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1.

図書
図書
1. Fractals, graphics, and mathematics education
Michael Frame and Benoit B. Mandelbrot, editors ; foreword by Lynn Arthur Steen
出版情報: [Washington, D.C.] : Mathematical Association of America, c2002  xiii, 206 p., [4] p. of plates ; 28 cm
シリーズ名: MAA notes ; 58
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Foreword / Lynn Arthur Steen
Preface
Introductory Essays
Some Reasons for the Effectiveness of Fractals in Mathematics Education / Benoit B. Mandelbrot ; Michael Frame1.：
Unsolved Problems and Still-Emerging Concepts in Fractal Geometry / 2.：
Fractals, Graphics, and Mathematics Education / 3.：
Mathematics and Society in the 20th Century / 4.：
Classroom Experiences
Teaching Fractals and Dynamical Systems at The Hotchkiss School / Melkana Brakalova ; David Coughlin5.：
Reflecting on Wada Basins: Some Fractals with a Twist / Dane Camp6.：
Learning and Teaching about Fractals / Donald M. Davis7.：
The Fractal Geometry of the Mandelbrot Set: Periods of the Bulbs / Robert L. Devaney8.：
Fractals--Energizing the Mathematics Classroom / Vicki Fegers ; Mary Beth Johnson9.：
Other Chaos Games / Sandy Fillebrown10.：
Creating and Teaching Undergraduate Courses and Seminars in Fractal Geometry: a Personal Experience / Michel Lapidus11.：
Exploring Fractal Dimensions by Experiment / Ron Lewis12.：
Fractal Themes at Every Level / Kenneth G. Monks13.：
Art and Fractals: Artistic Explorations of Natural Self-Similarity / Brianna Murratti14.：
Order and Chaos, Art and Magic: a First College Course in Quantitative Reasoning Based on Fractals and Chaos / David Peak15.：
A Software Driven Undergraduate Fractals Course / Douglas C. Ravenel16.：
A Final Word
The Fractal Ring from Art to Art through Mathematics, Finance, and the Sciences / 17.：
Appendices
Panorama of Fractals and Their Uses. An Alphabetic Wordbook-Index / 18.：
Reports of Some Field Experiences / 19.：
Guide to Topics
References
About the Editors and Other Contributors
Index
Foreword / Lynn Arthur Steen
Preface
Introductory Essays
2.

図書
図書
2. Finite elements : theory, fast solvers, and applications in solid mechanics. 2nd ed (pbk.)
Dietrich Braess ; translated by Larry L. Schumaker
出版情報: Cambridge : Cambridge University Press, 2001  xvii, 352 p. ; 23 cm
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Preface to the Third English Edition page
Preface to the First English Edition
Preface to the German Edition
Notation
Introduction / Chapter I：
Examples and Classification of PDE's / 1：
Examples
Classification of PDE's
Well-posed Problems
Problems
The Maximum Principle / 2：
Corollaries
Problem
Finite Difference Methods / 3：
Discretization
Discrete maximum principle
A Convergence Theory for Difference Methods / 4：
Consistency
Local and global error
Limits of the convergence theory
Conforming Finite Elements / Chapter II：
Sobolev Spaces
Introduction to Sobolev spaces
Friedrichs' inequality
Possible singularities of H1 functions
Compact imbeddings
Variational Formulation of Elliptic Boundary-Value Problems of Second Order
Variational formulation
Reduction to homogeneous boundary conditions
Existence of solutions
Inhomogeneous boundary conditions
The Neumann Boundary-Value Problem. A Trace Theorem
Ellipticity in H1
Boundary-value problems with natural boundary conditions
Neumann boundary conditions
Mixed boundary conditions
Proof of the trace theorem
Practical consequences of the trace theorem
The Ritz-Galerkin Method and Some Finite Elements
Model Problem
Some Standard Finite Elements / 5：
Requirements on the meshes
Significance of the differentiability properties
Triangular elements with complete polynomials
Remarks on C1 elements
Bilinear elements
Quadratic rectangular elements
Affine families
Choice of an element
Approximation Properties / 6：
The Bramble-Hilbert lemma
Bilinear quadrilateral elements
Inverse estimates
Clément's interpolation
Appendix: On the optimality of the estimates
Error Bounds for Elliptic Problems of Second Order / 7：
Remarks on regularity
Error bounds in the energy norm
L2 estimates
A simple L? estimate
The L2-projector
