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1.

図書

図書
Robert M. Mazo
出版情報: Oxford : Clarendon Press, 2002  xii, 289 p. ; 24 cm
シリーズ名: The international series of monographs on physics ; 112
Oxford science publications
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Historical Background / 1:
Robert Brown / 1.1:
Between Brown and Einstein / 1.2:
Albert Einstein / 1.3:
Marian von Smoluchowski / 1.4:
Molecular Reality / 1.5:
The Scope of this Book / 1.6:
Probability Theory / 2:
Probability / 2.1:
Conditional Probability and Independence / 2.2:
Random Variables and Probability Distributions / 2.3:
Expectations and Particular Distributions / 2.4:
Characteristic Function; Sums of Random Variables / 2.5:
Conclusion / 2.6:
Stochastic Processes / 3:
Distribution Functions / 3.1:
Classification of Stochastic Processes / 3.3:
The Fokker-Planck Equation / 3.4:
Some Special Processes / 3.5:
Calculus of Stochastic Processes / 3.6:
Fourier Analysis of Random Processes / 3.7:
White Noise / 3.8:
Einstein-Smoluchowski Theory / 3.9:
What is Brownian Motion? / 4.1:
Smoluchowski's Theory / 4.2:
Smoluchowski Theory Continued / 4.3:
Einstein's Theory / 4.4:
Diffusion Coefficient and Friction Constant / 4.5:
The Langevin Theory / 4.6:
Stochastic Differential Equations and Integrals / 5:
The Langevin Equation Revisited / 5.1:
Stochastic Differential Equations / 5.2:
Which Rule Should Be Used? / 5.3:
Some Examples / 5.4:
Functional Integrals / 6:
The Wiener Integral / 6.1:
Wiener Measure / 6.3:
The Feynman-Kac Formula / 6.4:
Feynman Path Integrals / 6.5:
Evaluation of Wiener Integrals / 6.6:
Applications of Functional Integrals / 6.7:
Some Important Special Cases / 7:
Several Cases of Interest / 7.1:
The Free Particle / 7.2:
The Distribution of Displacements / 7.3:
The Harmonically Bound Particle / 7.4:
A Particle in a Constant Force Field / 7.5:
The Uniaxial Rotor / 7.6:
An Equation for the Distribution of Displacements / 7.7:
Discussion / 7.8:
The Smoluchowski Equation / 8:
The Kramers-Klein Equation / 8.1:
Elimination of Fast Variables / 8.2:
The Smoluchowski Equation Continued / 8.4:
Passage over Potential Barriers / 8.5:
Concluding Remarks / 8.6:
Random Walk / 9:
The Random Walk / 9.1:
The One-Dimensional Pearson Walk / 9.2:
The Biased Random Walk / 9.3:
The Persistent Walk / 9.4:
Boundaries and First Passage Times / 9.5:
Random Remarks on Random Walks / 9.6:
Statistical Mechanics / 10:
Molecular Distribution Functions / 10.1:
The Liouville Equation / 10.2:
Projection Operators--The Zwanzig Equation / 10.3:
Projection Operators--The Mori Equation / 10.4:
Stochastic Equations from a Statistical Mechanical Viewpoint / 10.5:
The Langevin Equation A Heuristic View / 11.1:
The Fokker-Planck Equation--A Heuristic View / 11.2:
What is Wrong with these Derivations? / 11.3:
Eliminating Fast Processes / 11.4:
The Distribution Function / 11.5:
Two Exactly Treatable Models / 11.6:
Two Illustrative Examples / 12.1:
Brownian Motion in a Dilute Gas / 12.2:
The Particle Bound to a Lattice / 12.3:
The One-Dimensional Case / 12.5:
Brownian Motion and Noise / 12.6:
Limits on Measurement / 13.1:
Oscillations of a Fiber / 13.2:
A Pneumatic Example / 13.3:
Electrical Systems / 13.4:
Diffusion Phenomena / 13.5:
Brownian Motion in Configuration Space / 14.1:
Diffusion Controlled Reactions / 14.2:
The Effect of Forces / 14.3:
The Coagulation of Colloids / 14.4:
Taylor Diffusion / 14.5:
Rotational Diffusion / 15:
Fluorescence Depolarization / 15.1:
Non-Spherical Brownian Particles / 15.3:
Polymer Solutions / 15.4:
A Model for Dilute Solutions of Polymers / 16.1:
Hydrodynamic Interaction / 16.2:
The Equation of Motion / 16.3:
Diffusion and Intrinsic Viscosity / 16.4:
Historical Remarks and Additional Reading / 16.5:
Interacting Brownian Particles / 17:
Effects of Concentration / 17.1:
The Multiparticle Smoluchowski Equation / 17.2:
The Diffusion Coefficient / 17.4:
The Viscosity / 17.5:
Dynamics, Fractals, and Chaos / 17.6:
Brownian Dynamics / 18.1:
Brownian Paths as Fractals / 18.2:
Brownian Motion and Chaos / 18.3:
The Applicability of Stokes' Law / 18.4:
Functional Calculus / B:
An Operator Identity / C:
Euler Angles / D:
The Oseen Tensor / E:
Mutual Diffusion and Self-Diffusion / F:
Mutual Diffusion / F.1:
Self-Diffusion / F.2:
Relation between D[subscript m] and D[subscript s] / F.3:
References
Index
Historical Background / 1:
Robert Brown / 1.1:
Between Brown and Einstein / 1.2:
2.

