1.
図書
Ronald B. Guenther and John W. Lee
出版情報:
Englewood Cliffs, N.J. : Prentice-Hall, c1988 xii, 544 p. ; 25 cm
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2.
図書
Siegfried Flügge
3.
図書
Yvonne Choquet-Bruhat, Cécile DeWitt-Morette, and Margaret Dillard-Bleick
出版情報:
Amsterdam ; New York : North Holland Pub., 1977 xvii, 544 p. ; 25 cm
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Preface
Preface to the second edition
Contents
Conventions
Review of fundamental notions of analysis / I：
Differential calculus on banach spaces / II：
Differentiable manifolds / III：
Integration on manifolds / IV：
Riemannian manifolds, Kahlerian manifolds / V：
bis. Connections on a principle fibre bundle
Distributions / VI：
Supplements and additional problems
Subject Index
Errata to Part I
Preface
Preface to the second edition
Contents
4.
図書
Robert D. Richtmyer
5.
図書
Victor Guillemin, Shlomo Sternberg
出版情報:
Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1984 xi, 468 p. ; 24 cm
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Preface
Introduction / I：
Gaussian optics / 1：
Hamilton's method in Gaussian optics / 2：
Fermat's principle / 3：
From Gaussian optics to linear optics / 4：
Geometrical optics, Hamilton's method, and the theory of geometrical aberrations / 5：
Fermat's principle and Hamilton's principle / 6：
Interference and diffraction / 7：
Gaussian integrals / 8：
Examples in Fresnel optics / 9：
The phase factor / 10：
Fresnel's formula / 11：
Fresnel optics and quantum mechanics / 12：
Holography / 13：
Poisson brackets / 14：
The Heisenberg group and representation / 15：
The Groenwald-van Hove theorem / 16：
Other quantizations / 17：
Polarization of light / 18：
The coadjoint orbit of a semidirect product / 19：
Electromagnetism and the determination of symplectic structures / 20：
Epilogue: Why symplectic geometry?
The geometry of the moment map / II：
Normal forms / 21：
The Darboux-Weinstein theorem / 22：
Kaehler manifolds / 23：
Left-invariant forms and Lie algebra cohomology / 24：
Symplectic group actions / 25：
The moment map and some of its properties / 26：
Group actions and foliations / 27：
Collective motion / 28：
Cotangent bundles and the moment map for semidirect products / 29：
More Euler-Poisson equations / 30：
The choice of a collective Hamiltonian / 31：
Convexity properties of toral group actions / 32：
The lemma of stationary phase / 33：
Geometric quantization / 34：
Motion in a Yang-Mills field and the principle of general covariance / III：
The equations of motion of a classical particle in a Yang-Mills field / 35：
Curvature / 36：
The energy-momentum tensor and the current / 37：
The principle of general covariance / 38：
Isotropic and coisotropic embeddings / 39：
Symplectic induction / 40：
Symplectic slices and moment reconstruction / 41：
An alternative approach to the equations of motion / 42：
The moment map and kinetic theory / 43：
Complete integrability / IV：
Fibrations by tori / 44：
Collective complete integrability / 45：
Collective action variables / 46：
The Kostant-Symes lemma and some of its variants / 47：
Systems of Calogero type / 48：
Solitons and coadjoint structures / 49：
The algebra of formal pseudodifferential operators / 50：
The higher-order calculus of variations in one variable / 51：
Contractions of symplectic homogeneous spaces / V：
The Whitehead lemmas / 52：
The Hochschild-Serre spectral sequence / 53：
Galilean and Poincare elementary particles / 54：
Coppersmith's theory / 55：
References
Index
Preface
Introduction / I：
Gaussian optics / 1：
6.
図書
by Eugene R. Speer
7.