Computational Considerations / 8：
Assembling the stiffness matrix
Static condensation
Complexity of setting up the matrix
Effect on the choice of a grid
Local mesh refinement
Implementation of the Neumann boundary-value Problem
Nonconforming and Other Methods / Chapter III：
Abstract Lemmas and a Simple Boundary Approximation
Generalizations of Céa's lemma
Duality methods
The Crouzeix-Raviart element
A Simple approximation to curved boundaries
Modifications of the duality argument
Isoparametric Elements
Isoparametric triangular elements
Isoparametric quadrilateral elements
Further Tools from Functional Analysis
Negative norms
Adjoint operators
An abstract existence theorem
An abstract convergence theorem
Proof of Theorem 3.4
Saddle Point Problems
Saddle points and minima
The inf-sup condition
Mixed finite element methods
Fortin interpolation
Saddle point problems with penalty term
Typical applications
Mixed Methods for the Poisson Equation
The Poisson equation as a mixed problem
The Raviart - Thomas element
Interpolation by Raviart-Thomas elements
Implementation and postprocessing
Mesh-dependent norms for the Raviart-Thomas element
The Softening behaviour of mixed methods
The Stokes Equation
Nearly incompressible flows
Finite Elements for the Stokes Problems
An instable element
The Taylor-Hood element
The MINI element
The divergence-free nonconforming P1 element
A Posteriori Error Estimates
Residual estimators
Lower estimates
Remark on other estimators
Local mesh refinement and convergence
A Posteriori Error Estimates via the Hypercircle Method / 9：
The Conjugate Gradient Method / Chapter IV：
Classical Iterative Methods for Solving Linear Systems
Stationary linear processes
The Jacobi and Gauss-Seidel methods
The model problem
Overrelaxation
Gradient Methods
The general gradient method
Gradient methods and quadratic functions
Convergence behavior in the case of large condition numbers
Conjugate Gradient and the Minimal Residual Method
The CG algorithm
Analysis of the CG method as an optimal method
The minimal residual method
Indefinite and unsymmetric matrices
Preconditioning
Preconditioning by SSOR
Preconditioning by ILU
Remarks on parallelization
Nonlinear Problems
The Uzawa algorithm and its variants
An alternative
Multigrid Methods / Chapter V：
Multigrid Methods for Variational Problems
Smoothing properties of classical iterative methods
The multigrid idea
The algorithm
Transfer between grids
Convergence of Multigrid Methods
Discrete norms
Connection with the Sobolev norm
Approximation property
Convergence proof for the two-grid method
An alternative short proof
Some variants
Convergence for Several Levels
A recurrence formula for the W-cycle
An improvement for the energy norm
The convergence proof for the V-cycle
Nested Iteration
Computation of starting values
Complexity
Multigrid methods with a small number of levels
The CASCADE algorithm
Multigrid Analysis via Space Decomposition
Schwarz alternating method
Assumptions
Direct consequences
Convergence of multiplicative methods
Verification of A1
Local mesh refinements
The multigrid-Newton method
The nonlinear multigrid method
Starting values
Finite Elements in Solid Mechanics / Chapter VI：
Introduction to Elasticity Theory
Kinematics
The equilibrium equations
The Piola transform
Constitutive Equations
Linear material laws
Hyperelastic Materials
Linear Elasticity Theory
The variational problem
The displacement formulation
The mixed method of Hellinger and Reissner
The mixed method of Hu and Washizu
Nearly incompressible material
Locking
Locking of the Timoshenko beam and typical remedies
Membranes
Plane stress states
Plane strain states
Membrane elements
The PEERS element
Beams and Plates: The Kirchhoff Plate
The hypotheses
Note on beam models
Mixed methods for the Kirchoff plate
DKT elements
The Mindlin-Reissner Plate
The Helmholtz decomposition
The mixed formulation with the Helmholtz decomposition
MITC elements
The Model without a Helmboltz decomposition
References
Index
Preface to the Third English Edition page
Preface to the First English Edition
Preface to the German Edition
3.