図書

図書
edited by Makoto Maejima, Tokuzo Shiga
出版情報: New Jersey : World Scientific, c2002  xi, 430 p. ; 26 cm
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3.

図書

図書
Juan Arias de Reyna
出版情報: Berlin ; Tokyo : Springer, c2002  xviii, 175 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1785
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Preface
Introduction
About the notation
Fourier series and Hilbert Transform / Part I:
Hardy-Littlewood maximal function / 1:
Weak Inequality / 1.1:
Differentiability / 1.3:
Interpolation / 1.4:
A general inequality / 1.5:
Fourier Series / 2:
Dirichlet / 2.1:
Fourier Series of Continuous Functions / 2.3:
Banach continuity principle / 2.4:
Summability / 2.5:
The Conjugate Function / 2.6:
The Hilbert transform on R / 2.7:
The conjecture of Luzin / 2.8:
Hilbert Transform / 3:
The Hilbert Transform / 3.1:
Maximal Hilbert Transform / 3.6:
The Carleson-Hunt Theorem / Part II:
The Basic Step / 4:
Carleson maximal operator / 4.1:
Local norms / 4.3:
Dyadic Partition / 4.4:
Some definitions / 4.5:
Basic decomposition / 4.6:
The first term / 4.7:
Notation ?/? / 4.8:
The second term / 4.9:
The third term / 4.10:
First form of the basic step / 4.11:
Some comments about the proof / 4.12:
Choosing the partition ?? The norm || / 4.13:
Basic theorem, second form / 4.14:
Maximal inequalities / 5:
Maximal inequalities for ?(?, ×) / 5.1:
Maximal inequalities for Hf / 5.2:
Growth of Partial Sums / 6:
The seven trick / 6.1:
The exceptional set / 6.3:
Bound for the partial sums / 6.4:
Carleson Analysis of the Function / 7:
A musical interlude / 7.1:
The notes of f / 7.3:
The set X / 7.4:
The set S / 7.5:
Allowed pairs / 8:
The length of the notes / 8.1:
Well situated notes / 8.2:
The length of well situated notes / 8.3:
Pair Interchange Theorems / 8.4:
Choosing the shift m / 9.1:
A bound of || f|| ? / 9.3:
Selecting an allowed pair / 9.4:
All together / 10:
End of proof / 10.1:
Consequences / Part III:
Some spaces of functions / 11:
Decreasing rearrangement / 11.1:
The Lorentz spaces Lp,1(µ) and Lp,?(µ) / 11.3:
Marcinkiewicz interpolation theorem / 11.4:
Spaces near L1(µ) / 11.5:
The spaces Llog L(µ) and Lexp(µ) / 11.6:
The Maximal Operator of Fourier series / 12:
Maximal operator of Fourier series / 12.1:
The maximal space Q / 12.3:
The theorem of Antonov / 12.8:
Fourier transform on the line / 13:
Fourier transform / 13.1:
References
Comments
Subject Index
Preface
Introduction
About the notation
4.

