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1.

図書
図書
1. 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：
2.

図書
図書
2. 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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3.

図書
図書
3. 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
4.

図書
図書
4. 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
5.

図書
図書
5. 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：
6.

図書
図書
6. 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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目次情報: 続きを見る
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：
7.

図書
図書
7. 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：
8.

図書
図書
8. 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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9.

図書
図書
9. Variational methods : applications to nonlinear partial differential equations and Hamiltonian systems. 3rd ed
Michael Struwe
出版情報: Berlin : Springer, c2000  xviii, 274 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 34
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10.

図書
図書
10. Geometry : Euclid and beyond
Robin Hartshorne
出版情報: New York ; Tokyo : Springer, c2000  xi, 526 p., [2] p. of col. plates ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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Euclid's Geometry
Hilbert's Axioms
Geometry over Fields
Segment Arithmetic
Area
Construction Problems and Field Extensions
Non-Euclidean Geometry
Polyhedra
Euclid's Geometry
Hilbert's Axioms
Geometry over Fields
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