図書
図書
3. An introduction to maximum principles and symmetry in elliptic problems
L.E. Fraenkel
出版情報: Cambridge ; New York : Cambridge University Press, 2000  x, 340 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 128
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Preface
Some notation, terminology and basic calculus / 0：
Introduction / 1：
Some maximum principles for elliptic equations / 2：
Symmetry for a non-linear Poisson equation / 3：
Symmetry for the non-linear Poisson equation in RN / 4：
Monotonicity of positive solutions in a bounded set W / 5：
On the Newtonian potential / Appendix A：
Rudimentary facts about harmonic functions and the Poisson equation / Appendix B：
Construction of the primary function of Siegel type / Appendix C：
On the divergence theorem and related matters / Appendix D：
The edge-point lemma / Appendix E：
Notes on sources
References
Index
Preface
Some notation, terminology and basic calculus / 0：
Introduction / 1：
4.

図書
図書
4. Random walks on infinite graphs and groups (: hbk)
Wolfgang Woess
出版情報: Cambridge ; New York : Cambridge University Press, 2000  xi, 334 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 138
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5.

図書
図書
5. The geometry of spacetime : an introduction to special and general relativity
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
6.

図書
図書
6. Inside calculus
George R. Exner
出版情報: New York : Springer, c2000  xvii, 211 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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Limits
Continuity
The Language of Theorems
Theorems about Continuous Functions
Limit Proofs
Limit Theorems
Which Functions are Continuous?
Derivatives
Theorems about the Derivative
Other Limits
Limits
Continuity
The Language of Theorems
7.

図書
図書
7. Diophantine approximation on linear algebraic groups : transcendence properties of the exponential function in several variables
Michel Waldschmidt
出版情報: Berlin : Springer, c2000  xxiii, 633 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 326
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Introduction and Historical Survey / 1：
Linear Independence of Logarithms of Algebraic Numbers / Part I：
Transcendence Proofs in One Variable / 2：
Heights of Algebraic Numbers / 3：
The Criterion of Schneider-Lang / 4：
Zero Estimate / 5：
Measures of Linear Independence / 6：
A First Measure with a Simple Proof / 7：
Zero Estimate (Continued), by Damien ROY / 8：
Refined Measure / 9：
Multiplicities in Higher Dimension / III：
Multiplicity Estimates, by Damien ROY / 10：
Interpolation Determinants with One Derivative / 11：
On Baker's Method / 12：
The Linear Subgroup Theorem / Part IV：
Points Whose Coordinates are Logarithms of Algebraic Numbers / 13：
Lower Bounds for the Rank of Matrices / 14：
Simultaneous Approximation of Values of the Exponential Function in Several Variables / Part V：
A Quantitative Version of the Linear Subgroup Theorem / 15：
Applications to Diophantine Approximation / 16：
Algebraic Independence / 17：
References
Introduction and Historical Survey / 1：
Linear Independence of Logarithms of Algebraic Numbers / Part I：
Transcendence Proofs in One Variable / 2：
8.