図書
Jamal Nazrul Islam
出版情報:
Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1985 vi, 122 p. ; 24 cm
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Preface
Introduction / 1：
The Einstein equations for a rotating metric and some classes of solutions / 2：
The Kerr and Timimatsu-Sato solutions / 3：
Rotating neutral dust / 4：
rotating Einstein-Maxwell fields / 5：
Rotating charged dust / 6：
Appendix
References
Index
Preface
Introduction / 1：
The Einstein equations for a rotating metric and some classes of solutions / 2：
8.
図書
Bryce DeWitt
目次情報:
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Preface to the first edition
Preface to the second edition
Analysis over supernumbers / 1：
Supernumbers and superanalytic functions / 1.1：
Grassmann algebras
Supernumbers
c-numbers and a-numbers
Superanalytic functions of supernumbers
Integration of superanalytic functions of supernumbers
Real supernumbers. Differentiable functions of real c-numbers and their integrals / 1.2：
Complex conjugation
Functions, distributions and integrals over R[subscript c]
Fourier transforms over R[subscript c]
Functions and integrals over R[subscript a] / 1.3：
Basic definitions
Fourier transforms over R[subscript a]
Integrals over R[superscript n][subscript a]
Supervector spaces / 1.4：
Definition
Bases
Pure bases
Pure real bases
Standard bases
Linear transformations, supertranspositions and dual supervector spaces / 1.5：
Change of basis
Shifting indices. The supertranspose
Extensions of the supertransposition rules
Dual supervector spaces
Dual bases
Further index-shifting conventions
The supertrace and the superdeterminant / 1.6：
The supertrace
The superdeterminant
The superdeterminant in special cases
The superdeterminant in the general case
Integration over R[superscript m][subscript c] [times] R[superscript n][subscript a] / 1.7：
Notation
Integration
Homogeneous linear transformations of the a-number coordinates
Homogeneous linear transformations of all the coordinates
Nonlinear transformations
Gaussian integrals over R[superscript m][subscript c] [times] R[superscript n][subscript a]
Exercises
Comments on chapter 1
Supermanifolds / 2：
Definition and structure of supermanifolds / 2.1：
Topology of R[superscript m][subscript c] [times] R[superscript n][subscript a]. Differentiable mappings
Supermanifolds, charts and atlases
Scalar fields and supercurves
Diffeomorphisms and embeddings
Ordinary manifolds. Skeleton and body of a supermanifold
Projectively Hausdorff, compact, paracompact and orientable supermanifolds. Realizations of the body
Supervector structures on supermanifolds / 2.2：
Scalar fields as supervectors
Contravariant vector fields
Alternative presentation of contravariant vector fields
Components
Tangent spaces
Tangents to supercurves
Super Lie brackets, local frames and covariant vector fields / 2.3：
Supercommutators and antisupercommutators
A matter of notation
The super Lie bracket
Local frames
Super Lie brackets of local frame fields
Covariant vector fields
Differentials
Tensor fields / 2.4：
Tensors at a point
The supervector space T[superscript r] [subscript s](p)
Tensor products
Tensor and multitensor fields
Index-shifting conventions. Contractions
The unit tensor field
The Lie derivative / 2.5：
Explicit forms
Lie derivations as supervectors
The derivative mapping
Integral supercurves. Congruences
Dragging of tensor fields
Forms / 2.6：
The exterior product
Bases for forms
Derivations of forms
The exterior derivative
The inner product
Connections / 2.7：
The connection components
Multiple covariant derivatives. The torsion
The Riemann tensor field
The super Bianchi identity
Parallel transport. Supergeodesics
Distant parallelism
Riemannian supermanifolds / 2.8：
The metric tensor field
Canonical form of the metric tensor at a point
Canonical or orthosymplectic bases
Riemannian connections
The curvature tensor field
