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1.

図書

図書
Jan Cnops
出版情報: Boston : Birkhäuser, c2002  x, 211 p. ; 24 cm
シリーズ名: Progress in mathematical physics / editors-in-chief, Anne Boutet de Monvel, Gerald Kaiser ; v. 24
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Introduction
Clifford Algebras
Manifolds
Dirac Operators
Conformal Maps
Unique Continuation and the Cauchy Kernel
Boundary Values
Appendix
General Manifolds
The Additional Canterbury Tales
List of Symbols
Bibliography
Index
Introduction
Clifford Algebras
Manifolds
2.

図書

図書
Franz J. Vesely
出版情報: New York : Kluwer Academic/Plenum Publishers, c2001  xvi, 259 p. ; 26 cm
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The Three Pillars of Computational Physics / I:
Finite Differences / 1:
Interpolation Formulae / 1.1:
NGF Interpolation / 1.1.1:
NGB Interpolation / 1.1.2:
ST Interpolation / 1.1.3:
Difference Quotients / 1.2:
DNGF Formulae / 1.2.1:
DNGB Formulae / 1.2.2:
DST Formulae / 1.2.3:
Finite Differences in Two Dimensions / 1.3:
Sample Applications / 1.4:
Classical Point Mechanics / 1.4.1:
Diffusion and Thermal Conduction / 1.4.2:
Linear Algebra / 2:
Exact Methods / 2.1:
Gauss Elimination and Back Substitution / 2.1.1:
Simplifying Matrices: The Householder Transformation / 2.1.2:
LU Decomposition / 2.1.3:
Tridiagonal Matrices: Recursion Method / 2.1.4:
Iterative Methods / 2.2:
Jacobi Relaxation / 2.2.1:
Gauss-Seidel Relaxation (GSR) / 2.2.2:
Successive Over-Relaxation (SOR) / 2.2.3:
Alternating Direction Implicit Method (ADI) / 2.2.4:
Conjugate Gradient Method (CG) / 2.2.5:
Eigenvalues and Eigenvectors / 2.3:
Largest Eigenvalue and Related Eigenvector / 2.3.1:
Arbitrary Eigenvalue/-vector: Inverse Iteration / 2.3.2:
Potential Equation / 2.4:
Electronic Orbitals / 2.4.3:
Stochastics / 3:
Equidistributed Random Variates / 3.1:
Linear Congruential Generators / 3.1.1:
Shift Register Generators / 3.1.2:
Other Distributions / 3.2:
Fundamentals / 3.2.1:
Transformation Method / 3.2.2:
Generalized Transformation Method / 3.2.3:
Rejection Method / 3.2.4:
Multivariate Gaussian Distribution / 3.2.5:
Equidistribution in Orientation Space / 3.2.6:
Random Sequences / 3.3:
Markov Processes / 3.3.1:
Autoregressive Processes / 3.3.3:
Wiener-Levy Process / 3.3.4:
Markov Chains and the Monte Carlo method / 3.3.5:
Stochastic Optimization / 3.4:
Simulated Annealing / 3.4.1:
Genetic Algorithms / 3.4.2:
Everything Flows / II:
Ordinary Differential Equations / 4:
Initial Value Problems of First Order / 4.1:
Euler-Cauchy Algorithm / 4.1.1:
Stability and Accuracy of Difference Schemes / 4.1.2:
