1.
図書
Ioannis P. Stavroulakis, Stepan A. Tersian
出版情報:
Singapore ; River Edge, N.J. : World Scientific, c1999 x, 297 p. ; 23 cm
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First-order Partial Differential Equations / 1.：
Introduction
Linear First-order Equations / 2.：
The Cauchy Problem for First-order Quasi-linear Equations / 3.：
General Solutions of Quasi-linear Equations / 4.：
Fully-nonlinear First-order Equations / 5.：
Second-order Partial Differential Equations
Linear equations / 6.：
Classification and Canonical Forms of Equations in Two Independent Variables / 7.：
Classification of Almost-linear Equations in R[superscript n] / 8.：
One-Dimensional Wave Equation
The Wave Equation on the Whole Line. D'Alembert Formula / 9.：
The Wave Equation on the Half-line. Reflection Method / 10.：
Mixed Problem for the Wave Equation / 11.：
Inhomogeneous Wave Equation / 12.：
Conservation of the Energy / 13.：
Weak Derivatives and Weak Solutions / 14.：
One-Dimensional Diffusion Equation
Maximum-minimum Principle for the Diffusion Equation / 15.：
The Diffusion Equation on the Whole Line / 16.：
Diffusion on the Half-line / 17.：
Inhomogeneous Diffusion Equation on the Whole Line / 18.：
Shock Waves and Conservation Laws
Conservation laws / 19.：
Burgers' Equation / 20.：
Weak Solutions. Riemann Problem / 21.：
Discontinuous Solutions of Conservation Laws. Rankine-Hugoniot Condition / 22.：
The Laplace Equation
Harmonic functions. Maximum-minimum Principle / 23.：
Green's Identities / 24.：
Green's Functions / 25.：
Green's Functions for a Half-space and Sphere / 26.：
Harnack's Inequalities and Theorems / 27.：
Fourier Series and Fourier Method for PDEs
Fourier Series / 28.：
Orthonormal Systems. General Fourier series / 29.：
Fourier Method for the Diffusion Equation / 30.：
Fourier Method for the Wave Equation / 31.：
Fourier Method for the Laplace Equation / 32.：
Diffusion and Wave Equations in Higher Dimensions
Diffusion Equation in Three Dimensional Space / 33.：
Fourier Method for the Diffusion Equation in Higher Dimensions / 34.：
Kirchoff's Formula for the Wave Equation. Huygens' Principle / 35.：
Fourier Method for the Wave Equation on the Plane. Nodal Sets / 36.：
References
Answers and Hints to Selected Exercises
Index
First-order Partial Differential Equations / 1.：
Introduction
Linear First-order Equations / 2.：
2.
図書
by Zbigniew Haba
3.
図書
Michael Monastyrsky ; with a foreword by Freeman J. Dyson ; translated by Roger Cooke, James King, Victoria King
出版情報:
Boston : Birkhäuser, c1999 xiii, 215 p. ; 25 cm
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4.
図書
edited by Alexander I. Bobenko and Ruedi Seiler
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List of contributors
Introduction / Alexander I. Bobenko ; Ruedi Seiler
Geometry / I：
Discretization of Surfaces and Integrable Systems / Ulrich Pinkall1：
A Discrete Version of the Darboux Transform for Isothermic Surfaces / Udo Hertrich-Jeromin ; Tim Hoffmann2：
Discrete Amsler Surfaces and a Discrete Painleve III Equation / 3：
Discrete cmc Surfaces and Discrete Holomorphic Maps / 4：
Discrete Indefinite Affine Spheres / Wolfgang K. Schief5：
Geometry of Discrete Curves and Lattices and Integrable Difference Equations / Adam Doliwa ; Paolo Maria Santini6：
Classical Systems / II：
R-matrices and Integrable Discretizations / Yuri B. Suris7：
Discrete Painleve Equations and Symmetry Reduction on the Lattice / Frank W. Nijhoff8：
Lagrangian Description of Doubly Discrete Sine-Gordon Type Models / Nadja Kutz9：
Quantum Systems / III：
Spectra of Quantum Integrals / Johannes Kellendonk10：
Algebraic Quantization of Integrable Models in Discrete Space-Time / Ludwig D. Faddeev ; Alexander Yu. Volkov11：
Affine Toda Field Theory as a Three-dimensional Integrable System / Rinat M. Kashaev ; Nikolai Yu. Reshetikhin12：
Quantum Hyperbolic Invariants of Knots / 13：
Charge Transport in the Discretized Landau Model / Thomas Richter14：
Index
List of contributors
Introduction / Alexander I. Bobenko ; Ruedi Seiler
Geometry / I：
5.
図書
by Uwe Franz and René Schott
目次情報:
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Preface
Introduction / 1：
Preliminaries on Lie groups / 2：
Hopf algebras, quantum groups and braided spaces / 3：
Stochastic Processes on quantum groups / 4：
Markov Structure of quantum Levy Processes / 5：
Diffusions on braided spaces / 6：
Evolution equations and Levy processes on quantum groups / 7：
Gauss Laws in the sense of Bernstein on quantum groups / 8：
Phase retrieval for probability distributions on quantum groups / 9：
Limit theorems on quantum groups / 10：
Bibliography
Index
Preface
Introduction / 1：
Preliminaries on Lie groups / 2：
6.
図書
David A. Cox, Sheldon Katz
目次情報:
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Introduction
The quintic threefold
Toric geometry Mirror symmetry constructions
Hodge theory and Yukawa couplings
Moduli spaces Gromov-Witten invariants
Quantum cohomology Localization
Quantum differential equations
The mirror theorem Conclusion
Singular varieties
Physical theories
Bibliography
Index
Introduction
The quintic threefold
Toric geometry Mirror symmetry constructions
7.
図書
edited by Silvio Levy
8.
図書
Jean Piquet
出版情報:
Berlin : Springer-Verlag, c1999 x, 761 p. ; 24 cm
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The Equations of Motion / Chapter 1：
Introduction, the Equations / 1：
Some General Properties of Navier-Stokes Equations / 2：
References
Principles of Turbulent Flow Modeling / Chapter 2：
Introduction and Averaging Procedures
The Reynolds-Averaged Mean-Flow Equations
The Closure Problem / 3：
Homogeneous and Inhomogeneous Flows / 4：
The Eddy-Viscosity Concept / 5：
Two-Point Homogeneous Turbulence / Chapter 3：
Introduction
Homogeneous Turbulence ; Correlations and Spectra
The Dynamics of Second-Order Correlations
Theory of Homogeneous Isotropic Turbulence
Rapid Distorsion Theory
Second-Order Turbulence Modeling / Chapter 4：
Reynolds-Stress Modeling
The Transfer Term
Inhomogeneous Flow
Non Linear Ev and Ars Models
Intermittency Modeling
Definition of Turbulence Models / Appendix A：
Turbulent Two-Dimensional Shear Flows / Chapter 5：
Thin Free Shear Layers, Classification
Asymptotics of Wall Shear Layers
Channel and Pipe Flows
Zero-Pressure-Gradient Boundary Layers
Jets / 6：
Wakes / 7：
Complex Effects in Turbulent Flows / Chapter 6：
2D Boundary Layers in Pressure Gradients
Two-Dimensional Turbulent Separation
Classification of Three-Dimensional Flows
Three-Dimensional Turbulent Boundary Layers
Curvature Effects
Rotation Effects
Lateral Straining
Imposition of Sudden Strains / 8：
Roughness Effects / 9：
Freestream Turbulence / 10：
Three-Dimensional Duct Flow / 11：
Geometry Concepts
Subject Index
List of Symbols and Page of First Occurrence
The Equations of Motion / Chapter 1：
Introduction, the Equations / 1：
Some General Properties of Navier-Stokes Equations / 2：
9.