The Ricci tensor field
Flat Riemannian supermanifolds
Conformally related Riemannian supermanifolds. The Weyl tensor field
Conformally flat Riemannian supermanifolds
Killing vector fields
Conformal Killing vector fields
The global conformal group
Integration over supermanifolds / 2.9：
Integration over R[superscript m][subscript c] [times] R[superscript n][subscript a]. Measure functions
Locally finite atlases and partitions of unity
Integration over paracompact orientable supermanifolds
Integration over Riemannian supermanifolds
Integrals of total divergences
The compact case
An example
Comments on chapter 2
Super Lie groups. General theory / 3：
Definition and structure of super Lie groups / 3.1：
Canonical diffeomorphisms
Left- and right-invariant vector fields
Left- and right-invariant local frame fields
Left- and right-invariant congruences
One-parameter Abelian subgroups
The exponential mapping. Canonical coordinates
The super Lie algebra
The structure constants
The right and left auxiliary functions
Identities satisfied by the auxiliary functions
Construction of a super Lie group from its super Lie algebra
Realizations of super Lie groups / 3.2：
Orbits
Transitive realizations
Isotropy subgroups
Coset spaces
Killing flows
Properties of the coordinate components of the Q[subscript a]
A special canonical coordinate system
Coordinates for the coset spaces
Classification of transitive realizations
Matrix representations of super Lie groups
Contragredient representations
Inner automorphisms. The adjoint representation
Matrix representations of the super Lie algebra
Geometry of coset spaces / 3.3：
Invariant tensor fields
Differential equations for geometrical structures
Integrability of the differential equations
A special coordinate system
Condition for the existence of a group-invariant measure function
Condition for the existence of a group-invariant metric tensor field
Condition for the existence of a group-invariant connection
Solutions of the differential equations
Geometry of the group supermanifold
Identity of the left- and right-invariant connections
Parallelism at a distance in the group supermanifold
Integration over the group
A special class of super Lie groups
Comments on chapter 3
Super Lie groups. Examples / 4：
Construction of super Lie algebras and super Lie groups / 4.1：
Properties of the structure constants
Conventional super Lie groups, Z[subscript 2]-graded algebras
Unconventional super Lie groups
Structure of conventional super Lie Groups. The extending representation
Construction of a class of super Lie algebras
The classical super Lie groups / 4.2：
The group GL (m, n)
The group SL (m, n)
The group SL (m, m)/GL (1, 0)
The orthosymplectic group OSp (m, n)
The Kac notation
The group P(m)
The group Q(m)
The exceptional simple super Lie groups / 4.3：
The groups D(2, 1, [alpha])
The group F(4)
The structure of F(4)
Pseudorepresentation of F(4)
The group G(3)
The structure of G[subscript 2]
The structure of G(3)
Pseudorepresentation of G(3)
Super Lie groups of basic importance in physics / 4.4：
The super de Sitter group
The super Poincare group
The coset space: super Poincare group/SO(1, 3)
Killing flows and invariant connections
Riemannian geometry of the coset space
The super Lorentz group
The Cartan super Lie groups / 4.5：
The diffeomorphism group Diff(M)
The group SDiff(M, [mu])
The canonical transformation group Can(M, [omega])
The group of contact transformations
The case m = 0
The group W(n)
The groups S(n) and S(n)
The groups H(n) and H(n)
Comments on chapter 4
Selected applications of supermanifold theory / 5：
Superclassical dynamical systems / 5.1：
Configuration spaces
Supermanifolds as configuration spaces
Space of histories
The action functional and the dynamical equations
Infinitesimal disturbances and Green's functions
Reciprocity relations
The Peierls bracket
Peierls bracket identities