図書
図書
8. Geometry of curves ([pbk.])
John W. Rutter
出版情報: Boca Raton ; London : Chapman & Hall/CRC, c2000  xvii, 361 p. ; 24 cm
シリーズ名: Chapman and Hall mathematics series
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Introduction
Cartesian coordinates / 0.1：
Polar coordinates / 0.2：
The Argand diagram / 0.3：
Polar equations / 0.4：
Angles / 0.5：
Orthogonal and parallel vectors / 0.6：
Trigonometry / 0.7：
Lines, circles, and conics / 1：
Lines / 1.1：
The circle / 1.2：
Conics / 1.3：
The ellipse in canonical position / 1.4：
The hyperbola in canonical position / 1.5：
The parabola in canonical position / 1.6：
Classical geometric constructions of conics / 1.7：
Polar equation of a conic with a focus as pole / 1.8：
History and applications of conics / 1.9：
Conics: general position / 2：
Geometrical method for diagonalisation / 2.1：
Algebra / 2.2：
Algebraic method for diagonalisation / 2.3：
Translating to canonical form / 2.4：
Central conics referred to their centre / 2.5：
Practical procedures for dealing with the general conic / 2.6：
Rational parametrisations of conics / 2.7：
Some higher curves / 3：
The semicubical parabola: a cuspidal cubic / 3.1：
A crunodal cubic / 3.2：
An acnodal cubic / 3.3：
A cubic with two parts / 3.4：
History and applications of algebraic curves / 3.5：
A tachnodal quartic curve / 3.6：
Limacons / 3.7：
Equi-angular (logarithmic) spiral / 3.8：
Archimedean spiral / 3.9：
Application - Watt's curves / 3.10：
Parameters, tangents, normal / 4：
Parametric curves / 4.1：
Tangents and normals at regular points / 4.2：
Non-singular points of algebraic curves / 4.3：
Parametrisation of algebraic curves / 4.4：
Tangents and normals at non-singular points / 4.5：
Arc-length parametrisation / 4.6：
Some results in analysis / 4.7：
Contact, inflexions, undulations / 5：
Contact / 5.1：
Invariance of point-contact order / 5.2：
Inflexions and undulations / 5.3：
Geometrical interpretation of n-point contact / 5.4：
An analytical interpretation of contact / 5.5：
Cusps, non-regular points / 6：
Cusps / 6.1：
Tangents at cusps / 6.2：
Contact between a line and a curve at a cusp / 6.3：
Higher singularities / 6.4：
Curvature / 7：
Curves given by polar equation / 7.1：
Curves in the Argand diagram / 7.3：
An alternative formula / 7.4：
Curvature: applications / 8：
Inflexions of parametric curves at regular points / 8.1：
Vertices and undulations at regular points / 8.2：
Curvature of algebraic curves / 8.3：
Limiting curvature of algebraic curves at cusps / 8.4：
Circle of curvature / 9：
Centre of curvature and circle of curvature / 9.1：
Contact between curves and circles / 9.2：
The equation / 10：
Non-regular points / 10.2：
Inflexions / 10.4：
Vertices / 10.5：
Undulations / 10.6：
The five classes of limacons / 10.7：
An alternative equation / 10.8：
Evolutes / 11：
Definition and special points / 11.1：
A matrix method for calculating evolutes / 11.2：
Evolutes of the cycloid and the cardioid / 11.3：
Parallels, involutes / 12：
Parallels of a curve / 12.1：
Involutes / 12.2：
Roulettes / 13：
General roulettes / 13.1：
Parametrisation of circles / 13.2：
Cycloids: rolling a circle on a line / 13.3：
Trochoids: rolling a circle on or in a circle / 13.4：
Rigid motions / 13.5：
Non-regular points and inflexions of roulettes / 13.6：