図書
Erwin Kreyszig
出版情報:
New York : John Wiley & Sons, c1999 xvi, 1156, 97, 20 p. ; 26-27 cm
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How to Use this Student Solutions Manual and Study Guide
Ordinary Differential Equations (ODEs) / Part A：
First-Order ODEs / Chapter 1：
Second-Order Linear ODEs / Chapter 2：
Ordinary Differential Equations (Ode's)
First-Order ODE's / Chapter 3：
Higher Order Linear ODEs
Second Order Linear ODE's / Chapter 4：
Systems of ODEs. Phase Plane. Qualitative Methods
Higher Order Linear ODE's
Systems of ODE's Phase Plane, Qualitative Methods / Chapter 5：
Series Solutions of ODEs. Special Functions
Series Solutions of ODE's Special Functions / Chapter 6：
Laplace Transforms
Linear Algebra, Vector Calculus / Part B：
Linear Algebra: Matrices, Vectors, Determinants: Linear Systems / Chapter 7：
Matrices, Vectors, Determinants. Linear Systems / Chapter 8：
Linear Algebra: Matrix Eigenvalue Problems
Vector Differential Calculus: Grad, Div, Curl / Chapter 9：
Vector Integral Calculus: Integral Theorems / Chapter 10：
Vector Differential Calculus. Grad, Div, Curl / Part C：
Fourier Analysis, Partial Differential Equations
Fourier Series, Integrals, and Transforms / Chapter 11：
Vector Integral Calculus. Integral Theorems
Partial Differential Equations (PDE 's) / Chapter 12：
Fourier Analysis. Partial Differential Equations / Chapter 13：
Complex Numbers and Functions
Complex Integration / Chapter 14：
Power Series, Taylor Series / Chapter 15：
Partial Differential Equations (PDEs) / Chapter 16：
Laurent Series: Residue Integration
Conformal Mapping / Part D：
Complex Analysis
Complex Analysis and Potential Theory / Chapter 18：
Numerical Analysis Software / Part E：
Numerics in General / Chapter 19：
Numerical Linear Algebra / Chapter 20：
Numerics for ODE 's and PDE 's / Chapter 21：
Optimization, Graphs / Part F：
Laurent Series. Residue Integration
Unconstrained Optimization: Linear Programming / Chapter 22：
Graphs, Combinatorial Optimization / Chapter 23：
Probability / Part G：
Statistics
Data Analysis / Chapter 24：
Numeric Analysis
Probability Theory
Mathematical Statistics / Chapter 25：
References / Appendix 1：
Numeric Linear Algebra / Appendix 2：
Answers to Odd-Numbered Problems
Auxiliary Material / Appendix 3：
Numerics for ODEs and PDEs
Additional Proofs / Appendix 4：
Tables / Appendix 5：
Index
Unconstrained Optimization. Linear Programming
Graphs and Combinatorial Optimization
Probability, Statistics
Data Analysis. Probability Theory
Photo Credits
How to Use this Student Solutions Manual and Study Guide
Ordinary Differential Equations (ODEs) / Part A：
First-Order ODEs / Chapter 1：
10.
図書
by Volodymyr Koshmanenko
目次情報:
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Preface to the English Edition
Introduction
Quadratic Forms and Linear Operators / 1：
Singular Quadratic Forms / 2：
Singular Perturbations of Self-Adjoint Operators / 3：
Applications to Quantum Field Theory / 4：
References
Subject Index
Notation
Preface to the English Edition
Introduction
Quadratic Forms and Linear Operators / 1：
11.
図書
David E. Evans and Yasuyuki Kawahigashi
12.
図書
B.N. Mandal and Nanigopal Mandal
13.
図書
edited by S.A. Huggett ... [et al.]
出版情報:
Oxford : Oxford University Press, 1998 xviii, 431 p. ; 24 cm
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Plenary Lectures / I：
Roger Penrose - a personal appreciation / 1：
Hypercomplex manifolds and the space of framings / 2：
Gauge theory in higher dimensions / 3：
Noncommutative differential geometry and the structure of space-time / 4：
Einstein's equation and conformal structure / 5：
Twistors, geometry, and integrable systems / 6：
On four-dimensional Einstein manifolds / 7：
Loss of information in black holes / 8：
Fundamental geometry: the Penrose-Hameroff 'Orchor' model of consciousness / 9：
Implications of transience for spacetime structure / 10：
Geometric issues in quantum gravity / 11：
From quantum code-making to quantum code-breaking / 12：
Penrose tilings and quasicrystals revisited / 13：
Decaying neutrinos and the geometry of the universe / 14：
Quantum geometric origin of all forces in string theory / 15：
Space from the point of view of loop groups / 16：
Parallel / II：
Quantum Theory And Beyond / Session I：
The twistor diagram programme / 17：
Geometric models for quantum statistical inference / 18：
Spin networks and topology / 19：
The physics of spin networks / 20：
Geometry And Gravity / III：
The Sen conjecture for distinct fundamental monopoles / 21：
An unorthodox view of CG via characteristic surfaces / 22：
Amalgamated Codazzi Raychaudhuri identity for foliation / 23：
Abstract virtual reality complexity / 24：
Fundamental Questions In Quantum Mechanics / IV：
Interaction-free measurements / 25：
Quantum measurement problem and the gravitational field / 26：
Entanglement and quantum computation / 27：
Mathematical Aspects Of Twistor Theory / V：
Penrose transform for flag domains / 28：
Twistor solution of the holonomy problem / 29：
The Penrose transform and real integral geometry / 30：
Pythagorean spinors and Penrose twistors / 31：
Afterword / VI：
Plenary Lectures / I：
Roger Penrose - a personal appreciation / 1：
Hypercomplex manifolds and the space of framings / 2：
14.
図書
Ivar Stakgold
15.