Super Hilbert spaces / 5.2：
Linear operators
Physical observables
Quantum systems / 5.3：
Transition to the quantum theory
The Schwinger variational principle
External sources
Chronologically ordered form of the operator dynamical equations
The Feynman functional integral
A simple Fermi system / 5.4：
Action functional and Green's functions
Eigenvectors of x
The energy
A pure basis
An alternative representation
The functional integral representation of [x", t"|x', t']
Evaluation of the functional integral
The average superclassical trajectory
Propagator for x[subscript av](t)
The Fermi oscillator / 5.5：
Mode functions and Hamiltonian
Basic supervectors
Eigenvectors of x[subscript 1] and x[subscript 2]. Choice of pure basis
Coherent states
The functional integral representation of [a"*, t"
Direct evaluation of the functional integral
The importance of endpoint contributions
The stationary trajectory as a matrix element
The Feynman propagator
The Bose oscillator / 5.6：
Energy eigenvectors
Hamilton-Jacobi theory
The amplitude [x', t'|x', t'] and its functional integral representation
The functional-integral representation of [a"*, t"
The stationary path between coherent states
Energy eigenfunctions
Bose-Fermi supersymmetry / 5.7：
The simplest model
New conserved quantities
The Bose-Fermi supersymmetry group
Eigenvectors of Q[subscript 1] and Q[subscript 2]
The supersymmetry group as a transformation group
Auxiliary variable
Nonlinear Bose-Fermi supersymmetry
The supersymmetry group
The energy spectrum
Spontaneously broken supersymmetry
Comments on chapter 5
Applications involving topology / 6：
Nontrivial configuration spaces / 6.1：
Standard canonical systems
Green's functions
Equivalence of Peierls and Poisson brackets
Quantization / 6.2：
Problems with the naive quantization rule
Operator-valued forms. The projection m-form
The position operator
Vector operators
The momentum operator
Restriction to a local chart
Lack of uniqueness of the momentum operator
Overlapping charts. Transformation of coordinates
The position representation
The momentum operator in the position representation
The Schrodinger equation
The position representation of the projection m-form
Curved configuration spaces / 6.3：
A special class of systems
Covariant variation
Covariant differentiation with respect to t
The dynamical equations
Covariant functional differentiation
The Feynman functional integral and its meaning / 6.4：
Formal computation of det G[superscript +][x]
The functional integral
Normalization
Ambiguity in the functional integral
Homotopy
Homotopy mesh
The total amplitude
Change of homotopy mesh
The role of homology
The universal covering space
The total amplitude revisited
The Hamiltonian operator: a nonlattice derivation / 6.5：
Integration over phase space
Evaluation of the chronologically ordered Hamiltonian
Approximate evaluation of the path integral / 6.6：
Brief review of Hamilton-Jacobi theory
The Van Vleck-Morette determinant
Jacobi fields and the Green's function for the trajectory x[subscript c]
Determinantal relations
The loop expansion
The WKB approximation
The heat kernel expansion
Role of the two-loop term in the independent verification of (6.5.25)
New variables
Computation of the two-loop term
Supersymmetry and the Euler-Poincare characteristic / 6.7：
Inclusion of a-type dynamical variables
Green's functions and Peierls brackets
Energy and supersymmetry group
Basis supervectors
Differential representation of operators
The Euler-Poincare characteristic
Functional integral for the coherent-state transition amplitude
The Chern-Gauss-Bonnet formula
Comments on chapter 6
References
Index
Preface to the first edition
Preface to the second edition
Analysis over supernumbers / 1：
9.
図書
George Papanicolaou, editor
10.
図書
W.I. Fushchich and A.G. Nikitin ; translated by John R. Schulenberger
11.
図書
Donald Greenspan
12.