Envelopes / 14：
Evolutes as a model / 14.1：
Singular-set envelopes / 14.2：
Discriminant envelopes / 14.3：
Different definitions and singularities of envelopes / 14.4：
Limiting-position envelopes / 14.5：
Orthotomics and caustics / 14.6：
The relation between orthotomics and caustics / 14.7：
Orthotomics of a circle / 14.8：
Caustics of a circle / 14.9：
Singular points of algebraic curves / 15：
Intersection multiplicity with a given line / 15.1：
Homogeneous polynomials / 15.2：
Multiplicity of a point / 15.3：
Singular lines at the origin / 15.4：
Isolated singular points / 15.5：
Tangents and branches at non-isolated singular points / 15.6：
Branches for non-repeated linear factors / 15.7：
Branches for repeated linear factors / 15.8：
Cubic curves / 15.9：
Curvature at singular points / 15.10：
Projective curves / 16：
The projective line / 16.1：
The projective plane / 16.2：
The projective curve determined by a plane curve / 16.3：
Affine views of a projective curve / 16.5：
Plane curves as views of a projective curve / 16.6：
Tangent lines to projective curves / 16.7：
Boundedness of the associated affine curve / 16.8：
Summary of the analytic viewpoint / 16.9：
Asymptotes / 16.10：
Singular points and inflexions of projective curves / 16.11：
Equivalence of curves / 16.12：
Examples of asymptotic behaviour / 16.13：
Worked example / 16.14：
Practical work / 17：
Drawn curves / 18：
Personalising MATLAB for metric printing / 18.1：
Ellipse 1 and Ellipse 2 / 18.2：
Ellipse 3 / 18.3：
Parabola 1 / 18.4：
Parabola 2 / 18.5：
Parabola 3 / 18.6：
Hyperbola / 18.7：
Semicubical parabola / 18.8：
Polar graph paper / 18.9：
Further reading / 19：
Index
Introduction
Cartesian coordinates / 0.1：
Polar coordinates / 0.2：
9.

図書
図書
9. Numerical bifurcation analysis for reaction-diffusion equations
Zhen Mei
出版情報: Berlin : Springer, c2000  xiv, 414 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; 28
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Reaction-Diffusion Equations / 1：
Introduction / 1.1：
Bifurcations and Pattern Formations / 1.2：
Boundary Conditions / 1.3：
Continuation Methods / 2：
Parameterization of Solution Curves / 2.1：
Natural parameterization / 2.1.1：
Parameterization with arclength / 2.1.2：
Parameterization with pseudo-arclength / 2.1.3：
Local Parameterization of Solution Manifolds / 2.2：
Predictor-Corrector Methods / 2.3：
Euler-Newton method / 2.3.1：
A continuation-Lanczos algorithm / 2.3.2：
A continuation-Arnoldi algorithm / 2.3.3：
Computation of Multi-Dimensional Solution Manifolds / 2.4：
Detecting and Computing Bifurcation Points / 3：
Generic Bifurcation Points / 3.1：
One-parameter problems / 3.1.1：
Two-parameter problems / 3.1.2：
Test Functions / 3.2：
Test functions for turning points / 3.2.1：
Test functions for simple bifurcation point / 3.2.2：
Test functions for Hopf bifurcations / 3.2.3：
Minimally extended systems / 3.2.4：
Computing Simple Bifurcation Points / 3.3：
Simple bifurcation points / 3.3.1：
Extended systems / 3.3.2：
Newton-like methods / 3.3.3：
Rank-1 corrections for sparse problems / 3.3.4：
A numerical example / 3.3.5：
Computing Hopf Bifurcation Points / 3.4：
Hopf points / 3.4.1：
Newton method for extended systems / 3.4.2：