図書
Robert Friedman, John W. Morgan, editors
目次情報:
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Geometric invariant theory and the moduli of bundles: Geometric invariant theory / D. Gieseker
The numerical criterion
The moduli of stable bundles
References
Anti-self-dual connections and stable vector bundles: Hermitian bundles, Hermitian connections and their curvatures / J. Li
Hermitian-Einstein connections and stable vector bundles
The existence of Hermitian-Einstein metrics
An Introduction to gauge theory: The context of Gauge theory / J. W. Morgan
Principal bundles and connections
Curvature and characteristic classes
The space of connections
The ASD equations and the moduli space
Compactness and gluing theorems
The Donaldson polynomial invariants
The connected sum theorem
Computing Donaldson invariants: Overview / R. J. Stern
-2 spheres and the blowup formula
Simple-type criteria and elliptic surfaces
Elementary rational blowdowns
Taut configurations and Horikowa surfaces
Donaldson-Floer theory: Introduction / C. Taubes ; J. A. Bryan
Quantization
Simplicial decomposition of $\Cal{M}^0_X$
Half-infinite dimensional spaces
Geometric invariant theory and the moduli of bundles: Geometric invariant theory / D. Gieseker
The numerical criterion
The moduli of stable bundles
16.
図書
Walter E. Thirring ; with foreword by Elliott H. Lieb
出版情報:
Providence, R.I. : American Mathematical Society, c1998 xiii, 729 p. ; 26 cm
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17.
図書
by Krzysztof Maurin
18.
図書
J.-M. Souriau ; translated by C.H. Cushman-de Vries ; translation editors, R.H. Cushman, G.M. Tuynman
19.
図書
by C. Cercignani, V.I. Gerasimenko, D.Ya. Petrina
20.
図書
Yulia E. Karpeshina
21.
図書
John R. Taylor
出版情報:
Sausalito : University Science Books, c1997 xvii, 327 p. ; 26 cm
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22.
図書
I. Kuzin, S. Pohozaev
23.
図書
C. Constanda, J. Saranen and S. Seikkala (editors)
24.
図書
by Larry A. Lambe and David E. Radford
25.
図書
Paul Meakin
目次情報:
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Preface
Pattern formation far from equilibrium / 1：
Fractals and scaling / 2：
The basic models / 3：
Experimental studies / 4：
The growth of surfaces and interfaces / 5：
Instabilities / Appendix I：
Multifractals / Appendix II：
Bibliography
Preface
Pattern formation far from equilibrium / 1：
Fractals and scaling / 2：
26.
図書
Charles Li, Stephen Wiggins
27.
図書
Theodore Frankel
出版情報:
Cambridge : Cambridge University Press, 1997 xxii, 654 p. ; 27 cm
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Preface
Manifolds, Tensors and Exterior Forms / Part I：
Manifolds and vector fields / 1：
Tensors and exterior forms / 2：
Integration of differential forms / 3：
The Lie derivative / 4：
The Poincaré lemma and potentials / 5：
Holonomic and non-holonomic constraints / 6：
Geometry and Topology / Part II：
R3 and Minkowski space / 7：
The geometry of surfaces in R3 / 8：
Covariant differentiation and curvature / 9：
Geodesics / 10：
Relativity, tensors, and curvature / 11：
Curvature and topology: Synge's theorem / 12：
Betti numbers and de Rham's theorem / 13：
Harmonic forms / 14：
Lie Groups, Bundles and Chern Forms / Part III：
Lie groups / 15：
Vector bundles in geometry and physics / 16：
Fiber bundles, Gauss-Bonnet, and topological quantization / 17：
Connections and associated bundles / 18：
The Dirac equation / 19：
Yang-Mills fields / 20：
Betti numbers and covering spaces / 21：
Chern forms and homotopy groups / 22：
Forms in continuum mechanics / Appendix A：
Harmonic chains and Kirchhoff's circuit laws / Appendix B：
Symmetries, quarks, and meson masses / Appendix C：
Representations and hyperelastic bodies / Appendix D：
Orbits and Morse-Bott theory in compact Lie groups / Appendix E：
Preface
Manifolds, Tensors and Exterior Forms / Part I：
Manifolds and vector fields / 1：
28.
図書
Pavel I. Etingof, Igor B. Frenkel, Alexander A. Kirillov, Jr
目次情報:
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Introduction
Representations of finite-dimensional and affine
Lie algebras Knizhnik-Zamolodchikov equations
Solutions of the Knizhnik-Zamolodchikov equations
Free field realization Quantum groups
Local systems and configuration spaces
Monodromy of the Knizhnik-Zamolodchikov equations
Quantum affine algebras
Quantum Knizhnik-Zamolodchikov equations
Solutions of the quantum Knizhnik-Zamolodchikov equations for $\mathfrak {sl}_2$
Connection matrices for the quantum
Knizhnik-Zamolodchikov equations and elliptic functions
Current developments and future perspectives
References
Index
Introduction
Representations of finite-dimensional and affine
Lie algebras Knizhnik-Zamolodchikov equations
29.