Explicit Methods / 4.1.3:
Implicit Methods / 4.1.4:
Predictor-Corrector Method / 4.1.5:
Runge-Kutta Method / 4.1.6:
Extrapolation Method / 4.1.7:
Initial Value Problems of Second Order / 4.2:
Verlet Method / 4.2.1:
Nordsieck Formulation of the PC Method / 4.2.2:
Symplectic Algorithms / 4.2.4:
Numerov's Method / 4.2.6:
Boundary Value Problems / 4.3:
Shooting Method / 4.3.1:
Relaxation Method / 4.3.2:
Partial Differential Equations / 5:
Initial Value Problems I (Hyperbolic) / 5.1:
FTCS Scheme; Stability Analysis / 5.1.1:
Lax Scheme / 5.1.2:
Leapfrog Scheme (LF) / 5.1.3:
Lax-Wendroff Scheme (LW) / 5.1.4:
Lax and Lax-Wendroff in Two Dimensions / 5.1.5:
Initial Value Problems II (Parabolic) / 5.2:
FTCS Scheme / 5.2.1:
Implicit Scheme of First Order / 5.2.2:
Crank-Nicholson Scheme (CN) / 5.2.3:
Dufort-Frankel Scheme (DF) / 5.2.4:
Boundary Value Problems: Elliptic DE / 5.3:
Relaxation and Multigrid Techniques / 5.3.1:
ADI Method for the Potential Equation / 5.3.2:
Fourier Transform Method (FT) / 5.3.3:
Cyclic Reduction (CR) / 5.3.4:
Anchors Aweigh / III:
Simulation and Statistical Mechanics / 6:
Model Systems of Statistical Mechanics / 6.1:
A Nutshellfull of Fluids and Solids / 6.1.1:
Tricks of the Trade / 6.1.2:
Monte Carlo Method / 6.2:
Molecular Dynamics Simulation / 6.3:
Hard Spheres / 6.3.1:
Continuous Potentials / 6.3.2:
Beyond Basic Molecular Dynamics / 6.3.3:
Evaluation of Simulation Experiments / 6.4:
Pair Correlation Function / 6.4.1:
Autocorrelation Functions / 6.4.2:
Particles and Fields / 6.5:
Ewald summation / 6.5.1:
Particle-Mesh Methods (PM and P3M) / 6.5.2:
Stochastic Dynamics / 6.6:
Quantum Mechanical Simulation / 7:
Diffusion Monte Carlo (DMC) / 7.1:
Path Integral Monte Carlo (PIMC) / 7.2:
Wave Packet Dynamics (WPD) / 7.3:
Density Functional Molecular Dynamics (DFMD) / 7.4:
Hydrodynamics / 8:
Compressible Flow without Viscosity / 8.1:
Explicit Eulerian Methods / 8.1.1:
Particle-in-Cell Method (PIC) / 8.1.2:
Smoothed Particle Hydrodynamics (SPH) / 8.1.3:
Incompressible Flow with Viscosity / 8.2:
Vorticity Method / 8.2.1:
Pressure Method / 8.2.2:
Free Surfaces: Marker-and-Cell Method (MAC) / 8.2.3:
Lattice Gas Models for Hydrodynamics / 8.3:
Lattice Gas Cellular Automata / 8.3.1:
The Lattice Boltzmann Method / 8.3.2:
Direct Simulation Monte Carlo / Bird method / 8.4:
Appendixes
Machine Errors / A:
Discrete Fourier Transformation / B:
Fast Fourier Transform (FFT) / B.1:
Bibliography
Index
The Three Pillars of Computational Physics / I:
Finite Differences / 1:
Interpolation Formulae / 1.1:
3.