図書

図書
Bruce A. Magurn
出版情報: Cambridge : Cambridge University Press, 2002  xiv, 676 p. ; 24 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 87
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Preface
Preliminaries / Chapter 0:
Groups of Modules: K[subscript 0] / Part I:
Free Modules / Chapter 1:
Bases / 1A:
Matrix Representations / 1B:
Absence of Dimension / 1C:
Projective Modules / Chapter 2:
Direct Summands / 2A:
Summands of Free Modules / 2B:
Grothendieck Groups / Chapter 3:
Semigroups of Isomorphism Classes / 3A:
Semigroups to Groups / 3B:
Resolutions / 3C:
Stability for Projective Modules / Chapter 4:
Adding Copies of R / 4A:
Stably Free Modules / 4B:
When Stably Free Modules Are Free / 4C:
Stable Rank / 4D:
Dimensions of a Ring / 4E:
Multiplying Modules / Chapter 5:
Semirings / 5A:
Burnside Rings / 5B:
Tensor Products of Modules / 5C:
Change of Rings / Chapter 6:
K[subscript 0] of Related Rings / 6A:
G[subscript 0] of Related Rings / 6B:
K[subscript 0] as a Functor / 6C:
The Jacobson Radical / 6D:
Localization / 6E:
Sources of K[subscript 0] / Part II:
Number Theory / Chapter 7:
Algebraic Integers / 7A:
Dedekind Domains / 7B:
Ideal Class Groups / 7C:
Extensions and Norms / 7D:
K[subscript 0] and G[subscript 0] of Dedekind Domains / 7E:
Group Representation Theory / Chapter 8:
Linear Representations / 8A:
Representing Finite Groups Over Fields / 8B:
Semisimple Rings / 8C:
Characters / 8D:
Groups of Matrices: K[subscript 1] / Part III:
Definition of K[subscript 1] / Chapter 9:
Elementary Matrices / 9A:
Commutators and K[subscript 1](R) / 9B:
Determinants / 9C:
The Bass K[subscript 1] of a Category / 9D:
Stability for K[subscript 1](R) / Chapter 10:
Surjective Stability / 10A:
Injective Stability / 10B:
Relative K[subscript 1] / Chapter 11:
Congruence Subgroups of GL[subscript n](R) / 11A:
Congruence Subgroups of SL[subscript n](R) / 11B:
Mennicke Symbols / 11C:
Relations Among Matrices: K[subscript 2] / Part IV:
K[subscript 2](R) and Steinberg Symbols / Chapter 12:
Definition and Properties of K[subscript 2](R) / 12A:
Elements of St(R) and K[subscript 2](R) / 12B:
Exact Sequences / Chapter 13:
The Relative Sequence / 13A:
Excision and the Mayer-Vietoris Sequence / 13B:
The Localization Sequence / 13C:
Universal Algebras / Chapter 14:
Presentation of Algebras / 14A:
Graded Rings / 14B:
The Tensor Algebra / 14C:
Symmetric and Exterior Algebras / 14D:
The Milnor Ring / 14E:
Tame Symbols / 14F:
Norms on Milnor K-Theory / 14G:
Matsumoto's Theorem / 14H:
Sources of K[subscript 2] / Part V:
Symbols in Arithmetic / Chapter 15:
Hilbert Symbols / 15A:
Metric Completion of Fields / 15B:
The p-Adic Numbers and Quadratic Reciprocity / 15C:
Local Fields and Norm Residue Symbols / 15D:
Brauer Groups / Chapter 16:
The Brauer Group of a Field / 16A:
Splitting Fields / 16B:
Twisted Group Rings / 16C:
The K[subscript 2] Connection / 16D:
Appendix
Sets, Classes, Functions / A:
Chain Conditions, Composition Series / B:
Special Symbols
References
Index
Preface
Preliminaries / Chapter 0:
Groups of Modules: K[subscript 0] / Part I:
5.

図書

図書
Klaus Bichteler
出版情報: Cambridge : Cambridge University Press, 2002  xiii, 501 p. ; 24 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 89
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Preface
Introduction / Chapter 1:
Motivation: Stochastic Differential Equations / 1.1:
Wiener Process / 1.2:
The General Model / 1.3:
Integrators and Martingales / Chapter 2:
The Elementary Stochastic Integral / 2.1:
The Semivariations / 2.2:
Path Regularity of Integrators / 2.3:
Processes of Finite Variation / 2.4:
Martingales / 2.5:
Extension of the Integral / Chapter 3:
The Daniell Mean / 3.1:
The Integration Theory of a Mean / 3.2:
Countable Additivity in p-Mean / 3.3:
Measurability / 3.4:
Predictable and Previsible Processes / 3.5:
Special Properties of Daniell's Mean / 3.6:
The Indefinite Integral / 3.7:
Functions of Integrators / 3.8:
Ito's Formula / 3.9:
Random Measures / 3.10:
Control of Integral and Integrator / Chapter 4:
Change of Measure--Factorization / 4.1:
Martingale Inequalities / 4.2:
The Doob-Meyer Decomposition / 4.3:
Semimartingales / 4.4:
Previsible Control of Integrators / 4.5:
Levy Processes / 4.6:
Stochastic Differential Equations / Chapter 5:
Existence and Uniqueness of the Solution / 5.1:
Stability: Differentiability in Parameters / 5.3:
Pathwise Computation of the Solution / 5.4:
Weak Solutions / 5.5:
Stochastic Flows / 5.6:
Semigroups, Markov Processes, and PDE / 5.7:
Complements to Topology and Measure Theory / Appendix A:
Notations and Conventions / A.1:
Topological Miscellanea / A.2:
Measure and Integration / A.3:
Weak Convergence of Measures / A.4:
Analytic Sets and Capacity / A.5:
Suslin Spaces and Tightness of Measures / A.6:
The Skorohod Topology / A.7:
The L[superscript p]-Spaces / A.8:
Semigroups of Operators / A.9:
Answers to Selected Problems / Appendix B:
References
Index of Notations
Index
Answers
Full Indexes
Errata
Preface
Introduction / Chapter 1:
Motivation: Stochastic Differential Equations / 1.1:
6.