図書
by Anatoliy K. Prykarpatsky and Ihor V. Mykytiuk
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Preface
Background Notations
Dynamical systems with homogeneous configuration spaces / 1：
Dynamical systems with symmetries
Poisson structures / 1.1：
Lie group actions on manifolds / 1.2：
Symplectic structures on coadjoint representation orbits / 1.3：
Hamiltonian group actions / 1.4：
Invariant Hamiltonian systems with homogeneous configuration spaces / 1.5：
The existence of a maximal involutive set of functions on the orbits of semi-simple elements of a semi-simple Lie algebra / 2：
The algebra of invariant polynomials on a semi-simple Lie algebra / 2.1：
Semi-simple element orbits / 2.2：
Maximal involutive sets of functions on semi-simple elements orbits / 2.3：
The integrability criterion and spherical pairs of Lie groups / 3：
Criterion of integrability / 3.1：
Spherical pairs of complex Lie groups / 3.2：
Interpolation property of spherical pairs of compact Lie groups / 4：
Properties of spherical pairs of compact Lie algebras / 4.1：
Points in general position / 4.2：
Spherical pairs of classical simple Lie groups / 5：
Preliminary remarks / 5.1：
Involutions of simple Lie algebras / 5.2：
Spherical pairs of classical Lie algebras / 5.3：
Classification of spherical pairs of the exceptional simple Lie algebras / 6：
Classification of spherical pairs of semi-simple Lie groups / 7：
Spherical pairs of semi-simple Lie algebras / 7.1：
Geometric quantization and integrable dynamical systems
Connections on line bundles
Line bundles
Equivalence classes of line bundles
Connections
The integrality condition
Hermitian structures
Equivalence classes of line bundles with connections / 1.6：
Holomorphic line bundles / 1.7：
Derivations / 1.8：
Tensor products, square roots and invariant Hermitian structures / 1.9：
Parallel transport on a line bundle with a connection / 1.10：
Parallel transport and derivations / 1.11：
Flat partial connections
Flat F-connections
Maps of line bundles
Line bundles of differential forms
Geometric quantization
Polarizations
Geometric quantization and reduction
Introduction
Hamiltonian reduction
Quantization / 4.3：
Examples: geometric quantization of the oscillator type Hamiltonian systems
Geometric quantization of the generalized n-dimensional harmonic oscillator
Geometric quantization of geodesic flow on a sphere
Geometric quantization of the multidimensional Kepler problem
Geometric quantization of the MIC-Kepler problem / 5.4：
Structures on manifolds and algebraic integrability of dynamical systems
Poisson structures and dynamical systems with symmetries
Preliminary notes
Poisson structures on manifolds
Casimir functions and involution
Casimir functions associated with classical expansions of semi-simple Lie algebras
Alder-Kostant-Symes and Mishchenko-Fomenko theorems
The reduction method and Poisson structures on dual spaces of semi-direct sums of Lie algebras
The mapping canonicity of symplectic structures
Momentum mapping
Poisson structures on dual spaces of semi-direct sums of Lie algebras
Canonical mappings / 2.4：
Nonlinear Neumann type dynamical systems as integrable flows on coadjoint orbits of Lie groups
The Neumann problem
The Lie-Poisson bracket associated with the ad-semidirect sum of Lie algebras
The canonical symplectic structure on T(S[superscript n-1]) and its diffeomorphisms / 3.3：
An involutive system of integrals for the Neumann dynamical system on the sphere S[superscript n-1] / 3.4：
Generalized Neumann-Bogoliubov dynamical systems / 3.5：
Abelian integrals, integrable dynamical systems, and their Lax type representations
The Neumann-Rosochatius-Bogoliubov Hamiltonian system
Conservation laws
Lax type representation
Dual momentum mappings and their applications
Preliminaries
Dualities
The Neumann-Rosochatius system
The Lie algebraic setting of Benney-Kaup dynamical systems and associated via Moser Neumann-Bogoliubov oscillatory flows
The Novikov-Lax finite-dimensional invariant reductions on nonlocal submanifolds / 6.1：
The Moser map and its associated dual moment maps into loop Lie algebras / 6.3：
The finite-dimensional Moser type of reduction of modified Boussinesq and super-Korteweg-de Vries Hamiltonian systems via the gradient-holonomic algorithm and dual moment maps
The Moser type of finite-dimensional reduction of a Boussinesq hydrodynamic system and its Lie-algebraic integrability / 7.2：
The Neumann type of oscillatory super-Hamiltonian systems on the sphere S[superscript N] and their Lie algebraic super-integrability / 7.3：
Lax-type of flows on Grassmann manifolds and dual momentum mappings / 8：
Symplectic structures on loop Grassmann manifolds / 8.1：
An intrinsic loop Grassmannian structure and dual momentum mappings / 8.3：
On the geometric structure of integrable flows in Grassmann manifolds / 9：
Centrally extended symplectic structures and integrable flows on the loop Grassmann manifolds / 9.1：
Algebraic methods of quantum statistical mechanics and their applications
Current algebra representation formalism in nonrelativistic quantum mechanics
The current algebra in nonrelativistic quantum mechanics
Current algebra representations
Bogoliubov-Araki generating functional
Lie current algebra, Hamiltonian operator, and Bogoliubov functional equations
Hamiltonian operator
Gibbs states and the Kubo-Martin-Schwinger conditions
Stable states and the KMS condition
Functional-operator representations of the current Lie algebra
The Bogoliubov-Bloch functional equation / 2.5：
The reconstruction via Araki of the Hamiltonian operator and the Bogoluibov functional equation / 2.6：
Functional-operator solutions of the Bogoliubov functional equations / 2.7：
A generalized Virasoro algebra / 2.8：
The secondary quantization method and the spectrum of quantum excitations of a nonlinear Schrodinger type dynamical system
Preliminary notions
The second quantization representation
A generalized nonlinear Schrodinger type quantum dynamical system
The quantum inverse spectral transform method
The scattering operator
Eigenvalue states of the nonlinear Schrodinger type model / 3.6：
Quantum excitations of a bose gas with a positive momentum / 3.7：
Unitary representations of the generalized Virasoro algebra
Verma modules over the generalized Virasoro current algebra
Unitary irreducible modules with highest weight
Algebraic and differential geometric aspects of the integrability of nonlinear dynamical systems on infinite-dimensional functional manifolds
The current Lie algebra on S[superscript 1] and its functional representations
Basic notations
Associated cohomology complexes and their properties
Differential geometry analysis on real jet manifolds
Differential geometry analysis on jet supermanifolds
Euler variational derivative, external differential and tensors on infinite-dimensional functional spaces
Implectic operators and Poisson structures
Dynamical systems and bi-Hamiltonicity
The equivalence of dynamical systems as the Backlund transformation
The current Lie algebra on a cycle as a symmetry subalgebra of compatibly bi-Hamiltonian nonlinear dynamical systems on an axis
The Hamiltonicity of nonlinear dynamical systems on infinite-dimensional functional manifolds
A Lie-algebraic algorithm for investigating integrability
The gradient holonomic algorithm and Lax type representation
An adjoint Lax type equation and conservation laws
Lax type representation: differential algebraic approach
Lax type representation: geometric approach
Lagrangian and Hamiltonian formalisms for reduced infinite-dimensional dynamical systems with symmetries
General setting
Lagrangian reduction
Symplectic analysis and Hamiltonian fields
Discrete dynamical systems. One generalization
Non-isospectrally integrable dynamical systems: the generalized asymptotic structure of conservation laws
A nonstandard reduction problem
Lagrangian and Hamiltonian analysis of dynamical systems on functional manifolds. The Poisson-Dirac bracket / 3.8：
Conclusions / 3.9：
The algebraic structure of the gradient-holonomic algorithm for Lax type integrable nonlinear dynamical systems
Algebraic structure of the Lax type integrable dynamical system
The periodic problem and canonical variational relationships
The spectral gradient structure of Lax integrable many-dimensional nonlinear dynamical systems on operator manifolds / 4.4：
The integrability of Lie-invariant geometric objects generated by ideals in the Grassmann algebra
An effective Maurer-Cartan one-form construction
General structure of integrable one-forms augmenting the two-forms associated with a closed ideal in the Grassmann algebra
Cartan's invariant geometric object structure of the gradient-holonomic algorithm for Lax integrable nonlinear dynamical systems in partial derivatives
A loop algebra and the Yang-Baxter structure / 5.5：
The transfer matrix properties / 5.6：
The algebraic structure of the gradient-holonomic algorithm for the Lax-type nonlinear dynamical systems: the reduction via Dirac and the canonical quantization procedure
The generalized R-structure hierarchy
The Dirac quantization procedure for Moser induced finite-dimensional Neumann type Hamiltonian systems
The scalar and operator integrable Hamiltonian systems via the algebraic gradient-holonomic algorithm / 6.4：
Concluding remarks / 6.5：
Hamiltonian structures of hydrodynamical Benny type dynamical systems and their associated Boltzmann-Vlasov kinetic equations on an axis
The Boltzmann equation and an associated moment problem
A nonlinear completely integrable Schrodinger type dynamical system approximation
The complete integrability of a Benney type hydrodynamical system associated with a Boltzmann-Vlasov equation / 7.4：
Conclusion / 7.5：
Appendix
Basic definitions, examples / .1：
The tangent Lie algebra / .2：
Lie subgroups / .3：
Lie algebras / .4：
Cartan subalgebras / .5：
Semi-simple complex Lie algebras / .6：
References
Preface
Background Notations
Dynamical systems with homogeneous configuration spaces / 1：
30.
