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1. An Introduction to Tensors and Group Theory for Physicists. 1
by Nadir Jeevanjee
出版情報: Boston : Springer Science+Business Media, LLC, 2011
オンライン: http://dx.doi.org/10.1007/978-0-8176-4715-5
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2. Self-adjoint Extensions in Quantum Mechanics : General Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials
by D.M. Gitman, I.V. Tyutin, B.L. Voronov
出版情報: Boston : Birkhäuser Boston, 2012
シリーズ名: Progress in Mathematical Physics ; 62
オンライン: http://dx.doi.org/10.1007/978-0-8176-4662-2
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3. A Concise Introduction to Linear Algebra
by Géza Schay
出版情報: Boston : Birkhäuser Boston, 2012
オンライン: http://dx.doi.org/10.1007/978-0-8176-8325-2
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4. A New Approach to Differential Geometry using Clifford's Geometric Algebra
by John Snygg
出版情報: Boston : Springer Science+Business Media, LLC, 2012
オンライン: http://dx.doi.org/10.1007/978-0-8176-8283-5
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5. Classical Mechanics with Mathematica®
by Romano Antonio
出版情報: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2012
シリーズ名: Modeling and Simulation in Science, Engineering and Technology ;
オンライン: http://dx.doi.org/10.1007/978-0-8176-8352-8
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目次情報:
I Introduction to Linear Algebra and Differential Geometry.- 1 Vector Space and Linear Maps.- 2 Tensor Algebra.- 3 Skew-symmetric Tensors and Exterior Algebra.- 4 Euclidean and Symplectic Vector Spaces.- 5 Duality and Euclidean Tensors.- 6 Differentiable Manifolds.- 7 One-Parameter Groups of Diffeomorphisms.- 8 Exterior Derivative and Integration.- 9 Absolute Differential Calculus
10 An Overview of Dynamical Systems.- II Mechanics.- 11 Kinematics of a Point Particle.- 12 Kinematics of Rigid Bodies.- 13 Principles of Dynamics.- 14 Dynamics of a Material Point.- 15 General Principles of Rigid Body Dynamics.- 16 Dynamics of a Rigid Body.- 17 Lagrangian Dynamics.- 18 Hamiltonian Dynamics.- 19 Hamilton-Jacobi Theory.- 20 Completely Integrable Systems.- 21 Elements of Statistical Mechanics of Equilibrium.- 22 Impulsive Dynamics.- 23 Introduction to Fluid Mechanics
A First-Order PDE.- B Fourier’s Series.- References.- Index
I Introduction to Linear Algebra and Differential Geometry.- 1 Vector Space and Linear Maps.- 2 Tensor Algebra.- 3 Skew-symmetric Tensors and Exterior Algebra.- 4 Euclidean and Symplectic Vector Spaces.- 5 Duality and Euclidean Tensors.- 6 Differentiable Manifolds.- 7 One-Parameter Groups of Diffeomorphisms.- 8 Exterior Derivative and Integration.- 9 Absolute Differential Calculus
10 An Overview of Dynamical Systems.- II Mechanics.- 11 Kinematics of a Point Particle.- 12 Kinematics of Rigid Bodies.- 13 Principles of Dynamics.- 14 Dynamics of a Material Point.- 15 General Principles of Rigid Body Dynamics.- 16 Dynamics of a Rigid Body.- 17 Lagrangian Dynamics.- 18 Hamiltonian Dynamics.- 19 Hamilton-Jacobi Theory.- 20 Completely Integrable Systems.- 21 Elements of Statistical Mechanics of Equilibrium.- 22 Impulsive Dynamics.- 23 Introduction to Fluid Mechanics
A First-Order PDE.- B Fourier’s Series.- References.- Index
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6. Unbounded Self-adjoint Operators on Hilbert Space
by Konrad Schmüdgen
出版情報: Dordrecht : Springer Netherlands : Imprint: Springer, 2012
シリーズ名: Graduate Texts in Mathematics ; 265
オンライン: http://dx.doi.org/10.1007/978-94-007-4753-1
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目次情報: 続きを見る
I Basics onClosed Operators
1 Closed Operators and Adjoint Operators
2 Spectrum of Closed Operators
3 Some Classes of Unbounded Operators
II Spectral Theory
4 Spectral Measures and Spectral Integrals
5 Spectral Decomposition of Selfadjoint and Normal Operators
III Special Topics
6 One-Parameter Groups and Semigroups of Operators
7 Miscellaneous
IV Petirbations of Selfadjointness and of Spectra of Selfadjoint Operators
8 Perturbations of Selfadjoint Operators
9 Trace Class Perturbations of Spectra of Selfadjoint Operators
V Forms and Operators
10 Semibounded Forms and Selfadjoint Operators
11 Sectorial Forms and m-Sectorial Operators
12 Discrete Spectrum of Selfadjoint Operators
VI Selfadjoint Extention Theory of Symmetric Operators
13 Selfajoint Extensions: Cayley Transform and Krein Transform
14 Selfadjoint Extensions: Boundary Triplets
15 Sturm-Liouville Operators
One-Dimensional Moment Problem
