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1.

図書

図書
Frédéric Hélein
出版情報: Cambridge : Cambridge University Press, 2002  xxv, 264 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 150
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2.

図書

図書
Yasumasa Nishiura ; translated by Kunimochi Sakamoto
出版情報: Providence, R.I. : American Mathematical Society, c2002  xx, 311 p. ; 22 cm
シリーズ名: Translations of mathematical monographs ; v. 209
Iwanami series in modern mathematics
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Separation and unification of scales
Amplitude equations
Marginal stability criterion and pattern selection
Pattern formation
Method of singular limit analysis
Transient dynamics
Future perspectives
Bibliography
Index
Separation and unification of scales
Amplitude equations
Marginal stability criterion and pattern selection
3.

図書

図書
Wolfgang Lück
出版情報: Berlin ; Tokyo : Springer, c2002  xv, 595 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, v. 44
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4.

図書

図書
Jan Cnops
出版情報: Boston : Birkhäuser, c2002  x, 211 p. ; 24 cm
シリーズ名: Progress in mathematical physics / editors-in-chief, Anne Boutet de Monvel, Gerald Kaiser ; v. 24
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Introduction
Clifford Algebras
Manifolds
Dirac Operators
Conformal Maps
Unique Continuation and the Cauchy Kernel
Boundary Values
Appendix
General Manifolds
The Additional Canterbury Tales
List of Symbols
Bibliography
Index
Introduction
Clifford Algebras
Manifolds
5.

図書

図書
Donggao Deng ... [et al.], editors
出版情報: Providence, R.I. : American Mathematical Society : International Press, c2002  xvi, 326 p. ; 26 cm
シリーズ名: AMS/IP studies in advanced mathematics ; v. 25
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6.

図書

図書
Andrew J. Majda, Andrea L. Bertozzi
出版情報: Cambridge : Cambridge University Press, 2002  xii, 545 p. ; 26 cm
シリーズ名: Cambridge texts in applied mathematics
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Preface
An introduction to vortex dynamics for incompressible fluid flows / 1:
The vorticity-stream formulation of the Euler and the Navier-Stokes equations / 2:
Energy methods for the Euler and the Navier-Stokes equations / 3:
The particle-trajectory method for existence and uniqueness of solutions to the Euler equation / 4:
The search for singular solutions to the 3D Euler equations / 5:
Computational vortex methods / 6:
Simplified asympototic equations for slender vortex filaments / 7:
Weak solutions to the 2D Euler equations with initial vorticity in Lâê  / 8:
Introduction to vortex sheets, weak solutions and approximate-solution sequences for the Euler equation / 9:
Weak solutions and solution sequences in two dimensions / 10:
The 2D Euler equation: concentrations and weak solutions with vortex-sheet initial data / 11:
Reduced Hausdorff dimension, oscillations and measure-valued solutions of the Euler equations in two and three dimensions / 12:
The Vlasov-Poisson equations as an analogy to the Euler equations for the study of weak solutions / 13:
Index
Preface
An introduction to vortex dynamics for incompressible fluid flows / 1:
The vorticity-stream formulation of the Euler and the Navier-Stokes equations / 2:
7.

図書

図書
David F. Walnut
出版情報: Boston : Birkhäuser, c2002  xvii, 449 p. ; 25 cm
シリーズ名: Applied and numerical harmonic analysis / series editor, John J. Benedetto
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Preface
Preliminaries / Part I:
Functions and Convergence
Fourier Series
The Fourier Transform
Signals and Systems
The Haar System / Part II:
The Discrete Haar Transform
Orthonormal Wavelet Bases / Part III:
Mulitresolution Analysis
The Discrete Wavelet Transform
Smooth, Compactly Supported Wavelets
Other Wavelet Constructions / Part IV:
Biorthogonal Wavelets
Wavelet Packets
Applications / Part V:
Image Compression
Integral Operators
Review of Advanced Calculus and Linear Algebra / Appendix A:
Excursions in Wavelet Theory / Appendix B:
References Cited in the Text / Appendix C:
Index
Preface
Preliminaries / Part I:
Functions and Convergence
8.