図書
Roman Bezrukavnikov, Michael Finkelberg, Vadim Schechtman
31.
図書
Isabelle Catto, Claude Le Bris, Pierre-Louis Lions
目次情報:
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Preface
General Presentation / 1：
Convergence of the energy for the Thomas-Fermi-von Weizsacker model with Yukawa potential / 2：
Convergence of the energy for the Thomas-Fermi-von-Weizsacker model / 3：
Convergence of the density for the Thomas-Fermi-von-Weizsacker model with Yukawa potential / 4：
Convergence of the density for the Thomas-Fermi-von-Weizsacker model / 5：
Convergence of the energy via the convergence of the density / 6：
Bibliography
Preface
General Presentation / 1：
Convergence of the energy for the Thomas-Fermi-von Weizsacker model with Yukawa potential / 2：
32.
図書
Victor Kac
33.
図書
edited by Peter L. Antonelli and Bradley C. Lackey
34.
図書
M. V. Karasev, editor
35.
図書
Stephen Simons
36.
図書
Robert Vein, Paul Dale
目次情報:
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Preface
Determinants , first minors and cofactors / Chapter 1：
A summary of basic determinant theory / Chapter 2：
Intermediate determinant theory / Chapter 3：
Particular determinants / Chapter 4：
Further determinant theory / Chapter 5：
Applications of determinants in mathematical physics / Chapter 6：
Appendix
Bibliography
Index
Preface
Determinants , first minors and cofactors / Chapter 1：
A summary of basic determinant theory / Chapter 2：
37.
図書
N.P. Landsman
38.
図書
A.V. Bocharov ... [et al.] ; I.S. Krasilʹshchik, A.M. Vinogradov (editor) ; [translated from the Russian by A.M. Verbovetsky and I.S. Krasilʹshchik]
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Ordinary differential equations
First-order equations
The theory of classical symmetries
Higher symmetries
Conservation laws
Nonlocal symmetries
From symmetries of partial differential equations towards secondary ("quantized") calculus
Bibliography
Index
Ordinary differential equations
First-order equations
The theory of classical symmetries
39.
図書
by P.L. Antonelli and T.J. Zastawniak
40.
図書
by Anatoly Swishchuk
41.
図書
Don S. Lemons
出版情報:
Princeton, NJ : Princeton University Press, c1997 xi, 117 p. ; 24 cm
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Preface
Least Time / Ch. 1：
Calculus of Variations / Ch. 2：
Curved Light / Ch. 3：
Least Potential Energy / Ch. 4：
Least Action / Ch. 5：
Hamilton's Principle - Restricted / Ch. 6：
Hamilton's Principle - Extended / Ch. 7：
Index
Preface
Least Time / Ch. 1：
Calculus of Variations / Ch. 2：
42.
図書
Claus Müller
43.
図書
V.G. Osmolovskiĭ ; [translated from the Russian by Tamara Rozhkovskaya]
目次情報:
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Notation Linear perturbations of the operator div
Nonlinear perturbations of the operator div
Appendix
References
Notation Linear perturbations of the operator div
Nonlinear perturbations of the operator div
Appendix
44.
図書
by A.M. Meirmanov, V.V. Pukhnachov, S.I. Shmarev
45.
図書
edited by Jacques Hurtubise and François Lalonde ; technical editor, Gert Sabidussi
46.
図書
by Norman E. Hurt
47.
図書
edited by Michael Demuth, Bert-Wolfgang Schulze
48.
図書
Gregory L. Naber
49.
図書
by Vassili N. Kolokoltsov and Victor P. Maslov
目次情報:
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Preface
Idempotent Analysis / 1：
Analysis of Operators on Idempotent Semimodules / 2：
Generalized Solutions of Bellman's Differential Equation / 3：
Quantization of the Bellman Equation and Multiplicative Asymptotics / 4：
References
Appendix : Maslov Optimziation Theory / P. Del Moral
Optimality versus Randomness
Index
Preface
Idempotent Analysis / 1：
Analysis of Operators on Idempotent Semimodules / 2：
50.
図書
Sergio Albeverio ... [et al.]
51.
図書
Victor Kac
52.
図書
Bo Holm Jacobsen, Klaus Mosegaard, Paolo Sibani (eds.)
53.
図書
Lui Lam, editor
出版情報:
New York : Springer, c1997 xiv, 417 p. ; 25 cm
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54.
