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1.

図書

図書
édité par Gérard Iooss, Robert H.G. Helleman, Raymond Stora
出版情報: Amsterdam ; New York : North-Holland Pub. Co. , New York, N.Y. : Sole distributors for the USA and Canada, Elsevier Science Pub. Co., 1983  xxxi, 708 p., [1] leaf of plates ; 23 cm
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2.

図書

図書
Jerrold E. Marsden, Thomas J.R. Hughes
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, c1983  xviii, 556 p. ; 24 cm
シリーズ名: Prentice-Hall civil engineering and engineering mechanics series
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目次情報: 続きを見る
  Preface
Brief glossary of conventions and notations
A point of departure
Kinematics / 1:
Balance laws / 2:
Elastic materials / 3:
Boundary value problems / 4:
Constitutive inequalities / 5:
The role of geometry and functional analysis / 6:
Geometry and kinematics of bodies
Motions of simple bodies / 1.1:
Vector fields, one-forms, and pull-backs / 1.2:
The deformation gradient / 1.3:
Tensors, two-point tensors, and the covariant derivative / 1.4:
Conservation of mass / 1.5:
Flows and lie derivatives / 1.6:
Differential forms and the Piola transformation / 1.7:
Balance principles
The master balance law / 2.1:
The stress tensor and balance of momentum / 2.2:
Balance of energy / 2.3:
Classical spacetimes, covariant balance of energy, and the principle of virtual work / 2.4:
Thermodynamics II; the second law / 2.5:
Constitutive theory
The constitutive hypothesis / 3.1:
Consequences of thermodynamics, locality, and material frame indifference / 3.2:
Covariant constitutive theory / 3.3:
The elasticity tensor and thermoelastic solids / 3.4:
Material symmetries and isotropic elasticity / 3.5:
Linearization
The implicit function theorem / 4.1:
Linearization of nonlinear elasticity / 4.2:
Linear elasticity / 4.3:
Linearization stability / 4.4:
Hamiltonian and variational principles
The formal variational structure of elasticity / 5.1:
Linear Hamiltonian systems and classical elasticity / 5.2:
Abstract Hamiltonian and Lagrangian systems / 5.3:
Lagrangian field theory and nonlinear elasticity / 5.4:
Conservation laws / 5.5:
Reciprocity / 5.6:
Relativistic elasticity / 5.7:
Methods of functional analysis in elasticity
Elliptic operators and linear elastostatics / 6.1:
Abstract semigroup theory / 6.2:
Linear elastodynamics / 6.3:
Nonlinear elastostatics / 6.4:
Nonlinear elastodynamics / 6.5:
The energy criterion / 6.6:
A control problem for a beam equation / 6.7:
Selected topics in bifurcation theory / 7:
Basic ideas of static bifurcation theory / 7.1:
A survey of some applications to elastostatics / 7.2:
The traction problem near a natural state (Signorini's problem) / 7.3:
Basic ideas of dynamic bifurcation theory / 7.4:
A survey of some applications to elastodynamics / 7.5:
Bifurcations in the forced oscillations of a beam / 7.6:
Bibliography
Index
  Preface
Brief glossary of conventions and notations
A point of departure
3.

図書

図書
V.I. Arnold ; translated by Joseph Szücs ; English translation edited by Mark Levi
出版情報: New York ; Berlin : Springer-Verlag, c1983  x, 334 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 250
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Special Equations
First-Order Partial Differential Equations
Structural Stability
Perturbation Theory
Normal Forms
Local Bifurcation Theory
Samples of Examination Problems
Index
Special Equations
First-Order Partial Differential Equations
Structural Stability
4.

図書

図書
Jürg Fröhlich, editor
出版情報: Boston : Birkhäuser, 1983  vi, 426 p. ; 24 cm
シリーズ名: Progress in physics ; v. 7
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5.

図書

図書
Michael Artin, John Tate, editors
出版情報: Boston : Birkhäuser, 1983  359 p. ; 24 cm
シリーズ名: Progress in mathematics ; 35 . Arithmetic and geometry : papers dedicated to I.R. Shafarevich on the occasion of his sixtieth birthday / Michael Artin, John Tate, editors ; v. 1
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6.

図書

図書
Michael Artin, John Tate, editors
出版情報: Boston : Birkhäuser, 1983  481 p. ; 24 cm
シリーズ名: Progress in mathematics ; 36 . Arithmetic and geometry : papers dedicated to I.R. Shafarevich on the occasion of his sixtieth birthday / Michael Artin, John Tate, editors ; v. 2
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7.