I Basics onClosed Operators
1 Closed Operators and Adjoint Operators
2 Spectrum of Closed Operators
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7. Geography of Order and Chaos in Mechanics : Investigations of Quasi-Integrable Systems with Analytical, Numerical, and Graphical Tools
by Bruno Cordani
出版情報: New York, NY : Springer New York : Imprint: Birkhäuser, 2013
シリーズ名: Progress in Mathematical Physics ; 64
オンライン: http://dx.doi.org/10.1007/978-0-8176-8370-2
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目次情報: 続きを見る
Preface
List of Figures
1 Introductory Survey
2 Analytical Mechanics and Integrable Systems
3 Perturbation Theory
4 Numerical Tools I: ODE Integration
5 Numerical Tools II: Detecting Order, Chaos, and Resonances
6 The Kepler Problem
7 The KEPLER Program
8 Some Perturbed Keplerian Systems
9 The Multi-Body Gravitational Problem
Bibliography
Index
Preface
List of Figures
1 Introductory Survey
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8. Symmetries, Integrable Systems and Representations
edited by Kenji Iohara, Sophie Morier-Genoud, Bertrand Rémy
出版情報: London : Springer London : Imprint: Springer, 2013
シリーズ名: Springer Proceedings in Mathematics & Statistics ; 40
オンライン: http://dx.doi.org/10.1007/978-1-4471-4863-0
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目次情報: 続きを見る
A presentation of the deformed W1+1 algebra
Generating series of the Poincaré polynomials of quasihomogeneous Hilbert schemes
PBW filtration over Z and compatible bases for VZ(_) in type An and Cn
On the subgeneric restricted blocks of affine category O at the critical level
Slavnov determinants, Yang-Mills structure constants, and discrete KP
Monodromy of partial KZ functors for rational Cherednik algebras
Category of finite dimensional modules over an orthosymplectic Lie superalgebra: small rank examples
Monoidal categorifications of cluster algebras of type A and D
A classification of roots of symmetric Kac-Moody root systems and its application
Fermions acting on quasi-local operators in the XXZ model
The Romance of the Ising Model
A(1) n -Geometric Crystal corresponding to Dynkin index i = 2 and its ultra-discretization
A Z3-orbifold theory of lattice vertex operator algebra and Z3-orbifold constructions
Words, automata and Lie theory for tilings
Toward Berenstein-Zelevinsky data in affine type A, part III: Proof of the connectedness
Quiver varieties and tensor products, II
Derivatives of Schur, Tau and Sigma Functions on Abel-Jacobi Images
Padé interpolation for elliptic Painlevé equation
Non-commutative harmonic oscillators
The inversion formula of polylogarithms and the Riemann-Hilbert problem
Some remarks on the Quantum Hall Effect
Ordinary differential equations on rational elliptic surfaces
On the spectral gap of the Kac walk and other binary collision processes on d-dimensional lattice
A restricted sum formula for a q-analogue of multiple zeta values
A trinity of the Borcherds _-function
Sum rule for the eight-vertex model on its combinatorial line
A presentation of the deformed W1+1 algebra
Generating series of the Poincaré polynomials of quasihomogeneous Hilbert schemes
PBW filtration over Z and compatible bases for VZ(_) in type An and Cn
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9. The Sherrington-Kirkpatrick Model
by Dmitry Panchenko
出版情報: New York, NY : Springer New York : Imprint: Springer, 2013
シリーズ名: Springer Monographs in Mathematics ;
オンライン: http://dx.doi.org/10.1007/978-1-4614-6289-7
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目次情報: 続きを見る
Preface
1 The Free Energy and Gibbs Measure
2 The Ruelle Probability Cascades
3 The Parisi Formula
4 Toward a Generalized Parisi Ansatz
A Appendix
Bibliography
Notes and Comments
References
Index
Preface
1 The Free Energy and Gibbs Measure
2 The Ruelle Probability Cascades
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10. From Kinetic Models to Hydrodynamics : Some Novel Results
by Matteo Colangeli
出版情報: New York, NY : Springer New York : Imprint: Springer, 2013
シリーズ名: SpringerBriefs in Mathematics ;
オンライン: http://dx.doi.org/10.1007/978-1-4614-6306-1
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目次情報: 続きを見る
1. Introduction
2. From the Phase Space to the Boltzmann Equation
3. Methods of Reduced Description
4. Hydrodynamic Spectrum of Simple Fluids
5. Hydrodynamic Fluctuations from the Boltzmann Equation
6. 13 Moment Grad System
7. Conclusions
References.
1. Introduction
2. From the Phase Space to the Boltzmann Equation
3. Methods of Reduced Description