図書

図書
Giovanni Giachetta, Luigi Mangiarotti, Gennadi Sardanashvily
出版情報: Singapore : World Scientific, c2011  xi, 392 p. ; 24 cm
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4.

図書

図書
James J. Callahan
出版情報: New York : Springer, c2000  xvi, 451 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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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
5.

図書

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.:
6.

図書

図書
Claude Kipnis, Claudio Landim
出版情報: Berlin : Springer-Verlag, c1999  xvi, 442 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 320
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7.

図書

図書
Sergey N. Dorogovtsev
出版情報: Oxford ; New York : Oxford University Press, 2010  ix, 134 p. ; 25 cm
シリーズ名: Oxford master series in physics ; 20
Oxford master series in statistical, computational, and theoretical physics
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First steps towards networks / 1:
Euler's graph / 1.1:
Examples of graphs / 1.2:
Shortest path length / 1.3:
Lattices and fractals / 1.4:
Milgram's experiment / 1.5:
Directed networks / 1.6:
What are random networks? / 1.7:
Degree distribution / 1.8:
Clustering / 1.9:
Adjacency matrix / 1.10:
Classical random graphs / 2:
Two classical models / 2.1:
Loops in classical random graphs / 2.2:
Diameter of classical random graphs / 2.3:
The birth of a giant component / 2.4:
Finite components / 2.5:
Small and large worlds / 3:
The world of Paul Erdos / 3.1:
Diameter of the Web / 3.2:
Small-world networks / 3.3:
Equilibrium versus growing trees / 3.4:
Giant connected component at birth is fractal / 3.5:
Dimensionality of a brush / 3.6:
From the Internet to cellular nets / 4:
Levels of the Internet / 4.1:
The WWW / 4.2:
Cellular networks / 4.3:
Co-occurrence networks / 4.4:
Uncorrelated networks / 5:
The configuration model / 5.1:
Hidden variables / 5.2:
Neighbour degree distribution / 5.3:
Loops in uncorrelated networks / 5.4:
Statistics of shortest paths / 5.5:
Uncorrelated bipartite networks / 5.6:
Percolation and epidemics / 6:
Connected components in uncorrelated networks / 6.1:
Ultra-resilience phenomenon / 6.2:
Finite-size effects / 6.3:
k-cores / 6.4:
Epidemics in networks / 6.5:
Self-organization of networks / 7:
Random recursive trees / 7.1:
The Barabási-Albert model / 7.2:
General preferential attachment / 7.3:
Condensation phenomena / 7.4:
Accelerated growth / 7.5:
The BKT transition / 7.6:
Deterministic graphs / 7.7:
Correlations in networks / 8:
Degree-degree correlations / 8.1:
How to measure correlations / 8.2:
Assortative and disassortative mixing / 8.3:
Why are networks correlated? / 8.4:
Degree correlations and clustering / 8.5:
Weighted networks / 9:
The strength of weak ties / 9.1:
World-wide airport network / 9.2:
Modelling weighted networks / 9.3:
Motifs, cliques, communities / 10:
Cliques in networks / 10.1:
Statistics of motifs / 10.2:
Modularity / 10.3:
Detecting communities / 10.4:
Hierarchical architectures / 10.5:
Navigation and search / 11:
Random walks on networks / 11.1:
Biased random walks / 11.2:
Kleinberg's problem / 11.3:
Navigability / 11.4:
Google PageRank / 11.5:
Traffic / 12:
Traffic in the Internet / 12.1:
Congestion / 12.2:
Cascading failures / 12.3:
Interacting systems on networks / 13:
The Ising model on networks / 13.1:
Critical phenomena / 13.2:
Synchronization / 13.3:
Games on networks / 13.4:
Avalanches as branching processes / 13.5:
Optimization / 14:
Critique of preferential attachment / 14.1:
Optimized trade-offs / 14.2:
The power of choice / 14.3:
Outlook / 15:
Further reading
References
Index
From the Internet to cellular networks
First steps towards networks / 1:
Euler's graph / 1.1:
Examples of graphs / 1.2:
8.