図書

図書
C.J. Harris, J.M.E. Valença
出版情報: London ; New York : Academic Press, 1983  xi, 268 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 168
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8.

図書

図書
George Adomian
出版情報: New York : Academic Press, 1983  xvii, 331 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 169
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9.

図書

図書
Roger W. Brockett, Richard S. Millman, Hector J. Sussmann, editors
出版情報: Boston : Birkhäuser, 1983  vii, 340 p. ; 24 cm
シリーズ名: Progress in mathematics ; v. 27
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10.

図書

図書
Karl Petersen
出版情報: Cambridge [Cambridgeshire] : Cambridge University Press, 1983  xi, 329 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 2
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目次情報: 続きを見る
Preface
Introduction and preliminaries / 1:
The basic questions of ergodic theory / 1.1:
The basic examples / 1.2:
Hamiltonian dynamics / A.:
Stationary stochastic processes / B.:
Bernoulli shifts / C.:
Markov shifts / D.:
Rotations of the circle / E.:
Rotations of compact abelian groups / F.:
Automorphisms of compact groups / G.:
Gaussian systems / H.:
Geodesic flows / I.:
Horocycle flows / J.:
Flows and automorphisms on homogeneous spaces / K.:
The basic constructions / 1.3:
Factors
Products
Skew products
Flow under a function
Induced transformations
Inverse limits
Natural extensions
Some useful facts from measure theory and functional analysis / 1.4:
Change of variables
Proofs by approximation
Measure algebras and Lebesgue spaces
Conditional expectation
The Spectral Theorem
Topological groups, Haar measure, and character groups
The fundamentals of ergodic theory / 2:
The Mean Ergodic Theorem / 2.1:
The Pointwise Ergodic Theorem / 2.2:
Recurrence / 2.3:
Ergodicity / 2.4:
Strong mixing / 2.5:
Weak mixing / 2.6:
More about almost everywhere convergence / 3:
More about the Maximal Ergodic Theorem / 3.1:
Positive contractions
The maximal equality
Sign changes of the partial sums
The Dominated Ergodic Theorem and its converse
More about the Pointwise Ergodic Theorem / 3.2:
Maximal inequalities and convergence theorems
The speed of convergence in the Ergodic Theorem
Differentiation of integrals and the Local Ergodic Theorem / 3.3:
The Martingale convergence theorems / 3.4:
The maximal inequality for the Hilbert transform / 3.5:
The ergodic Hilbert transform / 3.6:
The filling scheme / 3.7:
The Chacon-Ornstein Theorem / 3.8:
More about recurrence / 4:
Construction of eigenfunctions / 4.1:
Existence of rigid factors
Almost periodicity
Construction of the eigenfunction
Some topological dynamics / 4.2:
Topological ergodicity and mixing
Equicontinuous and distal cascades
Uniform distribution mod 1
Structure of distal cascades
The Szemeredi Theorem / 4.3:
Furstenberg's approach to the Szemeredi and van der Waerden Theorems
Topological multiple recurrence, van der Waerden's Theorem, and Hindman's Theorem
Weak mixing implies weak mixing of all orders along multiples
Outline of the proof of the Furstenberg-Katznelson Theorem
The topological representation of ergodic transformations / 4.4:
Preliminaries
Recurrence along IP-sets
Perturbation to uniformity
Uniform polynomials
Conclusion of the argument
Two examples / 4.5:
Metric weak mixing without topological strong mixing
A prime transformation
Entropy / 5:
Entropy in physics, information theory, and ergodic theory / 5.1:
Physics
Information theory
Ergodic theory
Information and conditioning / 5.2:
Generators and the Kolmogorov-Sinai Theorem / 5.3:
More about entropy / 6:
More examples of the computation of entropy / 6.1:
Entropy of an automorphism of the torus
Entropy of a skew product
Entropy of an induced transformation
The Shannon-McMillan-Breiman Theorem / 6.2:
Topological entropy / 6.3:
Introduction to Ornstein Theory / 6.4:
Finitary coding between Bernoulli shifts / 6.5:
Sketch of the proof
Reduction to the case of a common weight
Framing the code
What to put in the s
Sociology
Construction of the isomorphism
References
Index
Preface
Introduction and preliminaries / 1:
The basic questions of ergodic theory / 1.1:
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