図書
Bernard F. Schutz
出版情報:
Cambridge ; New York : Cambridge University Press, 1980 xii, 250 p. ; 24 cm
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Preface
Some basic mathematics / 1：
The space R[superscript n] and its topology / 1.1：
Mappings / 1.2：
Real analysis / 1.3：
Group theory / 1.4：
Linear algebra / 1.5：
The algebra of square matrices / 1.6：
Bibliography / 1.7：
Differentiable manifolds and tensors / 2：
Definition of a manifold / 2.1：
The sphere as a manifold / 2.2：
Other examples of manifolds / 2.3：
Global considerations / 2.4：
Curves / 2.5：
Functions on M / 2.6：
Vectors and vector fields / 2.7：
Basis vectors and basis vector fields / 2.8：
Fiber bundles / 2.9：
Examples of fiber bundles / 2.10：
A deeper look at fiber bundles / 2.11：
Vector fields and integral curves / 2.12：
Exponentiation of the operator d/d[lambda] / 2.13：
Lie brackets and noncoordinate bases / 2.14：
When is a basis a coordinate basis? / 2.15：
One-forms / 2.16：
Examples of one-forms / 2.17：
The Dirac delta function / 2.18：
The gradient and the pictorial representation of a one-form / 2.19：
Basis one-forms and components of one-forms / 2.20：
Index notation / 2.21：
Tensors and tensor fields / 2.22：
Examples of tensors / 2.23：
Components of tensors and the outer product / 2.24：
Contraction / 2.25：
Basis transformations / 2.26：
Tensor operations on components / 2.27：
Functions and scalars / 2.28：
The metric tensor on a vector space / 2.29：
The metric tensor field on a manifold / 2.30：
Special relativity / 2.31：
Lie derivatives and Lie groups / 2.32：
Introduction: how a vector field maps a manifold into itself / 3.1：
Lie dragging a function / 3.2：
Lie dragging a vector field / 3.3：
Lie derivatives / 3.4：
Lie derivative of a one-form / 3.5：
Submanifolds / 3.6：
Frobenius' theorem (vector field version) / 3.7：
Proof of Frobenius' theorem / 3.8：
An example: the generators of S[superscript 2] / 3.9：
Invariance / 3.10：
Killing vector fields / 3.11：
Killing vectors and conserved quantities in particle dynamics / 3.12：
Axial symmetry / 3.13：
Abstract Lie groups / 3.14：
Examples of Lie groups / 3.15：
Lie algebras and their groups / 3.16：
Realizations and representations / 3.17：
Spherical symmetry, spherical harmonics and representations of the rotation group / 3.18：
Differential forms / 3.19：
The algebra and integral calculus of forms / A：
Definition of volume -- the geometrical role of differential forms / 4.1：
Notation and definitions for antisy mmetric tensors / 4.2：
Manipulating differential forms / 4.3：
Restriction of forms / 4.5：
Fields of forms / 4.6：
Handedness and orientability / 4.7：
Volumes and integration on oriented manifolds / 4.8：
N-vectors, duals, and the symbol [epsilon][subscript ij...k] / 4.9：
Tensor densities / 4.10：
Generalized Kronecker deltas / 4.11：
Determinants and [epsilon][subscript ij...k] / 4.12：
Metric volume elements / 4.13：
The differential calculus of forms and its applications / B：
The exterior derivative / 4.14：
Notation for derivatives / 4.15：
Familiar examples of exterior differentiation / 4.16：
Integrability conditions for partial differential equations / 4.17：
Exact forms / 4.18：
Proof of the local exactness of closed forms / 4.19：
Lie derivatives of forms / 4.20：
Lie derivatives and exterior derivatives commute / 4.21：
Stokes' theorem / 4.22：
Gauss' theorem and the definition of divergence / 4.23：
A glance at cohomology theory / 4.24：
Differential forms and differential equations / 4.25：
Frobenius' theorem (differential forms version) / 4.26：
Proof of the equivalence of the two versions of Frobenius' theorem / 4.27：
Conservation laws / 4.28：
Vector spherical harmonics / 4.29：
Applications in physics / 4.30：
Thermodynamics
Simple systems / 5.1：
Maxwell and other mathematical identities / 5.2：
Composite thermodynamic systems: Caratheodory's theorem / 5.3：
Hamiltonian mechanics
Hamiltonian vector fields / 5.4：
Canonical transformations / 5.5：
Map between vectors and one-forms provided by [characters not reproducible] / 5.6：
Poisson bracket / 5.7：
Many-particle systems: symplectic forms / 5.8：
Linear dynamical systems: the symplectic inner product and conserved quantities / 5.9：
Fiber bundle structure of the Hamiltonian equations / 5.10：
Electromagnetism / C：
Rewriting Maxwell's equations using differential forms / 5.11：
Charge and topology / 5.12：
The vector potential / 5.13：
Plane waves: a simple example / 5.14：
Dynamics of a perfect fluid / D：
