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1.

図書

図書
Ernst Hairer, Christian Lubich, Gerhard Wanner
出版情報: Berlin ; Tokyo : Springer, c2002  xiii, 515 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; v. 31
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2.

図書

図書
Alberto Abbondandolo
出版情報: Boca Raton : Chapman & Hall/CRC, c2001  xi, 189 p. ; 24 cm
シリーズ名: Research notes in mathematics ; 425
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3.

図書

図書
Kai-Seng Chou, Xi-Ping Zhu
出版情報: Boca Raton, Flo. : Chapman & Hall/CRC, c2001  ix, 255 p. ; 24 cm
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目次情報: 続きを見る
Preface
Basic Results / 1:
Short time existence / 1.1:
Facts from the parabolic theory / 1.2:
The evolution of geometric quantities / 1.3:
Invariant Solutions for the Curve Shortening Flow / 2:
Travelling waves / 2.1:
Spirals / 2.2:
The support function of a convex curve / 2.3:
Self-similar solutions / 2.4:
The Curvature-Eikonal Flow for Convex Curves / 3:
Blaschke Selection Theorem / 3.1:
Preserving convexity and shrinking to a point / 3.2:
Gage-Hamilton Theorem / 3.3:
The contracting case of the ACEF / 3.4:
The stationary case of the ACEF / 3.5:
The expanding case of the ACEF / 3.6:
The Convex Generalized Curve Shortening Flow / 4:
Results from the Brunn-Minkowski Theory / 4.1:
The AGCSF for [sigma] in (1/3, 1) / 4.2:
The affine curve shortening flow / 4.3:
Uniqueness of self-similar solutions / 4.4:
The Non-convex Curve Shortening Flow / 5:
An isoperimetric ratio / 5.1:
Limits of the rescaled flow / 5.2:
Classification of singularities / 5.3:
A Class of Non-convex Anisotropic Flows / 6:
The decrease in total absolute curvature / 6.1:
The existence of a limit curve / 6.2:
Shrinking to a point / 6.3:
A whisker lemma / 6.4:
The convexity theorem / 6.5:
Embedded Closed Geodesics on Surfaces / 7:
Basic results / 7.1:
The limit curve / 7.2:
Convergence to a geodesic / 7.3:
The Non-convex Generalized Curve Shortening Flow / 8:
The number of convex arcs / 8.1:
Removal of interior singularities / 8.3:
The almost convexity theorem / 8.5:
Bibliography
Index
Preface
Basic Results / 1:
Short time existence / 1.1:
4.

図書

図書
Gordon E. Swaters
出版情報: Boca Raton, Fla. ; London : Chapman & Hall/CRC, c2000  274 p. ; 25 cm
シリーズ名: Chapman & Hall/CRC monographs and surveys in pure and applied mathematics ; 102
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5.

図書

図書
V.E. Zakharov, editor ; [translation edited by A.B. Sossinsky]
出版情報: Providence, R.I. : American Mathematical Society, c1998  x, 197 p. ; 27 cm
シリーズ名: American Mathematical Society translations ; ser. 2, v. 182 . Advances in the mathematical sciences : (Formerly Advances in Soviet mathematics) / [editoral committee, V.I. Arnold, S.G. Gindikin, V.P. Maslov] ; 36
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Invariants of wave systems and web geometry / A. M. Balk ; E. V. Ferapontov
Stability of weak-turbulence Kolmogorov spectra / V. E. Zakharov
Energy transfer in the spectrum of surface gravity waves by resonance five wave-wave interactions / V. A. Kalmykov
Wave resonances in systems with discrete spectra / E. Kartashova
Hamiltonian formalism for Rossby waves / L. I. Piterbarg
Weakly nonlinear waves on the surface of an ideal finite depth fluid
Invariants of wave systems and web geometry / A. M. Balk ; E. V. Ferapontov
Stability of weak-turbulence Kolmogorov spectra / V. E. Zakharov
Energy transfer in the spectrum of surface gravity waves by resonance five wave-wave interactions / V. A. Kalmykov
6.

図書

図書
Victor L. Berdichevsky
出版情報: Harlow, Essex, England : Longman, 1997  x, 267 p. ; 24 cm
シリーズ名: Pitman monographs and surveys in pure and applied mathematics ; vol. 90
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7.

図書

図書
editors, M.-H. Saito, Y. Shimizu & K. Ueno
出版情報: Singapore : World Scientific, c1998  xii, 480 p. ; 23 cm
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8.

図書

図書
edited by A. Astolfi, F. Gordillo and A.J. van der Schaft
出版情報: Oxford : Published for the International Federation of Automatic Control by Elsevier, 2003  vii, 305 p ; 30 cm.
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9.

図書

図書
Benedict Leimkuhler, Sebastian Reich
出版情報: Cambridge : Cambridge University Press, 2004  xvi, 379 p. ; 24 cm.
シリーズ名: Cambridge monographs on applied and computational mathematics ; 14
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目次情報: 続きを見る
Introduction / 1:
Numerical methods / 2:
Hamiltonian mechanics / 3:
Geometric integrators / 4:
The modified equations / 5:
Higher order methods / 6:
Contained mechanical systems / 7:
Rigid Body dynamics / 8:
Adaptive geometric integrators / 9:
Highly oscillatory problems / 10:
Molecular dynamics / 11:
Hamiltonian PDEs / 12:
Introduction / 1:
Numerical methods / 2:
Hamiltonian mechanics / 3:
10.

図書

図書
L.A. Bunimovich ... [et al.] ; edited by D. Szász
出版情報: Berlin ; Tokyo : Springer-Verlag, c2000  viii, 458 p. ; 24 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 101 . Mathematical physics ; 2
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目次情報: 続きを見る
Mathematics / Part I:
A Geometric Approach to Semi-Dispersing Billiards / D. Burago ; S. Ferleger ; A. Kononenko1:
On the Sequences of Collisions Among Hard Spheres in Infinite Spacel / T. J. Murphy ; E. G. D. Cohen2:
Hard Ball Systems and Semi-Dispersive Billiards: Hyperbolicity and Ergodicity / N. Simanyi3:
Decay of Correlations for Lorentz Gases and Hard Balls / N. Chernov ; L.-S Young4:
Entropy Values and Entropy Bounds / 5:
Existence of Transport Coefficients / L. A. Bunimovich6:
Interacting Particles / C. Liverani7:
Scaling Dynamics of a Massive Piston in an Ideal Gas / J. L. Lebowitz ; J. Piasecki ; Ya G. Sinai8:
Physics / Part II:
Kinetic Theory Estimates for the Kolmogorov-Sinai Entropy, and the Largest Lyapunov Exponents for Dilute, Hard-Ball Gases and for Dilute, Random Lorentz Gases / H. van Beijeren ; R. van Zon ; J. R. Dorfman
Simulation of Billiards and of Hard-Body Fluids / H. A. Posch ; R. Hirschl
The Lorentz Gas: a Paradigm for Nonequilibrium Stationary States / C. P. Dettmann
T. Tl, J. Vollmer: Entropy Balance, Multibaker Maps, and the Dynamics of the Lorentz Gas
Boltzmanns Ergodic Hypothesis, a Conjecture for Centuries? / D. SzaszAppendix 1:
Mathematics / Part I:
A Geometric Approach to Semi-Dispersing Billiards / D. Burago ; S. Ferleger ; A. Kononenko1:
On the Sequences of Collisions Among Hard Spheres in Infinite Spacel / T. J. Murphy ; E. G. D. Cohen2:
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