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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7.

図書

図書
edited by Roland Glowinski, Hideo Kawarada, Jacques Periaux
出版情報: Tokyo : Gakkōtosho, c2002  346 p. ; 27 cm
シリーズ名: GAKUTO international series ; . Mathematical sciences and applications ; vol. 16
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8.

図書

図書
K.P.S. Bhaskara Rao
出版情報: London : Taylor and Francis, c2002  xi, 167 p. ; 24 cm
シリーズ名: Algebra, logic and applications series ; 17
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Elementary Results on Rings
Foreword
Matrix Algebra Over Rings
Regular Elements in a Ring
Preface
Regularity - Principal Ideal Rings
Regularity - Basics / 1:
Regularity - Integral Domains
Elementary results on rings
Regularity - Commutative Rings
Special Topics / 2:
Matrix algebra over rings
Elementary notions / 2.1:
Determinants / 2.2:
The [partial differential]/[partial differential]a[subscript ij] notation / 2.3:
Rank of a matrix / 2.4:
Compound matrices / 2.5:
Regular elements in a ring / 3:
The Moore-Penrose equations / 3.1:
Regular elements and regular matrices / 3.2:
A Theorem of Von Neumann / 3.3:
Inverses of matrices / 3.4:
M-P inverses / 3.5:
Regularity - principal ideal rings / 4:
Some results on principal ideal rings / 4.1:
Smith Normal Form Theorem / 4.2:
Regular matrices over Principal Ideal Rings / 4.3:
An algorithm for Euclidean domains / 4.4:
Reflexive g-inverses of matrices / 4.5:
Some special integral domains / 4.6:
Examples / 4.7:
Regularity - basics / 5:
Regularity of rank one matrices / 5.1:
A basic result on regularity / 5.2:
A result of Prasad and Robinson / 5.3:
Regularity - integral domains / 6:
Regularity of matrices / 6.1:
All reflexive g-inverses / 6.2:
M-P inverses over integral domains / 6.3:
Generalized inverses of the form PCQ / 6.4:
{1,2,3}- and {1,2,4}-inverses / 6.5:
Group inverses over integral domains / 6.6:
Drazin inverses over integral domains / 6.7:
Regularity - commutative rings / 7:
Commutative rings with zero divisors / 7.1:
Rank one matrices / 7.2:
Rao-regular matrices / 7.3:
Regular matrices over commutative rings / 7.4:
All generalized inverses / 7.5:
M-P inverses over commutative rings / 7.6:
Group inverses over commutative rings / 7.7:
Drazin inverses over commutative rings / 7.8:
Special topics / 8:
Generalized Cramer Rule / 8.1:
A rank condition for consistency / 8.2:
Minors of reflexive g-inverses / 8.3:
Bordering of regular matrices / 8.4:
Regularity over Banach algebras / 8.5:
Group inverses in a ring / 8.6:
M-P inverses in a ring / 8.7:
Group inverse of the companion matrix / 8.8:
Bibliography
Index
Elementary Results on Rings
Foreword
Matrix Algebra Over Rings
9.

図書

図書
edited by Zoltán Daróczy, Zsolt Páles
出版情報: Dordrecht : Kluwer Academic, c2002  x, 360 p. ; 25 cm
シリーズ名: Advances in mathematics ; v. 3
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10.

