
図書
Jürgen Appell, editor
87.
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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88.
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：
89.
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：
90.
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
91.
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：
92.
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：
93.
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
94.
図書
Victor P. Havin, Nikolai K. Nikolski, editors
95.
図書
William McLean
出版情報:
Cambridge ; New York : Cambridge University Press, 2000 xiv, 357 p. ; 24 cm
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96.
図書
Karin Gatermann
97.
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
98.
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
99.
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
100.
図書
Luis G. Gorostiza, B. Gail Ivanoff, editors
図書