Branch Switching at Simple Bifurcation Points / 4：
Structure of Bifurcating Solution Branches / 4.1：
Behavior of the Linearized Operator / 4.2：
Euler-Newton Continuation / 4.3：
Branch Switching via Regularized Systems / 4.4：
Other Branch Switching Techniques / 4.5：
Bifurcation Problems with Symmetry / 5：
Basic Group Concepts / 5.1：
Equivariant Bifurcation Problems / 5.2：
Equivariant Branching Lemma / 5.3：
A Semi-linear Elliptic PDE on the Unite Square / 5.4：
Liapunov-Schmidt Method / 6：
Liapunov-Schmidt Reduction / 6.1：
Equivariance of the Reduced Bifurcation Equations / 6.2：
Derivatives and Taylor Expansion / 6.3：
Equivalence, Determinacy and Stability / 6.4：
Simple Bifurcation Points / 6.5：
Truncated Liapunov-Schmidt Method / 6.6：
Branch Switching at Multiple Bifurcation Points / 6.7：
Branch switching with prescribed tangents / 6.7.1：
Branch switching with scaling techniques / 6.7.2：
Corank-2 Problems with Dm-symmetry / 6.8：
Semilinear elliptic PDEs on a square / 6.8.1：
A semilinear elliptic PDE on a hexagon / 6.8.2：
Center Manifold Theory / 7：
Center Manifolds and Their Properties / 7.1：
Approximation of Center Manifolds / 7.2：
Symmetry and Normal Form / 7.3：
Hopf bifurcations / 7.4.1：
Waves in Reaction-Diffusion Equations / 7.5：
Oscillating waves / 7.5.1：
Long waves / 7.5.2：
Long time and large spatial behavior / 7.5.3：
A Bifurcation Function for Homoclinic Orbits / 8：
A Bifurcation Function / 8.1：
Approximation of Homoclinic Orbits / 8.2：
Solving the Adjoint Variational Problem / 8.3：
Preserving the inner product / 8.3.1：
Systems with continuous symmetries / 8.3.2：
The Approximate Bifurcation Function / 8.4：
Examples / 8.5：
Freire et al.'s circuit / 8.5.1：
Kuramoto-Sivashinsky equation / 8.5.2：
One-Dimensional Reaction-Diffusion Equations / 9：
Linear Stability Analysis / 9.1：
The general system / 9.2.1：
The Brusselator equations / 9.2.2：
Solution Branches at Double Bifurcations / 9.3：
The reflection symmetry and its induced action / 9.3.1：
(k,m) = (odd, odd) or (odd, even) / 9.3.2：
(k,m) = (even, even) / 9.3.3：
Central Difference Approximations / 9.3.4：
General systems / 9.4.1：
Numerical Results for the Brusselator Equations / 9.4.2：
The length <$>\ell = 1<$>, diffusion rates d1 = 1, d2 = 2 / 9.5.1：
The length <$>\ell = 10<$>, diffusion rates d1 = 1, d2 = 2 / 9.5.2：
Reaction-Diffusion Equations on a Square / 10：
D4-Symmetry / 10.1：
Eigenpairs of the Laplacian / 10.2：
Bifurcation Points / 10.3：
Steady state bifurcation points / 10.4.1：
Hopf bifurcation points / 10.4.2：
Mode Interactions / 10.5：
Steady/steady state mode interactions / 10.5.1：
Hopf/steady state mode interactions / 10.5.2：
Hopf/Hopf mode interactions / 10.5.3：
Kernels of Du G0 and <$>(D_u G_0)^{\ast}<$> / 10.6：
Simple and Double Bifurcations / 10.7：
Simple bifurcations / 10.8.1：
Double bifurcations induced by the D4 symmetries / 10.8.2：
Normal Forms for Hopf Bifurcations / 11：
Domain Symmetries and Their Extensions / 11.1：
Actions of D4 on the Center Eigenspace / 11.3：
The Normal Form / 11.4：
Analysis of the Normal Form / 11.5：
Odd parity / 11.5.1：
Even parity / 11.5.2：
Brusselator Equations / 11.6：
Linear stability analysis / 11.6.1：
Bifurcation scenario / 11.6.2：
Nonlinear degeneracy / 11.6.3：