図書

図書
Martin A. Moskowitz
出版情報: Singapore ; New Jersey : World Scientific, c2002  ix, 149 p. ; 23 cm
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Preface and Acknowledgments
First Concepts / 1:
Fundamentals of the complex field / 1.1:
Holomorphic functions / 1.2:
Some important examples / 1.3:
The Cauchy-Riemann equations / 1.4:
Some elementary differential equations / 1.5:
Conformality / 1.6:
Power series / 1.7:
Integration Along a Contour / 2:
Curves and their trajectories / 2.1:
Change of Parameter and a Fundamental Inequality / 2.2:
Some important examples of contour integration / 2.3:
The Cauchy theorem in simply connected domains / 2.4:
Some immediate consequences of Cauchy's theorem for a simply connected domain / 2.5:
The Main Consequences of Cauchy's theorem / 3:
The Cauchy theorem in multiply connected domains and the pre-residue theorem / 3.1:
The Cauchy integral formula and its consequences / 3.2:
Analyticity, Taylor's theorem and the identity theorem / 3.3:
The area formula and some consequences / 3.4:
Application to spaces of square integrable holomorphic functions / 3.5:
Spaces of holomorphic functions and Montel's theorem / 3.6:
The maximum modulus theorem and Schwarz' lemma / 3.7:
Singularities / 4:
Classification of isolated singularities, the theorems of Riemann and Casorati-Weierstrass / 4.1:
The principle of the argument / 4.2:
Rouche's theorem and its consequences / 4.3:
The study of a transcendental equation / 4.4:
Laurent expansion / 4.5:
The calculation of residues at an isolated singularity, the residue theorem / 4.6:
Application to the calculation of real integrals / 4.7:
A more general removable singularities theorem and the Schwarz reflection principle / 4.8:
Conformal Mappings / 5:
Linear fractional transformations, equivalence of the unit disk and the upper half plane / 5.1:
Automorphism groups of the disk, upper half plane and entire plane / 5.2:
Annuli / 5.3:
The Riemann mapping theorem for planar domains / 5.4:
Applications of Complex Analysis to Lie Theory / 6:
Applications of the identity theorem: Complete reducibility of representations according to Hermann Weyl and the functional equation for the exponential map of a real Lie group / 6.1:
Application of residues: The surjectivity of the exponential map for U(p,q) / 6.2:
Application of Liouville's theorem and the maximum modulus theorem: The Zariski density of cofinite volume subgroups of complex Lie groups / 6.3:
Applications of the identity theorem to differential topology and Lie groups / 6.4:
Bibliography
Index
Preface and Acknowledgments
First Concepts / 1:
Fundamentals of the complex field / 1.1:
11.

図書

図書
edited by Bernold Fiedler
出版情報: Amsterdam ; Tokyo : Elsevier Science, 2002-  3 v. ; 25 cm
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Principal structures / B. Hasselblatt ; A. KatokVolume 1A:
Entropy, Isomorphism and Equivalence / J.-P. Thouvenot
Hyperbolic dynamics
Invariant measures for hyperbolic dynamical systems / N. Chernov
Periodic orbits and zeta functions / M. Pollicott
Hyperbolic dynamics and Riemannian geometry / G. Knieper
Topological Methods in Dynamics / J. Franks ; M. Misiurewicz
One-Dimensional Maps / M. Jakobson ; G. Sawiatek
Ergodic theory and dynamics of G-spaces / R. Feres
Symbolic and algebraic dynamical systems / D. Lind ; K. Schmidt
Homogeneous flows, applications to number theory, and related topics / D. Kleinbock ; N. Shah ; A. Starkov
Random transformations in ergodic theory / A. Furman
Rational billiards and flat structures / H. Masur ; S. Tabachnikov
Variational methods for Hamiltonian systems / P.H. Rabinowitz
Pseudoholomorphic curves and dynamics in three dimensions / H. Hofer ; K. Wysocki ; E. Zehnder
Finite-Dimensional Methods / A:
Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators / N. Kopell ; G.B. Ermentrout1:
Invariant manifolds and Lagrangian dynamics in the ocean and atmosphere / C. Jones ; S. Winkler2:
Geometric singular perturbation analysis of neuronal dynamics / J.E. Rubin ; D. Terman3:
Numerics / B:
Numerical continuation, and computation of normal forms / W.-J. Beyn ; A. Champneys ; E. Doedel ; W. Govaerts ; Y.A. Kuznetsov ; B. Sandstede4:
Set oriented numerical methods for dynamical systems / M. Dellnitz ; O. Junge5:
Numerics and exponential smallness / V. Gelfreich6:
Shadowability of chaotic dynamical systems / C. Grebogi ; L. Poon ; T. Sauer ; J.A. Yorke ; D. Auerbach7:
Numerical analysis of dynamical systems / J. Guckenheimer8:
Topological Methods / C:
Conley index / K. Mischaikow ; M. Mrozek9:
Functional differential equations / R.D. Nussbaum10:
Partial Differential Equations / D:
Navier--Stokes equations and dynamical systems / C. Bardos ; B. Nicolaenko11:
The nonlinear Schrodinger equation as both a PDE and a dynamical system / D. Cai ; D.W. McLaughlin ; K.T.R. McLaughlin12:
Pattern formation in gradient systems / P.C. Fife13:
Blow-up in nonlinear heat equations from the dynamical systems point of view / M. Fila ; H. Matano14:
The Ginzburg--Landau equation in its role as a modulation equation / A. Mielke15:
Parabolic equations: asymptotic behavior and dynamics on invariant manifolds / P. Polacik16:
Global attractors in partial differential equations / G. Raugel17:
Stability of travelling waves / 18:
Preface List of Contributors Contents of Volume 1A
Partially Hyperbolic Dynamical Systems / Ya. Pesin
Smooth Ergodic Theory and Nonuniformly Hypoerbolic Dynamics / L. Barreira
Appendix / O. Sarig
Stochastic-Like Behaviour in Nonuniformly Expanding Maps / S. Luzzatto
Homoclinic Bifurcations, Dominated Splitting, and Robust Transivity / E.R. Pujals ; M. Sambarino
Random Dynamics / Yu. Kifer ; P.-D. Liu
An Introduction to Veech Surfaces / P. Hubert ; T.A. Schmidt
Ergodic Theory of Translation Surfaces
On the Lyapunov Exponents of the Kontsevich-Zorich Cocycle / G. Forni
Counting Problems in Moduli Space / A. Eskin
On the Interplay Between Measurable and Topological Dynamics / E. Glasner ; B. Weiss
Spectral Properties and Combinatorial Constructions in Ergodic Theory
Combinatorial and Diophantine Applications of Ergodic Theory / V. Bergelson
Appendix A / A. Leibman
Appendix B / A. Quas ; M. Wierdl
Pointwise Ergodic Theorems for Actions of Groups / A. Nevo
Global Attractors in PDE / A.V. Babin
Hamiltonian PDEs / S.B. Kuksin
Extended Hamiltonian Systems / D. Bambusi ; M.I. Weinstein
Author Index of Volume 1A
Subject Index of Volume 1A
Author Index
Subject Index
Principal structures / B. Hasselblatt ; A. KatokVolume 1A:
Entropy, Isomorphism and Equivalence / J.-P. Thouvenot
Hyperbolic dynamics
12.