図書

図書
Albert Furrer, Joël Mesot, Thierry Strässle
出版情報: Hackensack : World Scientific, c2009  xiv, 301 p. ; 24 cm
シリーズ名: Series on neutron techniques and applications ; v. 4
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Preface
Introduction / 1:
Why neutron scattering? / 1.1:
Basic properties of the neutron / 1.2:
Basic principles of Neutron Scattering / 2:
Aim of a neutron scattering experiment / 2.1:
Neutron scattering cross-section / 2.2:
Correlation functions / 2.3:
Coherent and incoherent scattering / 2.4:
Principle of detailed balance / 2.5:
Magnetic scattering / 2.6:
Polarized neutrons / 2.7:
Dynamical neutron scattering / 2.8:
Further reading / 2.9:
Instrumentation / 3:
Neutron sources / 3.1:
Historical evolution of neutron sources / 3.1.1:
Practical requirements for neutron sources / 3.1.2:
Fission sources / 3.1.3:
Spallation sources / 3.1.4:
Moderation of neutrons / 3.1.5:
Instrument component / 3.2:
Beam tubes and static collimators / 3.2.1:
Neutron guides / 3.2.2:
Time-of-flight monochromators / 3.2.3:
Monochromators (and analyzer) crystals / 3.2.4:
Neutron beam filters / 3.2.5:
Spin polarizers (and spin analyzers) / 3.2.6:
Guide fields and spin flippers / 3.2.7:
Detectors / 3.2.8:
Neutrons instruments / 3.3:
Introductory remarks / 3.3.1:
Powder diffractometers / 3.3.2:
Single-crystal diffractometers / 3.3.3:
Small-angle scattering instruments / 3.3.4:
Reflectometers / 3.3.5:
Time-of-flight spectrometers / 3.3.6:
Triple-axis spectrometers / 3.3.7:
Backscattering spectrometers / 3.3.8:
Spin-echo spectrometers / 3.3.9:
Sample environment / 3.4:
Temperature / 3.4.1:
Magnetic field / 3.4.2:
Pressure / 3.4.3:
Structure Determinations / 3.5:
Cross section / 4.1:
Examples of structure factors / 4.2:
Polycrystalline materials / 4.3:
Single crystals / 4.4:
Rotating crystal method / 4.4.1:
Laue method / 4.4.2:
Extinction and absorption / 4.5:
Characterization of residual stress / 4.6:
Exercises / 4.7:
Solutions / 4.9:
Lattice Dynamics / 5:
Cross section for one-phonon scattering / 5.1:
Phonon dispersion relations and polarization vectors / 5.2:
Linear chain with identical atoms / 5.2.1:
Linear chain with two different atoms / 5.2.2:
Experimental / 5.2.3:
Incoherent scattering phonon density of states / 5.3:
Multi-phonon processes: coherent scattering / 5.4:
Exercise / 5.5:
Liquids and Amorphous Materials / 5.7:
Static structure factor / 6.1:
Diffusion / 6.3:
Magnetic Structures / 6.4:
General cross section / 7.1:
Paramagnets / 7.2:
Ferromagnets / 7.3:
Antiferromagnets / 7.4:
Helical spin structures (magnetic spiral structures) / 7.5:
Magnetic ordering wavevector / 7.6:
Zero-field magnetization / 7.7:
Spin densities / 7.8:
Magnetic Excitations / 7.9:
Magnetic cluster excitations / 8.1:
Dimers / 8.1.1:
Trimers / 8.1.2:
Tetramers / 8.1.3:
N-mers / 8.1.4:
Spin waves / 8.2:
The random-phase approximation / 8.2.1:
Solitons / 8.3:
Solution / 8.4:
Crystal-Field Transitions / 9:
Elementary concept of crystal fields / 9.1:
Crystal-field interaction of f-election system / 9.2:
Neutron cross-section / 9.3:
Interaction of the crystal-field spilt ions / 9.4:
Intermultiplet crystal-field transitions / 9.5:
Calculation of thermodynamic magnetic properties / 9.6:
phase Transitions / 9.7:
Structural phase transitions / 10.1:
Phase transitions in ice / 10.3:
Magnetic Phase transitions / 10.4:
Quantum Phase transitions / 10.5:
Superconductivity / 10.6:
The flux-line lattice / 11.1:
Phonon density of states / 11.3:
Phonon energies and linewidths / 11.4:
Relaxation effects of crystal-field transitions / 11.5:
Spin fluctuations in high-temperature superconductors / 11.6:
Superfluidity / 11.7:
Liquid 4He / 12.1:
Phase diagram / 12.2.1:
Elementary excitations / 12.2.2:
The condensate fraction / 12.2.3:
Liquid 3He / 12.2.4:
Defects in Solids / 12.3.1:
Short-range order of point defects / 13.1:
Macro-defects / 13.3:
The triangulation method / 13.4:
Resonant and local modes / 13.5:
Surface and Interface / 13.6:
Specular reflection / 14.1:
Off-specular reflection / 14.3:
Grazing incidence scattering scattering / 14.4:
Hydrogen Dynamics / 14.5:
Dynamics of the hydrogen bond / 15.1:
Hydrogen tunneling / 15.3:
Dirac ?-function and Lattice Sims / 15.4:
Neutron Scattering Lengths and Cross Sections / Appendix B:
Paul Spin Operators / Appendix C:
Cross Section for Magnetic Neutron Scattering / Appendix D:
Crystal Lattice and reciporocal Lattice / Appendix E:
The 3-j and 6-j Symbols / Appendix F:
Impulse Approximation / Appendix G:
List of Symbols
Bibliography
Index
Preface
Introduction / 1:
Why neutron scattering? / 1.1:
9.