Steady/Steady State Mode Interactions / 12：
Induced Actions / 12.1：
Interaction of Two D4-Modes / 12.2：
Interaction of two even modes / 12.2.1：
Interaction of an even mode with an odd mode / 12.2.2：
Interaction of two odd modes / 12.2.3：
Mode Interactions of Three Modes / 12.3：
Induced actions / 12.3.1：
Interactions of the modes (m,n,k) =(even, odd, odd) / 12.3.2：
Interactions of the modes (m,n,k) =(even, odd, even) / 12.3.3：
Interactions of Four Modes / 12.4：
Interactions of the modes (m, n, k, l) = (even, odd, even, odd) / 12.4.1：
Interactions of the modes (m, n, k, l) = (even, even, even, odd) / 12.4.2：
Reactions with Z2-Symmetry / 12.5：
Hopf/Steady State Mode Interactions / 13：
Normal Forms / 13.1：
Bifurcation Scenario / 13.4：
Calculations of the Normal Form / 13.5：
Homotopy of Boundary Conditions / 14：
Homotopy of boundary conditions / 14.1：
Boundary conditions for different components / 14.1.2：
Mixed boundary conditions along the sides / 14.1.3：
Dynamical boundary conditions / 14.1.4：
A Brief Review of Sturm-Liouville Theory / 14.2：
Laplacian with Robin Boundary Conditions / 14.3：
Variational Form / 14.4：
Continuity of Solutions along the Homotopy / 14.5：
Neumann and Dirichlet Problems / 14.6：
Properties of Eigenvalues / 14.7：
One-dimensional problems / 14.7.1：
Two-dimensional problems / 14.7.2：
Bifurcations along a Homotopy of BCs / 15：
Stability and Symmetries / 15.1：
Variations of Bifurcations along the Homotopy / 15.3：
(κ1, κ2) = (odd, even) or (even, odd) / 15.4.1：
(κ1, κ2) = (odd, odd) / 15.4.2：
(κ1, κ2) = (even, even) / 15.4.3：
A Numerical Example / 15.5：
Discretization with finite difference methods / 15.5.1：
Homotopy of (κ1(μ), κ2(μ)) from (1,2) to (2,3) / 15.5.2：
Homotopy of (κl(μ), κ2(μ)) from (1,3) to (2,4) / 15.5.3：
Homotopy of (κ1(μ), κ2(μ)) from (2,4) to (3,5) / 15.5.4：
Forced Symmetry-Breaking in BCs / 15.6：
Bifurcation points / 15.6.1：
Bifurcation scenarios / 15.6.2：
A Mode Interaction on a Homotopy of BCs / 16：
Symmetries and Normal Forms / 16.1：
Generic Bifurcation Behavior / 16.3：
Solutions with the modes φ1, φ2 / 16.3.1：
Pure φ3-mode solutions / 16.3.2：
Interactions of three modes / 16.3.3：
Scales of Solution Branches / 16.4：
Secondary Bifurcations / 16.5：
Secondary Hopf bifurcations / 16.5.1：
Truncated Bifurcation Equations / 16.6：
Derivatives with respect to homotopy parameter / 16.6.1：
Reduced Stability / 16.7：
Stability of solution branches at (0, λ1(μ),μ) / 16.7.1：
Stability of solution branches at (0, λ2(μ), μ) / 16.7.2：
Stability of solution branches at mode interaction / 16.7.3：
Solution branches along (0; λ1(μ),μ) / 16.8：
Solution branches along (0, λ2(μ),μ) / 16.8.2：
Mode interaction / 16.8.3：
Switching and continuation of solution branches / 16.8.4：
List of Figures
List of Tables
Bibliography
Index
Reaction-Diffusion Equations / 1：
Introduction / 1.1：
Bifurcations and Pattern Formations / 1.2：
10.

図書
図書
10. Coding theory, cryptography and related areas : proceedings of an International Conference on Coding Theory, Cryptography and Related Areas, held in Guanajuato, Mexico, in April 1998
Johannes Buchmann ... [et al.] (eds.)
出版情報: Berlin ; New York : Springer-Verlag, c2000  viii, 259 p. ; 24 cm
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