図書

図書
edited by Giuseppe Da Prato, Luciano Tubaro
出版情報: New York : M. Dekker, c2002  ix, 460 p. ; 26 cm
シリーズ名: Lecture notes in pure and applied mathematics ; v. 227
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Preface
Contributors
The Semi-Martingale Property of the Square of White Noise Integrators / Luigi Accardi ; Andreas Boukas1.:
SPDEs Leading to Local, Relativistic Quantum Vector Fields with Indefinite Metric and Nontrivial S-Matrix / Sergio Albeverio ; Hanno Gottschalk ; Jiang-Lun Wu2.:
Considerations on the Controllability of Stochastic Linear Heat Equations / Viorel Barbu ; Gianmario Tessitore3.:
Stochastic Differential Equations for Trace-Class Operators and Quantum Continual Measurements / Alberto Barchielli ; Anna Maria Paganoni4.:
Invariant Measures of Diffusion Processes: Regularity, Existence, and Uniqueness Problems / Vladimir I. Bogachev ; Michael Rockner5.:
On the Theory of Random Attractors and Some Open Problems / Tomas Caraballo ; Jose Antonio Langa6.:
Invariant Densities for Stochastic Semilinear Evolution Equations and Related Properties of Transition Semigroups / Anna Chojnowska-Michalik7.:
On Some Generalized Solutions of Stochastic PDEs / Pao-Liu Chow8.:
Riemannian Geometry on the Path Space / A. B. Cruzeiro ; P. Malliavin9.:
A Note on Regularizing Properties of Ornstein-Uhlenbeck Semigroups in Infinite Dimensions / Giuseppe Da Prato ; Marco Fuhrman ; Jerzy Zabczyk10.:
White Noise Approach to Stochastic Partial Differential Equations / T. Deck ; S. Kruse ; J. Potthoff ; H. Watanabe11.:
Some Results on Invariant States for Quantum Markov Semigroups / Franco Fagnola ; Rolando Rebolledo12.:
Stochastic Problems in Fluid Dynamics / Franco Flandoli13.:
Limit Theorems for Random Interface Models of Ginzburg-Landau [down triangle, open open phi] Type / Giambattista Giacomin14.:
Second Order Hamilton-Jacobi Equations in Hilbert Spaces and Stochastic Optimal Control / Fausto Gozzi15.:
Approximations of Stochastic Partial Differential Equations / Istvan Gyongy16.:
Regularity and Continuity of Solutions to Stochastic Evolution Equations / Anna Karczewska17.:
Some New Results in the Theory of SPDEs in Sobolev Spaces / N. V. Krylov18.:
Lyapunov Function Approaches and Asymptotic Stability of Stochastic Evolution Equations in Hilbert Spaces--A Survey of Recent Developments / Kai Liu ; Aubrey Truman19.:
Strong Feller Infinite-Dimensional Diffusions / Bohdan Maslowski ; Jan Seidler20.:
Optimal Stopping Time and Impulse Control Problems for the Stochastic Navier-Stokes Equations / J. L. Menaldi ; S. S. Sritharan21.:
On Martingale Problem Solutions for Stochastic Navier-Stokes Equation / R. Mikulevicius ; B. Rozovskii22.:
SPDEs Driven by a Homogeneous Wiener Process / Szymon Peszat23.:
Applications of Malliavin Calculus to SPDEs / Marta Sanz-Sole24.:
Stochastic Curvature Driven Flows / Nung Kwan Yip25.:
Preface
Contributors
The Semi-Martingale Property of the Square of White Noise Integrators / Luigi Accardi ; Andreas Boukas1.:
13.