Role of Lie derivatives / 5.15：
The comoving time-derivative / 5.16：
Equation of motion / 5.17：
Conservation of vorticity / 5.18：
Cosmology / E：
The cosmological principle / 5.19：
Lie algebra of maximal symmetry / 5.20：
The metric of a spherically symmetric three-space / 5.21：
Construction of the six Killing vectors / 5.22：
Open, closed, and flat universes / 5.23：
Connections for Riemannian manifolds and gauge theories / 5.24：
Introduction / 6.1：
Parallelism on curved surfaces / 6.2：
The covariant derivative / 6.3：
Components: covariant derivatives of the basis / 6.4：
Torsion / 6.5：
Geodesics / 6.6：
Normal coordinates / 6.7：
Riemann tensor / 6.8：
Geometric interpretation of the Riemann tensor / 6.9：
Flat spaces / 6.10：
Compatibility of the connection with volume-measure or the metric / 6.11：
Metric connections / 6.12：
The affine connection and the equivalence principle / 6.13：
Connections and gauge theories: the example of electromagnetism / 6.14：
Solutions and hints for selected exercises / 6.15：
Notation
Index
Appendix
Preface
Some basic mathematics / 1：
The space R[superscript n] and its topology / 1.1：
13.
図書
Walter Thirring ; translated by Evans M. Harrell
14.
図書
Robert Carroll
15.
図書
Gregory L. Naber
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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
16.
図書
Aleksey I. Prilepko, Dmitry G. Orlovsky, Igor A. Vasin
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Inverse problems for equations of parabolic type
inverse problems for equations of hyperbolic type
inverse problems for equations of elliptic type
inverse problems in dynamics of viscous incompressible fluid
some topics from functional analysis and operator theory
abstract inverse problems for first order equations and their applications in mathematical physics
two-point inverse problems for first order equations
inverse problems for equations of second order
applications of
Inverse problems for equations of parabolic type
inverse problems for equations of hyperbolic type
inverse problems for equations of elliptic type
17.
図書
James J. Callahan
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Relativity before 1905
Special relativityùkinematics
Special relativityùkinetics
Arbitrary frames
Surfaces and curvatures
Intrinsic geometry
General relativity
Consequences
Relativity before 1905
Special relativityùkinematics
Special relativityùkinetics
18.
図書
by Zbigniew Haba
19.
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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20.
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：
21.
図書
by Uwe Franz and René Schott
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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：
22.
図書
David A. Cox, Sheldon Katz
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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
23.
図書
edited by Silvio Levy
24.
図書
by Volodymyr Koshmanenko
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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：
25.
図書
Herbert Meschkowski.Translated by Robert Schlapp
26.
図書
David E. Evans and Yasuyuki Kawahigashi
27.
図書
B.N. Mandal and Nanigopal Mandal
28.
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：
29.
図書
Ivar Stakgold
30.
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
31.
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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32.
図書
by Krzysztof Maurin
33.
図書
J.-M. Souriau ; translated by C.H. Cushman-de Vries ; translation editors, R.H. Cushman, G.M. Tuynman
34.
図書
by C. Cercignani, V.I. Gerasimenko, D.Ya. Petrina
35.
図書
Yulia E. Karpeshina
36.
図書
I. Kuzin, S. Pohozaev
37.
図書
C. Constanda, J. Saranen and S. Seikkala (editors)
38.
図書
by Larry A. Lambe and David E. Radford
39.
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：
40.
図書
Charles Li, Stephen Wiggins
41.
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：
42.
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
43.
図書
by Anatoliy K. Prykarpatsky and Ihor V. Mykytiuk
目次情報:
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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：
44.
図書
Roman Bezrukavnikov, Michael Finkelberg, Vadim Schechtman
45.
図書
Isabelle Catto, Claude Le Bris, Pierre-Louis Lions
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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：
46.