図書
edited by W. Thirring ; with a preface by F. Dyson
出版情報:
New York : Springer, c1997 xi, 675 p. ; 24 cm
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Introduction
Review / Part I：
The Stability of Matter: From Atoms to Stars / I.1：
Exact Results on Atoms / Part II：
Lower Bound to the Energy of Complex Atoms / P. Hertel ; W. ThirringII.1：
Improved Lower Bound on the Indirect Coulomb Energy / S. OxfordII.2：
Monotonicity of the Molecular Electronic Energy in the Nuclear Coordinates / II.3：
Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle / R. BenguriaII.4：
Atomic and Molecular Negative Ions / II.5：
Bound on the Maximum Negative Ionization of Atoms and Molecules / II.6：
Approximate Neutrality of Large-Z Ions / l.M. Sigal ; B.SimonIL.7：
Universal Nature of van der Waals Forces for Coulomb Systems / II.8：
Electron Density Near the Nucleus of a Large Atom / O.J. HeilmannII.9：
Proof of a Conjecture About Atomic and Molecular Cores Related to ScottÆs Correction / A. lantchenko ; H. SiedentopII.10：
Asymptotics of Natural and Artificial Atoms in Strong Magnetic Fields / J.P. Solovej ; J. YngvasonII.11：
Ground States of Large Quantum Dots in Magnetic Fields / II.12：
General Results with Applications to Atoms / Part III：
Kinetic Energy Bounds and Their Application to the Stability ofMatter / III.1：
Inequalities for the Moments of the Eigenvalues of the Schrodinger Hamiltonian and Their Relation to Sobolev Inequalities / III.2：
On Semi-Classical Bounds for Eigenvalues of Schrodinger Operators / M. AizenmanIII.3：
The Number of Bound States of One-Body Schrodinger Operators and the Weyl Problem / III.4：
Variational Principle for Many-Fermion Systems / III.5：
Thomas-Fermi and Related Theories / Part IV：
Thomas-Fermi and Related Theoies of Atoms and Molecules / IV.1：
The Hartree-Fock Theory for Coulomb Systems / B. SimonIV.2：
There Are No Unfilled Shells in Unrestricted Hartree-Fock Theory / V. Bach ; M. LossIV.3：
Many-Body Atomic Potentials in Thomas-Fermi Theory / IV.4：
The Positivity of the Pressure in Thomas-Fermi Theory / IV.5：
The Thomas-Fermi-von Weizsacker Theory of Atoms and Molecules / H. BrezisIV.6：
Analysis of the Thomas-Fermi-von Weizsacker Equation for an Infinite Atom Without Electron Repulsion / IV.7：
The Most Negative Ion in the Thomas-Fermi-von Weizsacker Theory of Atoms and Molecules / IV.8：
Stability of Matter / Part V：
Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter / V.1：
Stability of Coulomb Systems with Magnetic Fields. I. The One-Electron Atom / J. FrohlichV.2：
Stability of Coulomb Systems with Magnetic Fields. II. The Many-Electron Atom and the One-Electron Molecule / V.3：
Stability of Matter in Magnetic Fields / V.4：
The Chandrasekhar Theory of Stellar Collapse as the Limit of Quantum Mechanics / H.-T. YauV.5：
One-Electron Relativistic Molecules with Coulomb Interaction / I. DaubechiesV.6：
The Stability and Instability of Relativistic Matter / V.7：
Stability of Relativistic Matter Via Thomas-Fermi Theory / V.8：
Stability and Instability of Relativistic Electrons in Classical Electromagnetic Fields / V.9：
The Thermodynamic Limit for Real Matter with Coulomb Forces / Part VI：
The Stability of Matter / VI.1：
Existence of Thermodynamics for Real Matter with Coulomb Forces / J.L. LebowitzVI.2：
The Thermodynamic Limit for Jellium / H. NarnhoferVI.3：
Quantum Electrodynamics / Part VII：
Self Energy of Electrons in Non-perturbative QED / VII.1：
Renormalization of the Regularized Electron-Positron Field / VII.2：
Ground States in Non-relativistic Quantum Electrodynamics / M. GriesemerVII.3：
Bosonic Systems / Part VIII：
Ground State Energy of the Low Density Bose Gas / VIII.1：
Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional / R. SeiringerVIII.3：
The Bose Gas: A Subtle Many-Body Problem / VIII.4：
The N5/3 Law for Bosons / VIII.5：
The N7/5 Law for Charged Bosons / J.G. ConlonVIII.6：
Ground State Energy of the One-Component Charged Bose Gas / VIII.7：
Publications of Elliott / H.Lieb
Introduction
Review / Part I：
The Stability of Matter: From Atoms to Stars / I.1：
55.
図書
by G.P. Cherepanov
56.
図書
Martin Schottenloher
57.
図書
by D. Ya. Petrina
58.
図書
V.A. Malyshev, R.A. Minlos
目次情報:
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Introduction
Extended introduction
Construction of a nonequilibrium dynamics
Construction of an equilibrium dynamics
Spectral analysis of the Euclidean field transfer matrix
Asymptotic completeness for interacting fermion systems
The method of Bethe-Salpeter kernels (Dyson's equation)
Guide to the Literature
References
Introduction
Extended introduction
Construction of a nonequilibrium dynamics
59.
図書
Charles F. Stevens
出版情報:
Cambridge, Mass. : MIT Press, 1995 x, 233 p. ; 24 cm
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60.
図書
V.V. Shaidurov
61.
図書
edited by Rafał Abłamowicz and Pertti Lounesto
62.
図書
editor, Louis H. Kauffman
63.
図書
L.J. Mason and N.M.J. Woodhouse
64.
図書
U. Fano, A.R.P. Rau
出版情報:
San Diego ; Tokyo : Academic Press, c1996 xiv, 333 p. ; 24 cm
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Introduction: Symmetry and the Selection of Variables
Algebraic Elements
Reduction Procedure and Irreducible Tensorial Sets
Further Aspects of Reduction
Structure of the Book
Quaternions
State Representatives and r -Transformations: Their Construction and Properties / Part A：
Infinitesimal Rotations and Angular Momentum
Basic Relations
Analytical Example: Infinitesimal Transformation of Cartesian Coordinates
The Angular Momentum Matrices of Quantum Mechanics
The Fundamental Representation
Frame Reversal and Complex Conjugation
Analytical Representation and Implications of Frame Reversal
Contragradience and the Construction of Invariants
Cartesian Base for Integer j
[greater than or equal to sign here]1
Standard r -Transformation Matrices and Their Applications
Explicit Form and Properties
Macroscopic Applications
Applications to Quantum Physics
Coordinate Inversion and Parity Eigenfunctions
Reduction of Direct Products (Addition of Angular Momenta)
Structure and Properties of the Reducing Matrix
Reduction of r -Transformation Products
Irreducible Product Sets
Symmetrization of Wigner Coefficients: Invariant Triple Product and 3-j
Coefficients
Tensorial Aspects of Quantum Physics / Part B：
Tensorial Sets of Quantum Operators
The Liouville Representation of Quantum Mechanics
Quantum Mechanics of Particles with Spin 1/2
Two-Level Systems
Particles With Spin j >1/2: Wigner-Eckart Theorem
Systems with 2j +1 Levels
Transfer of Angular Momentum
Calculation of Matrix Elements
Recoupling Transformations: 6-j and 9-j
Transformation Matrices and Their Analysis
Symmetrized Recoupling: 6-j and9-j
Products of Operators
Combining Operators of Different Systems
Illustrations
Partially Filled Shells of Atoms or Nuclei
Qualitative Discussion
Shell-wide Treatment
Algebra of Triple Tensors and Its Applications
Symmetries of Higher Dimensions / Part C：
Discrete Transformations of Coordinates
Point Symmetry Operations and Their Groups
Characters of Group Representations and Their Applications
Symmetries of Molecules and Crystals
Rotation Groups in Higher Dimensions: Multiparticle Problems
Four-Dimensional Rotations: the Coulomb-Kepler Problem
Orthogonal Groups in Higher Dimensions
Further Developments
Lorentz Transformations and the Lorentz and Poincare Groups
Lorentz Transformations
Generators and Representations of the Lorentz Group
The Inhomogenous Lorentz (Poincare) Group
Field Representations
Symmetries of the Scattering Continuum
Symmetries of Radial Eigenfunctions
The Full Noninvariance Group of Hydrogen
Dynamics as Symmetry Transformations
Bibliography
Index
Introduction: Symmetry and the Selection of Variables
Algebraic Elements
Reduction Procedure and Irreducible Tensorial Sets
65.