図書

図書
L.D. Faddeev, L.A. Takhtajan ; translated from the Russian by A.G. Reyman
出版情報: Berlin ; Tokyo : Springer-Verlag, c1987  ix, 592 p. ; 24 cm
シリーズ名: Springer series in Soviet mathematics
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10.

図書

図書
Siegfried Flügge
出版情報: Berlin ; New York : Springer-Verlag, 1971  2 v. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 177-178
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11.

図書

図書
editors, P.H. Damgaard and H. Hüffel
出版情報: Singapore : World Scientific, c1988  xii, 496 p. ; 26 cm
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12.

図書

図書
by R. Courant
出版情報: New York : Wiley, c1962  xxii, 830 p. ; 24 cm
シリーズ名: Methods of mathematical physics / by R. Courant and D. Hilbert ; v. 2
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Partial table of contents
The Algebra Of Linear Transformations And Quadratic Forms
Transformation to Principal Axes of Quadratic and Hermitian Forms
Minimum-Maximum Property of Eigenvalues
Series Expansion Of Arbitrary Functions
Orthogonal Systems of Functions
Measure of Independence and Dimension Number
Fourier Series
Legendre Polynomials
Linear Integral Equations
The Expansion Theorem and Its Applications
Neumann Series and the Reciprocal Kernel
The Fredholm Formulas
The Calculus Of Variations
Direct Solutions
The Euler Equations
Vibration And Eigenvalue Problems
Systems of a Finite Number of Degrees of Freedom
The Vibrating String
The Vibrating Membrane
Green's Function (Influence Function) and Reduction of Differential Equations to Integral Equations
Application Of The Calculus Of Variations To Eigenvalue Problems
Completeness and Expansion Theorems
Nodes of Eigenfunctions
Special Functions Defined By Eigenvalue Problems
Bessel Functions
Asymptotic Expansions
Additional Bibliography
Index
Partial table of contents
The Algebra Of Linear Transformations And Quadratic Forms
Transformation to Principal Axes of Quadratic and Hermitian Forms
13.

図書

図書
Reginald J. Stephenson
出版情報: New York : Wiley , Tokyo : Toppan, c1969  xiii, 375 p. ; 22 cm
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14.

図書

図書
Flügge, Siegfried
出版情報: Berlin : Springer-Verlag, 1955-1956  2 v. ; 26 cm
シリーズ名: Handbuch der Physik / herausgegeben von S. Flügge = Encyclopedia of physics / editor in chief, S. Flügge ; Bd. 1-2
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15.

図書

図書
Charles Nash, Siddhartha Sen
出版情報: London ; Tokyo : Academic Press, 1983  x, 311 p. ; 24 cm
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Preface
Basic Notions of Topology and the Value of Topological Reasoning
Differential Geometry
Manifolds and Differential Forms
The Fundamental Group
The Homology Groups
The Higher Homotopy Groups
Cohomology and De Rham Cohomology
Fibre Bundles and Further Differential Geometry
Morse Theory
Defects, Textures, and Homotopy Theory
Yang-Mills Theories
Instantons and Monopoles
Subject Index
Preface
Basic Notions of Topology and the Value of Topological Reasoning
Differential Geometry
16.

図書

図書
Louis A. Pipes, Lawrence R. Harvill
出版情報: New York ; Tokyo : McGraw-Hill, c1971  xxii, 1015 p. ; 23 cm
シリーズ名: International series in pure and applied mathematics
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17.

図書

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:
18.

図書

図書
edited by M. Sh. Birman ; translated from Russian by J.R. Schulenberger
出版情報: New York : Consultants Bureau, 1971  v, 121 p. ; 28 cm
シリーズ名: Topics in mathematical physics ; v. 4
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19.