図書
Victor Kac
47.
図書
edited by Peter L. Antonelli and Bradley C. Lackey
48.
図書
M. V. Karasev, editor
49.
図書
Stephen Simons
50.
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：
51.
図書
N.P. Landsman
52.
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]
目次情報:
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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
53.
図書
by P.L. Antonelli and T.J. Zastawniak
54.
図書
by Anatoly Swishchuk
55.
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：
56.
図書
Claus Müller
57.
図書
V.G. Osmolovskiĭ ; [translated from the Russian by Tamara Rozhkovskaya]
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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
58.
図書
by A.M. Meirmanov, V.V. Pukhnachov, S.I. Shmarev
59.
図書
edited by Jacques Hurtubise and François Lalonde ; technical editor, Gert Sabidussi
60.
図書
by Norman E. Hurt
61.
図書
edited by Michael Demuth, Bert-Wolfgang Schulze
62.
図書
George W. Mackey
63.
図書
Gregory L. Naber
64.
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：
65.
図書
Sergio Albeverio ... [et al.]
66.
図書
Victor Kac
67.
図書
Martin Schottenloher
68.
図書
by D. Ya. Petrina
69.
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
70.
図書
V.V. Shaidurov
71.
図書
edited by Rafał Abłamowicz and Pertti Lounesto
72.
図書
editor, Louis H. Kauffman
73.
図書
L.J. Mason and N.M.J. Woodhouse
74.
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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75.
図書
Vladislav V. Kravchenko and Michael V. Shapiro
76.
図書
Michel Willem
77.
図書
by Yuri E. Gliklikh
78.
図書
M.G. Calkin
出版情報:
Singapore : World Scientific, c1996 ix, 216 p. ; 23 cm
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79.
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：
80.
図書
Vladimir E. Nazaikinskii, Victor E. Shatalov, Boris Yu. Sternin
81.
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：
82.
図書
C. Grosche
出版情報:
Singapore : World Scientific, c1996 xi, 280 p. ; 23 cm
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83.
図書
by Krishan L. Duggal and Aurel Bejancu
84.
図書
Ludwig Pittner
85.
図書
by Y.M. Berezansky and Y.G. Kondratiev
86.
図書
Pietro Fré, Paolo Soriani
出版情報:
Singapore : World Scientific, c1995 xiii, 468 p. ; 23 cm
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87.
図書
Willi-Hans Steeb
出版情報:
Singapore : World Scientific, c1996 xi, 360 p. ; 23 cm
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88.
図書
Samuel D. Lindenbaum
出版情報:
Singapore : World Scientific, c1996 xi, 464 p. ; 23 cm
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89.
図書
Yunping Jiang
90.
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：
91.
図書
edited by Ian Knowles
出版情報:
Boston : International Press, c1995 216 p. ; ill. ; 24 cm
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92.
図書
A.S. Fokas and I.M. Gelfand, editors
93.
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
94.
図書
N.N. Lebedev
95.
図書
edited by V.S. Vladimirov ; translated from the Russian by Eugene Yankovsky
出版情報:
Moscow : Mir Publishers , Berlin ; Tokyo : Springer, 1986 288 p. ; 24 cm
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96.
図書
Hans Triebel
97.
図書
by Nicholas Woodhouse
出版情報:
Oxford : Clarendon Press, 1980 xi, 316 p. ; 24 cm
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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：
98.
図書
Robert D. Richtmyer, K.W. Morton
99.
図書
[edited by] Ronald E. Mickens
出版情報:
New York : Van Nostrand Reinhold Co., c1985 x, 357 p. ; 24 cm
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100.
図書
Michael Reed, Barry Simon
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Preliminaries
Hilbert Spaces
Banach Spaces
Topological Spaces
Locally Convex Spaces
Bounded Operators
The Spectral Theorem
Unbounded Operators
The Fourier Transform
Supplementary Material
List of Symbols
Index
Preliminaries
Hilbert Spaces
Banach Spaces
図書