図書
Rafał Abłamowicz, Pertti Lounesto, Josep M. Parra, editors
出版情報:
Boston : Birkhäuser, 1996 xvii, 322 p. ; 26 cm
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66.
図書
Karl Heinz Hoffmann, Michael Schreiber (Eds.)
出版情報:
Berlin : Springer, c1996 xiv, 379 p. ; 25 cm
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67.
図書
Vladislav V. Kravchenko and Michael V. Shapiro
68.
図書
Michel Willem
69.
図書
by Yuri E. Gliklikh
70.
図書
M.G. Calkin
出版情報:
Singapore : World Scientific, c1996 ix, 216 p. ; 23 cm
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71.
図書
by John W. Morgan
出版情報:
Princeton, NJ : Princeton University Press, 1996 vi, 128 p. ; 24 cm
シリーズ名:
Mathematical notes ; 44
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Introduction / 1：
Clifford Algebras and Spin Groups / 2：
Spin Bundles and the Dirac Operator / 3：
The Seiberg-Witten Moduli Space / 4：
Curvature Identities and Bounds / 5：
The Seiberg-Witten Invariant / 6：
Invariants of Kahler Surfaces / 7：
Bibliography
Introduction / 1：
Clifford Algebras and Spin Groups / 2：
Spin Bundles and the Dirac Operator / 3：
72.
図書
Vladimir E. Nazaikinskii, Victor E. Shatalov, Boris Yu. Sternin
73.
図書
George A. Baker, Jr., Peter Graves-Morris
目次情報:
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Introduction and definitions / 1：
Elementary developments / 2：
Pade approximants and numerical methods / 3：
Connection with continued fractions / 4：
Stieltjes series and Polya series / 5：
Convergence theory / 6：
Extensions of Pade approximants / 7：
Multiseries approximants / 8：
Connection with integral equations and quantum mechanics / 9：
Connection with numerical analysis / 10：
Connection with quantum field theory / 11：
Bibliography
Appendix: a FORTRAN program
Introduction and definitions / 1：
Elementary developments / 2：
Pade approximants and numerical methods / 3：
74.
図書
C. Grosche
出版情報:
Singapore : World Scientific, c1996 xi, 280 p. ; 23 cm
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75.
図書
by Krishan L. Duggal and Aurel Bejancu
76.
図書
Ludwig Pittner
77.
図書
Valerij V. Kozlov
78.
図書
by Y.M. Berezansky and Y.G. Kondratiev
79.
図書
Pietro Fré, Paolo Soriani
出版情報:
Singapore : World Scientific, c1995 xiii, 468 p. ; 23 cm
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80.
図書
Robert D. Richtmyer, K.W. Morton
出版情報:
Malabar, Fla. : Krieger Pub. Co., 1994 xiv, 405 p. ; 24 cm
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81.
図書
Willi-Hans Steeb
出版情報:
Singapore : World Scientific, c1996 xi, 360 p. ; 23 cm
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82.
図書
Samuel D. Lindenbaum
出版情報:
Singapore : World Scientific, c1996 xi, 464 p. ; 23 cm
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83.
図書
Yunping Jiang
84.
図書
by Pratul Bandyopadhyay
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Preface
Manifold and Differential Forms / 1：
Spinor Structure and Twistor Geometry / 2：
Quantization / 3：
Quantization and Gauge Field / 4：
Fermions and Topology / 5：
Topological Field Theory / 6：
References
Index
Preface
Manifold and Differential Forms / 1：
Spinor Structure and Twistor Geometry / 2：
85.
図書
edited by Ian Knowles
出版情報:
Boston : International Press, c1995 216 p. ; ill. ; 24 cm
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86.
図書
A.S. Fokas and I.M. Gelfand, editors
87.
図書
Guri I. Marchuk, Valeri I. Agoshkov, Victor P. Shutyaev
出版情報:
Boca Raton, Fla. : CRC Press, c1996 275 p. ; 25 cm
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Principles of Construction of Adjoint Operators in Non-Linear Problems
Properties of Adjoint Operators Constructed on the Basis of Various Principles
Solvability of Main and Adjoint Equations in Non-Linear Problems
Transformation Groups, Conservation Laws and Construction of the Adjoint Operators in Non-Linear Problems
Perturbation Algorithms in Non-Linear Problems
Adjoint Equations and the N-th Order Perturbation Algorithms in Non-Linear Problems of Transport Theory
Adjoint and
Principles of Construction of Adjoint Operators in Non-Linear Problems
Properties of Adjoint Operators Constructed on the Basis of Various Principles
Solvability of Main and Adjoint Equations in Non-Linear Problems
88.
図書
Grigory Isaakovich Barenblatt
目次情報:
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Preface
Introduction
Dimensions, dimensional analysis and similarity / 1：
The application of dimensional analysis to the construction of intermediate asymptotic solutions to problems of mathematical physics / 2：
Self-similar solutions
Self-similarities of the second kind: first examples / 3：
Self-similarities of the second kind: further examples / 4：
Classification of similarity rules and self-similarity solutions / 5：
Recipe for application of similarity analysis
Scaling and transformation groups. Renormalization groups / 6：
Self-similar solutions and travelling waves / 7：
Invariant solutions: special problems of the theory / 8：
Scaling in deformation and fracture in solids / 9：
Scaling in turbulence / 10：
Scaling in geophysical fluid dynamics / 11：
Scaling: miscellaneous special problems / 12：
The application of dimensional analysis to the construction of intermediate asymptotic solutions to problems of mathematical physics. Self-similar solutions
Scaling and transformation groups
Renormalization groups
Preface
Introduction
Dimensions, dimensional analysis and similarity / 1：
89.
図書
Louis H. Kauffman
90.