図書

図書
edited by Walter A. Carnielli, Marcelo E. Coniglio, Itala M. Loffredo D'Ottaviano
出版情報: New York : M. Dekker, c2002  xviii, 552 p. ; 26 cm
シリーズ名: Lecture notes in pure and applied mathematics ; v. 228
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Preface
Contributors
Paraconsistency and Systems of Paraconsistent Logic / Part I:
A Taxonomy of C-Systems / Walter A. Carnielli ; Joao Marcos1.:
Paraconsistent Classical Logic / Bryson Brown2.:
The Logic of Opposition / F. G. Asenjo3.:
Categorical Consequence for Paraconsistent Logic / Fred Johnson ; Peter W. Woodruff4.:
Ontological Causes of Inconsistency and a Change-Adaptive, Logical Solution / Guido Vanackere5.:
An Adaptive Logic for Pragmatic Truth / Joke Meheus6.:
A Multiple Worlds Semantics for a Paraconsistent Nonmonotonic Logic / Ana Teresa Martins ; Marcelino Pequeno ; Tarcisio Pequeno7.:
An Inductive Annotated Logic / Newton C. A. da Costa ; Decio Krause8.:
On NCG[subscript w]: A Paraconsistent Sequent Calculus / Jose Eduardo de A. Moura ; Itala M. Loffredo D'Ottaviano9.:
Paraconsistency as Related to Other Logics / Part II:
A, Still Adorable / Robert K. Meyer ; John K. Slaney10.:
Fuzzy Relevant Logic / Graham Priest11.:
On Some Remarkable Relations between Paraconsistent Logics, Modal Logics, and Ambiguity Logics / Diderik Batens12.:
The Dialogical Dynamics of Adaptive Paraconsistency / Shahid Rahman ; Jean Paul van Bendegem13.:
An Inconsistency-Adaptive Proof Procedure for Logic Programming / Timothy Vermeir14.:
Referential and Inferential Many-Valuedness / Grzegorz Malinowski15.:
When Is a Substructural Logic Paraconsistent? Structural Conditions for Paraconsistency in Ternary Frames / Marcelo Finger16.:
Beyond Truth(-Preservation) / R. E. Jennings ; D. Sarenac17.:
Paraconsistency in Chang's Logic with Positive and Negative Truth Values / Renato A. Lewin ; Marta S. Sagastume18.:
Fault-Tolerance and Rota-Metropolis Cubic Logic / Daniele Mundici19.:
The Annotated Logics OP[subscript BL] / Guillermo Ortiz Rico20.:
Definability and Interpolation in Extensions of Johansson's Minimal Logic / Larisa Maksimova21.:
Philosophical Aspects of Paraconsistency / Part III:
Toward a Mathematics of Impossible Pictures / Chris Mortensen22.:
Ambiguity Is Not Enough / B. H. Slater23.:
Are Paraconsistent Negations Negations? / Jean-Yves Beziau24.:
On the Role of Adjunction in Para(in) consistent Logic / Max Urchs25.:
Between Consistency and Paraconsistency: Perspectives from Evidence Logic / Don Faust26.:
Kinds of Inconsistency / Gregory R. Wheeler27.:
Paraconsistent Logic vs. Meinongian Logic / Jacek Pasniczek28.:
Can a Paraconsistent Theorist Be a Logical Monist? / Otavio Bueno29.:
Preface
Contributors
Paraconsistency and Systems of Paraconsistent Logic / Part I:
14.