図書

図書
Andrzej Trautman
出版情報: Napoli : Bibliopolis, c1984  145 p. ; 23 cm
シリーズ名: Monographs and textbooks in physical science ; 2
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20.

図書

図書
G.I. Barenblatt ; translated from Russian by Norman Stein ; translation editor, Milton van Dyke
出版情報: New York : Consultants Bureau, c1979  xvii, 218 p. ; 24 cm
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21.

図書

図書
Lui Lam, editor
出版情報: New York : Springer, c1997  xiv, 417 p. ; 25 cm
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22.

図書

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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目次情報: 続きを見る
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:
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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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24.

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図書
A.S. Fokas and I.M. Gelfand, editors
出版情報: Boston : Birkhäuser, c1997  viii, 350 p. ; 26 cm
シリーズ名: Progress in nonlinear differential equations and their applications / editor, Haim Brezis ; v. 26
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25.

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図書
Valerij V. Kozlov
出版情報: Berlin ; New York : Springer-Verlag, c1996  xi, 378 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 31
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図書
L.J. Mason and N.M.J. Woodhouse
出版情報: Oxford ; New York : Clarendon Press, 1996  x, 364 p. ; 25 cm
シリーズ名: London Mathematical Society monographs ; new ser., 15
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図書
Karl Heinz Hoffmann, Michael Schreiber (Eds.)
出版情報: Berlin : Springer, c1996  xiv, 379 p. ; 25 cm
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28.

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図書
by André Lichnerowicz
出版情報: Dordrecht ; Boston : Kluwer Academic, c1994  xii, 278 p. ; 25 cm
シリーズ名: Mathematical physics studies ; v. 14
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29.

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図書
Bryce DeWitt
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1984  xiv, 316 p. ; 24 cm
シリーズ名: Cambridge monographs on mathematical physics
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目次情報: 続きを見る
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:
30.

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図書
by Claude E. Shannon and Warren Weaver
出版情報: Urbana : University of Illinois Press, 1949  v [i.e. vii], 117 p. ; 24 cm
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目次情報:
The mathematical theory of communication / by C.E. Shannon
Recent contributions to the mathematical theory of communication / by W. Weaver
The mathematical theory of communication / by C.E. Shannon
Recent contributions to the mathematical theory of communication / by W. Weaver
31.

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図書
Robert D. Richtmyer, K.W. Morton
出版情報: New York : Interscience Publishers, c1967  xiv, 405 p. ; 24 cm
シリーズ名: Interscience tracts in pure and applied mathematics ; no. 4
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Michael Reed, Barry Simon
出版情報: New York ; Tokyo : Academic Press, c1979  xv, 463 p. ; 24 cm
シリーズ名: Methods of modern mathematical physics / Michael Reed, Barry Simon ; 3
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Walter Thirring ; translated by Evans M. Harrell
出版情報: New York : Springer-Verlag, c1986  x, 261 p. ; 25 cm
シリーズ名: A course in mathematical physics / Walter Thirring ; 2
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Parry Moon, D.E. Spencer
出版情報: Berlin : Springer-Verlag, 1971  vi, 236 p. ; 25 cm
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J.R. Acton and P.T. Squire
出版情報: Bristol ; Boston : A. Hilger, c1985  x, 219 p. ; 24 cm
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edited by R. L. Dobrushin
出版情報: Dordrecht ; Tokyo : D. Reidel Pub. Co., c1986  xiv, 261 p. ; 25 cm
シリーズ名: Mathematics and its applications ; . Soviet series
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by Yvonne Choquet-Bruhat, Cécile DeWitt-Morette, with Margaret Dillard-Bleick
出版情報: Amsterdam ; Tokyo : North-Holland, 1982-1989  2 v. ; 25 cm
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Preface
Review of fundamental notions of analysis / Chapters: I:
Differential calculus on Banach spaces / II:
Differentiable manifolds, finite dimensional case / III:
Integration on manifolds / IV:
Riemannian manifolds Kahlerian manifolds / V:
bis. Connections on a principle fibre bundle
Distributions / VI:
Differentiable manifolds, infinite dimensional case / VII:
References
Symbols
Index
Preface
Review of fundamental notions of analysis / Chapters: I:
Differential calculus on Banach spaces / II:
38.