図書

図書
M. Takesaki
出版情報: Berlin ; Tokyo : Springer, c2002-c2003  3 v. ; 25 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 124-125, 127 . Operator algebras and non-commutative geometry ; 5-6, 8
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Preface
Ergodic Transformaton Groups and the Associated von Neumann Algebras / Chapter XIII:
Approximately Finite Dimensional von Neumann Algebras / Chapter XIV:
Nuclear C*-Algebras / Chapter XV:
Injective von Neumann Algebras / Chapter XVI:
Non-Commutative Ergodic Theory / Chapter XVII:
Structure of Approximately Finite Dimensional Factors / Chapter XVIII:
Subfactors of a Factor of Tape II1 / Chapter XIX:
Fundaments of Banach Algebras and C*-Algebras / Appendix:
Topologies and Density Theorems in Operator Algebras
Conjugate Spaces
Tensor Products of Operator Algebras and Direct Integrals
Types of von Neumann Algebras and Traces
Appendix: Polish Spaces and Standard Borel Spaces
Preface
Ergodic Transformaton Groups and the Associated von Neumann Algebras / Chapter XIII:
Approximately Finite Dimensional von Neumann Algebras / Chapter XIV:
9.

図書

図書
Zhuoqun Wu ... [et al.]
出版情報: Singapore : World Scientific, c2001  xvii, 502 p. ; 23 cm
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Preface
Newtonian Filtration Equations / Chapter 1:
Introduction / 1.1:
Physical examples / 1.1.1:
Definitions of generalized solutions / 1.1.2:
Special solutions / 1.1.3:
Existence and Uniqueness of Solutions: One Dimensional Case / 1.2:
Uniqueness of solutions / 1.2.1:
Existence of solutions / 1.2.2:
Comparison theorems / 1.2.3:
Some extensions / 1.2.4:
Existence and Uniqueness of Solutions: Higher Dimensional Case / 1.3:
Comparison theorem and uniqueness of solutions / 1.3.1:
Regularity of Solutions: One Dimensional Case / 1.3.2:
Lemma / 1.4.1:
Regularity of solutions / 1.4.2:
Regularity of Solutions: Higher Dimensional Case / 1.4.3:
Generalized class B[subscript 2] / 1.5.1:
Some lemmas / 1.5.2:
Properties of functions in the generalized class B[subscript 2] / 1.5.3:
Holder continuity of solutions / 1.5.4:
Properties of the Free Boundary: One Dimensional Case / 1.6:
Finite propagation of disturbances / 1.6.1:
Localization and extinction of disturbances / 1.6.2:
Differential equation on the free boundary / 1.6.3:
Continuously differentiability of the free boundary / 1.6.4:
Some further results / 1.6.5:
Properties of the Free Boundary: Higher Dimensional Case / 1.7:
Monotonicity and Holder continuity of the free boundary / 1.7.1:
Lipschitz continuity of the free boundary / 1.7.2:
Initial Trace of Solutions / 1.7.3:
Harnack inequality / 1.8.1:
Main result / 1.8.2:
Extension of existence and uniqueness theorem / 1.8.3:
Other Problems / 1.9:
Equations with strongly nonlinear sources / 1.9.1:
Asymptotic properties of solutions / 1.9.2:
Non-Newtonian Filtration Equations / Chapter 2:
Introduction Preliminary Knowledge / 2.1:
Introduction Physical example / 2.1.1:
Basic spaces and some lemmas / 2.1.2:
Existence of Solutions / 2.1.3:
The case u[subscript 0] [set membership] C[superscript [infinity] subscript 0](R[superscript N]) or u[subscript 0] [set membership] L[superscript 1](R[superscript N]) [intersection of] L[superscript [infinity](R[superscript N]) / 2.2.1:
The case u[subscript 0] [set membership] L[superscript 1 subscript loc](R[superscript N]) / 2.2.2:
Some remarks / 2.2.3:
Harnack Inequality and the Initial Trace of Solutions / 2.3:
Local Harnack inequality / 2.3.1:
Global Harnack inequality / 2.3.2:
Initial trace of solutions / 2.3.3:
Regularity of Solutions / 2.4:
Boundedness of solutions / 2.4.1:
Boundedness of the gradient of solutions / 2.4.2:
Holder continuity of the gradient of solutions / 2.4.3:
Uniqueness of Solutions / 2.5:
Auxiliary propositions / 2.5.1:
Uniqueness theorem and its proof / 2.5.2:
Properties of the Free Boundary / 2.6:
p-Laplacian equation with strongly nonlinear sources / 2.6.1:
General Quasilinear Equations of Second Order / 2.7.2:
Weakly Degenerate Equations in One Dimension / 3.1:
Uniqueness of bounded and measurable solutions / 3.2.1:
Existence of continuous solutions / 3.2.2:
Weakly Degenerate Equations in Higher Dimension / 3.2.3:
Existence of continuous solutions for equations with two points of degeneracy / 3.3.1:
Uniqueness of BV solutions / 3.3.2:
Existence of BV solutions / 3.3.3:
Strongly Degenerate Equations in One Dimension / 3.3.4:
Definitions of solutions with discontinuity / 3.4.1:
Interior discontinuity condition / 3.4.2:
Uniqueness of BV solutions of the Cauchy problem / 3.4.3:
Formulation of the boundary value problem / 3.4.4:
Boundary discontinuity condition / 3.4.5:
Uniqueness of BV solutions of the first boundary value problem / 3.4.6:
Existence of BV solutions of the first boundary value problem / 3.4.7:
Equations with degeneracy at infinity / 3.4.8:
Properties of the curves of discontinuity / 3.4.10:
Degenerate Equations in Higher Dimension without Terms of Lower Order / 3.5:
Uniqueness of bounded and integrable solutions / 3.5.1:
A lemma on weak convergence / 3.5.2:
General Strongly Degenerate Equations in Higher Dimension / 3.5.3:
Appendix Classes BV and BV[subscript x] / 3.6.1:
Nonlinear Diffusion Equations of Higher Order / Chapter 4:
Similarity Solutions of a Fourth Order Equation / 4.1:
Definition of similarity solutions / 4.2.1:
Existence and uniqueness of global solutions of the Cauchy problem / 4.2.2:
Properties of solutions at zero points / 4.2.3:
Properties of unbounded solutions / 4.2.5:
Bounded solutions on the half line / 4.2.6:
Bounded solutions on the whole line / 4.2.7:
Properties of solutions in typical cases k = 1,2,3,4 / 4.2.8:
Behavior of similarity solutions as t [right arrow] 0[superscript +] / 4.2.9:
Equations with Double-Degeneracy / 4.3:
Weighted energy equality of solutions / 4.3.1:
Some auxiliary inequalities / 4.3.4:
Asymptotic behavior of solutions / 4.3.5:
Extinction of solutions at finite time / 4.3.7:
Nonexistence of nonnegative solutions / 4.3.8:
Infinite propagation case / 4.3.9:
Cahn-Hilliard Equation with Constant Mobility / 4.4:
Existence of classical solutions / 4.4.1:
Blowing-up of solutions / 4.4.2:
Global existence of solutions for small initial value / 4.4.3:
Cahn-Hilliard Equations with Positive Concentration Dependent Mobility / 4.5:
A modified Campanato space / 4.5.1:
Holder norm estimates for a linear problem / 4.5.2:
Zero potential case / 4.5.3:
General case / 4.5.4:
Thin Film Equation / 4.6:
Definition of generalized solutions / 4.6.1:
Approximate solutions / 4.6.2:
Nonnegativity of solutions / 4.6.3:
Zeros of nonnegative solutions / 4.6.5:
Monotonicity of the support of solutions / 4.6.6:
Cahn-Hilliard Equation with Degenerate Mobility / 4.7:
Models with degenerate mobility / 4.7.1:
Definition of physical solutions / 4.7.2:
Physical solutions / 4.7.3:
Bibliography
Preface
Newtonian Filtration Equations / Chapter 1:
Introduction / 1.1:
10.