図書
edited by W. Thirring ; with a preface by F. Dyson
出版情報:
Berlin ; Tokyo : Springer-Verlag, c1991 viii, 565 p. ; 25 cm
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Introduction
Review / Part I：
The Stability of Matter: From Atoms to Stars / I.1：
Exact Results on Atoms / Part II：
Lower Bound to the Energy of Complex Atoms / P. Hertel ; W. ThirringII.1：
Improved Lower Bound on the Indirect Coulomb Energy / S. OxfordII.2：
Monotonicity of the Molecular Electronic Energy in the Nuclear Coordinates / II.3：
Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle / R. BenguriaII.4：
Atomic and Molecular Negative Ions / II.5：
Bound on the Maximum Negative Ionization of Atoms and Molecules / II.6：
Approximate Neutrality of Large-Z Ions / l.M. Sigal ; B.SimonIL.7：
Universal Nature of van der Waals Forces for Coulomb Systems / II.8：
Electron Density Near the Nucleus of a Large Atom / O.J. HeilmannII.9：
Proof of a Conjecture About Atomic and Molecular Cores Related to ScottÆs Correction / A. lantchenko ; H. SiedentopII.10：
Asymptotics of Natural and Artificial Atoms in Strong Magnetic Fields / J.P. Solovej ; J. YngvasonII.11：
Ground States of Large Quantum Dots in Magnetic Fields / II.12：
General Results with Applications to Atoms / Part III：
Kinetic Energy Bounds and Their Application to the Stability ofMatter / III.1：
Inequalities for the Moments of the Eigenvalues of the Schrodinger Hamiltonian and Their Relation to Sobolev Inequalities / III.2：
On Semi-Classical Bounds for Eigenvalues of Schrodinger Operators / M. AizenmanIII.3：
The Number of Bound States of One-Body Schrodinger Operators and the Weyl Problem / III.4：
Variational Principle for Many-Fermion Systems / III.5：
Thomas-Fermi and Related Theories / Part IV：
Thomas-Fermi and Related Theoies of Atoms and Molecules / IV.1：
The Hartree-Fock Theory for Coulomb Systems / B. SimonIV.2：
There Are No Unfilled Shells in Unrestricted Hartree-Fock Theory / V. Bach ; M. LossIV.3：
Many-Body Atomic Potentials in Thomas-Fermi Theory / IV.4：
The Positivity of the Pressure in Thomas-Fermi Theory / IV.5：
The Thomas-Fermi-von Weizsacker Theory of Atoms and Molecules / H. BrezisIV.6：
Analysis of the Thomas-Fermi-von Weizsacker Equation for an Infinite Atom Without Electron Repulsion / IV.7：
The Most Negative Ion in the Thomas-Fermi-von Weizsacker Theory of Atoms and Molecules / IV.8：
Stability of Matter / Part V：
Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter / V.1：
Stability of Coulomb Systems with Magnetic Fields. I. The One-Electron Atom / J. FrohlichV.2：
Stability of Coulomb Systems with Magnetic Fields. II. The Many-Electron Atom and the One-Electron Molecule / V.3：
Stability of Matter in Magnetic Fields / V.4：
The Chandrasekhar Theory of Stellar Collapse as the Limit of Quantum Mechanics / H.-T. YauV.5：
One-Electron Relativistic Molecules with Coulomb Interaction / I. DaubechiesV.6：
The Stability and Instability of Relativistic Matter / V.7：
Stability of Relativistic Matter Via Thomas-Fermi Theory / V.8：
Stability and Instability of Relativistic Electrons in Classical Electromagnetic Fields / V.9：
The Thermodynamic Limit for Real Matter with Coulomb Forces / Part VI：
The Stability of Matter / VI.1：
Existence of Thermodynamics for Real Matter with Coulomb Forces / J.L. LebowitzVI.2：
The Thermodynamic Limit for Jellium / H. NarnhoferVI.3：
Quantum Electrodynamics / Part VII：
Self Energy of Electrons in Non-perturbative QED / VII.1：
Renormalization of the Regularized Electron-Positron Field / VII.2：
Ground States in Non-relativistic Quantum Electrodynamics / M. GriesemerVII.3：
Bosonic Systems / Part VIII：
Ground State Energy of the Low Density Bose Gas / VIII.1：
Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional / R. SeiringerVIII.3：
The Bose Gas: A Subtle Many-Body Problem / VIII.4：
The N5/3 Law for Bosons / VIII.5：
The N7/5 Law for Charged Bosons / J.G. ConlonVIII.6：
Ground State Energy of the One-Component Charged Bose Gas / VIII.7：
Publications of Elliott / H.Lieb
Introduction
Review / Part I：
The Stability of Matter: From Atoms to Stars / I.1：
91.
図書
edited by N.N. Bogolubov and A.M. Kurbatov ; translated from the Russian by A. Ermilov
92.
図書
edited by N.N. Bogolubov, A.M. Kurbatov and A.S. Shumovsky ; translated from the Russian by A. Ermilov
93.
図書
J.B. Griffiths
目次情報:
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Introduction / 1：
Elements of General Relativity / 2：
Colliding Impulsive Gravitational Waves / 3：
Plane Waves / 4：
Geometrical Considerations / 5：
The Field Equations / 6：
Boundary Conditions / 7：
Singularity Structure / 8：
The Szekeres Class of Vacuum Solutions / 9：
Other Vacuum Solutions with Aligned Polarization / 10：
Erns's Equation for Colliding Gravitational Waves / 11：
Solution Generating Techniques / 12：
Vacuum Solutions with Non-Aligned Polarization / 13：
The Initial Value Problem / 14：
Colliding Electromagnetic Waves: The Bell-Szekeres Solution / 15：
Ernst's Equation for Colliding Electromagnetic Waves / 16：
Colliding Electromagnetic Waves: Exact Solutions / 17：
Colliding Electromagnetic Waves: Diagonal Solutions / 18：
Electromagnetic Waves Colliding with Gravitational Waves / 19：
Other Sources / 20：
Related Results / 21：
Conclusions and Prospects / 22：
Introduction / 1：
Elements of General Relativity / 2：
Colliding Impulsive Gravitational Waves / 3：
94.
図書
N.M.J. Woodhouse
出版情報:
Oxford : Clarendon Press , New York : Oxford University Press, 1992, c1991 xi, 307 p. ; 24 cm
シリーズ名:
Oxford mathematical monographs
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Symplectic Geometry / 1：
Lagrangian and Hamiltonian Mechanics / 2：
Symmetry / 3：
Hamilton-Jacobi Theory / 4：
Complex Polarizations / 5：
Elementary Relativistic Systems / 6：
Classical Fields / 7：
Prequantization / 8：
Quantization / 9：
The Metaplectic Correction / 10：
Symplectic Geometry / 1：
Lagrangian and Hamiltonian Mechanics / 2：
Symmetry / 3：
95.
図書
Tristan Hübsch
出版情報:
Singapore : World Scientific, c1992 xv, 362 p. ; 23 cm
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96.
図書
K.R. Parthasarathy
97.
図書
Robert Hermann
98.
図書
Philippe Blanchard, Erwin Brüning
99.
図書
Alphonse Charlier ... [et al.] ; translated by Amanda Taylor
目次情報:
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Tensor analysis
Minkowski space
covariant formulation of electromagnetism
the Cayley-Klein parameters
vector algebra
application of Clifford algebra to bosons
Klein-Gordon equation; fermions
Dirac equation
Tensor analysis
Minkowski space
covariant formulation of electromagnetism
100.
図書
J. Debrus, A.C. Hirshfeld (eds.) ; edited in cooperation with the Deutsche Physikalische Gesellschaft
出版情報:
Berlin ; Tokyo : Springer-Verlag, c1991 x, 323 p. ; 25 cm
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図書