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Sergio Albeverio ... [et al.]
出版情報: Orlando ; Tokyo : Academic Press, 1986  xi, 514 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; 122
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delivered by C.N. Yang, R. Penrose, A. Borel at the ETH Zürich ; edited by K. Chandrasekharan
出版情報: Berlin ; Tokyo : Published for the Eidgenössische Technische Hochschule Zürich [by] Springer-Verlag, c1986  119 p. ; 24 cm
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Charles F. Stevens
出版情報: Cambridge, Mass. : MIT Press, 1995  x, 233 p. ; 24 cm
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Chun Wa Wong
出版情報: New York : Oxford University Press, 1991  x, 386 p. ; 25 cm
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Vectors and Fields in Space / 1:
Transformations, Matrices and Operators / 2:
Fourier Series and Fourier Transform / 3:
Differential Equations in Physics / 4:
Special Functions / 5:
Functions of a Complex Variable / 6:
Vectors and Fields in Space / 1:
Transformations, Matrices and Operators / 2:
Fourier Series and Fourier Transform / 3:
42.

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図書
Albert S. Schwarz ; [translator, Silvio Levy]
出版情報: Berlin ; New York : Springer-Verlag, c1994  xi, 296 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 308
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Anthony Joseph
出版情報: Berlin ; Tokyo : Springer-Verlag, c1995  ix, 383 p. ; 24 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 29
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44.

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Dietrich Stauffer, H. Eugene Stanley
出版情報: Berlin ; Tokyo : Springer-Verlag, c1990  ix, 191 p., 16 p. of col. plates ; 24 cm
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by V. Kourganoff, with the collaboration of I.W. Busbridge
出版情報: Oxford : Clarendon Press, 1952  xv, 281 p ; 24 cm
シリーズ名: The international series of monographs on physics
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図書
Harold S. Mickley, Thomas K. Sherwood, Charles E. Reed
出版情報: New York : McGraw-Hill , Tokyo : Kogakusha, c1957  xii, 413 p. ; 21 cm
シリーズ名: McGraw-Hill chemical engineering series
International student edition
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G.M. Khenkin (ed.)
出版情報: Berlin ; New York : Springer-Verlag, c1993  286 p. ; 24 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 54 . Several complex variables ; 5
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図書
Harold S. Mickley, Thomas K. Sherwood, Charles E. Reed
出版情報: New York : McGraw-Hill, 1957  xii, 413 p. ; 24 cm
シリーズ名: McGraw-Hill chemical engineering series
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H.W. Wyld
出版情報: Reading, Mass. : W.A. Benjamin, Advanced Book Program, 1976  xvi, 628 p. ; 24 cm
シリーズ名: Lecture notes and supplements in physics ; 15
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Editor's Foreword
Preface
Homogeneous Boundary Value Problems and Special Functions / Part I:
the Partial Differential Equations of Mathematical Physics / Chapter 1:
Separation of Variables and Ordinary Differential Equations / Chapter 2:
Bessel Functions and Applications / Chapter 3 Spherical Harmonics and Applications:
Normal Mode Eigenvalue Problems / Chapter 5:
Summary of Part I Summary of Results from Separating Variables in Laplace's Equation and Helmholtz' Equation / Chapter 6 Spherical Bessel Functions and Applications:
Inhomogeneous Problems Green's Functions and Integral Equations / Part II:
Dielectric and Magnetic Media / Chapter 7:
Green's Functions / Chapter 8:
Complex Variables; Basic Theory / Chapter 9 Integral Equations:
Evaluation of Integrals / Chapter 11:
Dispersion Relations / Chapter 12:
Special Functions / Chapter 13:
Integral Transforms in the Complex Plane / Chapter 14:
Bibliography
Index
Editor's Foreword
Preface
Homogeneous Boundary Value Problems and Special Functions / Part I:
50.

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Louis A. Pipes
出版情報: New York : McGraw-Hill , Tokyo : Kogakusha, 1958  xi, 723 p. ; 22 cm
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