図書

図書
George Greaves
出版情報: Berlin ; Tokyo : Springer, c2001  xii, 304 p. ; 24 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, v. 43
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Introduction
The Structure of Sifting Arguments / 1:
The Sieves of Eratosthenes and Legendre / 1.1:
The Contribution of Eratosthenes / 1.1.1:
Legendre's Sieve / 1.1.2:
An Estimate for n(X) / 1.1.3:
The Distribution of Primes / 1.1.4:
Examples of Sifting Situations / 1.2:
Notations / 1.2.1:
The Integers in an Interval (Y - X, Y ) / 1.2.2:
Numbers Given by Polynomial Expressions / 1.2.3:
Arithmetic Progressions / 1.2.4:
Sums of Two Squares / 1.2.5:
Polynomials with Prime Arguments / 1.2.6:
A General Formulation of a Sifting Situation / 1.3:
The Basic Formulation / 1.3.1:
Legendre's Sieve in a General Setting / 1.3.2:
A Generalised Formulation / 1.3.3:
A Further Generalisation / 1.3.4:
Sifting Density / 1.3.5:
The Sifting Limit Β(k) / 1.3.6:
Composition of Sieves / 1.3.7:
Notes on Chapter 1 / 1.4:
Selberg's Upper Bound Method / 2:
The Sifting Apparatus / 2.1:
Selberg's Theorem / 2.1.1:
The Numbers (lambda)(d) / 2.1.2:
A Simple Application / 2.1.3:
General Estimates of G(x) and E(D, P) / 2.2:
An Estimate by Rankin's Device / 2.2.1:
Asymptotic Formulas / 2.2.2:
The Error Term / 2.2.3:
Applications / 2.3:
Prime Twins and Goldbach's Problem / 2.3.1:
Polynomial Sequences / 2.3.3:
Notes on Chapter 2 / 2.4:
Combinatorial Methods / 3:
The Construction of Combinatorial Sieves / 3.1:
Preliminary Discussion of Brun's Ideas / 3.1.1:
Fundamental Inequalities and Identities / 3.1.2:
Buchstab's Identity / 3.1.3:
The Combinatorial Sieve Lemma / 3.1.4:
Brun's Pure Sieve / 3.2:
Inequalities and Identities / 3.2.1:
The "Pure Sieve" Theorem / 3.2.2:
A Corollary / 3.2.3:
Prime Twins / 3.2.4:
A Modern Edition of Brun's Sieve / 3.3:
Rosser's Choice of X / 3.3.1:
A Technical Estimate / 3.3.2:
A Simplifying Approximation / 3.3.3:
A Combinatorial Sieve Theorem / 3.3.4:
Brun's Version of his Method / 3.3.5:
Brun's Choice of x / 3.4.1:
The Estimations / 3.4.2:
The Result / 3.4.3:
Notes on Chapter 3 / 3.5:
Rosser's Sieve / 4:
Approximations by Continuous Functions / 4.1:
The Recurrence Relations / 4.1.1:
Partial Summation / 4.1.2:
The Leading Terms / 4.1.3:
The Functions F and f / 4.2:
The Difference-Differential Equations / 4.2.1:
The Adjoint Equation and the Inner Product / 4.2.2:
Solutions of the Adjoint Equation / 4.2.3:
Particular Values of F(s) and f(s) / 4.2.4:
Asymptotic Analysis as k -> $(infinity$) / 4.2.5:
The Convergence Problem / 4.3:
The Auxiliary Functions / 4.3.1:
Adjoints and Inner Products / 4.3.2:
The Case k
A Sieve Theorem Following Rosser / 4.4:
The Case k >/= 1/2: a First Result / 4.4.1:
Theorem 1 when k
An Improved Version of Proposition 1 / 4.4.3:
A Two-Sided Estimate / 4.4.4:
Extremal Examples / 4.5:
The Linear Case / 4.5.1:
The Case k=1/2 / 4.5.2:
Notes on Chapter 4 / 4.6:
The Sieve with Weights / 5:
Simpler Weighting Devices / 5.1:
Logarithmic Weights / 5.1.1:
Modified Logarithmic Weights / 5.1.2:
Some Applications / 5.1.3:
More Elaborate Weighted Sieves / 5.2:
An Improved Weighting Device / 5.2.1:
Buchstab's Weights / 5.2.2:
A Weighted Sieve Following Rosser / 5.3:
Combining Sieving and Weighting / 5.3.1:
The Reduction Identities / 5.3.2:
An Identity for the Main Term / 5.3.3:
The Estimate for the Main Term / 5.3.4:
Notes on Chapter 5 / 5.4:
The Remainder Term in the Linear Sieve / 6:
The Bilinear Nature of Rosser's Construction / 6.1:
The Factorisation of x.d / 6.1.1:
Discretisations of Rosser's Sieve / 6.1.2:
Specification of Details / 6.1.3:
The Leading Contributions to the Main Term / 6.1.4:
The Remainder Term / 6.1.5:
Sifting Short Intervals / 6.2:
The Smoothed Formulation / 6.2.1:
The Remainder Sums / 6.2.2:
Trigonometrical Sums / 6.2.3:
Notes on Chapter 6 / 6.3:
Lower Bound Sieves when k > 1 / 7:
An Extension of Selberg's Upper Bound / 7.1:
The Integral Equation and the Function $(sigma$) (s) / 7.1.1:
The Estimation of G(s) / 7.1.2:
A Lower Bound Sieve via Buchstab's Identity / 7.2:
Buchstab's Iterations / 7.2.1:
The Buchstab Transform of the $(lambda$)2 Method / 7.2.2:
The Sifting Limit as k -> $(infinity$) / 7.2.3:
Selberg's a2 a" Method / 7.3:
The Improved Sifting Limit for Large k / 7.3.1:
Notes on Chapter 7 / 7.4:
References
Index
Introduction
The Structure of Sifting Arguments / 1:
The Sieves of Eratosthenes and Legendre / 1.1:
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