図書

図書
Joseph L. Taylor
出版情報: Providence, R.I. : American Mathematical Society, c2002  xvi, 507 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 46
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Selected problems in one complex variable
Holomorphic functions of several variables
Local rings and varieties
The Nullstellensatz Dimension
Homological algebra Sheaves and sheaf cohomology
Coherent algebraic sheaves
Coherent analytic sheaves Stein spaces
Frechet sheaves-Cartan's theorems
Projective varieties Algebraic vs. analytic-Serre's theorems
Lie groups and their representations
Algebraic groups
The Borel-Weil-Bott theorem
Bibliography
Index
Selected problems in one complex variable
Holomorphic functions of several variables
Local rings and varieties
15.

図書

図書
by A.K. Gupta and T. Varga
出版情報: Dordrecht : Kluwer Academic Publishers, c2002  ix, 350 p. ; 25 cm
シリーズ名: Mathematical modelling : theory and applications ; v. 14
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Preface
Financial Mathematics / 1:
Mortality / 2:
Life Insurances and Annuities / 3:
Premiums / 4:
Reserves / 5:
Answers to Odd-Numbered Problems
Compound Interest Tables / Appendix 1:
Illustrative Mortality Table / Appendix 2:
References
Symbol Index
Subject Index
Preface
Financial Mathematics / 1:
Mortality / 2:
16.

図書

図書
by D.A. Vladimirov
出版情報: Dordrecht : Kluwer Academic, c2002  xxi, 604 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 540
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17.

図書

図書
William E. Hartnett
出版情報: New York : J. Wiley, c1964  xiv, 154 p. ; 22 cm
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18.

図書

図書
Roger Peyret
出版情報: New York : Springer, c2002  xi, 432 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 148
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Introduction
Fundamentals of Spectral Methods
Fourier Method
Chebyshev Method
Time-Dependent Equations
Navier-Stokes Equations for Incompressible Fluids
Vorticity-Streamfunction Equations
Velocity-Streamfunction Equations
Velocity-Pressure Equations
Stiff and Singular Problems
Domain Decomposition Method
Appendices
References
Index
Introduction
Fundamentals of Spectral Methods
Fourier Method
19.

図書

図書
D.Ya. Petrina, V.I. Gerasimenko and P.V. Malyshev ; translated from the Russian by P.V. Malyshev and D.V. Malyshev
出版情報: London : Taylor & Francis, 2002  ix, 338 p. ; 24 cm
シリーズ名: Advanced studies in contemporary mathematics ; v. 8
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Problem for the BBGKY Hierarchy
Equilibrium States
Canonical Ensemble
Grand Canonical Ensemble
Thermodynamic Limit for Non-equilibrium Systems
Stationary Solutions of the BBGKY Hierarchy of Equations / Appendix 1:
Existence of the Hamiltonian Dynamics of Infinitely Many Particles / Appendix 2:
References
Index
Problem for the BBGKY Hierarchy
Equilibrium States
Canonical Ensemble
20.

図書

図書
Jürgen Jost
出版情報: Berlin ; Tokyo : Springer, c2002  xvi, 278 p. ; 24 cm
シリーズ名: Universitext
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Preface
Topological Foundations / 1:
Manifolds and Di erentiable Manifolds / 1.1:
Homotopy of Maps. The Fundamental Group / 1.2:
Coverings / 1.3:
Global Continuation of Functions on Simply-Connected Manifolds / 1.4:
Di erential Geometry of Riemann Surfaces / 2:
The Concept of a Riemann Surface / 2.1:
Some Simple Properties of Riemann Surfaces / 2.2:
Metrics on Riemann Surfaces / 2.3:
Triangulations of Compact Riemann Surfaces / 2.3.A:
Discrete Groups of Hyperbolic Isometries. Fundamental Polygons. Some Basic Concepts of Surface Topology and Geometry / 2.4:
The Topological Classi cation of Compact Riemann Surfaces / 2.4.A:
The Theorems of Gauss-Bonnet and Riemann-Hurwitz / 2.5:
A General Schwarz Lemma / 2.6:
Conformal Structures on Tori / 2.7:
Harmonic Maps / 3:
Review: Banach and Hilbert Spaces. The Hilbert Space L2 / 3.1:
The Sobolev Space W 1; 2 = H1; 2 / 3.2:
The Dirichlet Principle. Weak Solutions of the Poisson Equation / 3.3:
Harmonic and Subharmonic Functions / 3.4:
The C -Regularity Theory / 3.5:
Maps Between Surfaces. The Energy Integral. De nition and Simple Properties of Harmonic Maps / 3.6:
Existence of Harmonic Maps / 3.7:
Regularity of Harmonic Maps / 3.8:
Uniqueness of Harmonic Maps / 3.9:
Harmonic Di eomorphisms / 3.10:
Metrics and Conformal Structures / 3.11:
Teichmuller Spaces / 4:
The Basic De nitions / 4.1:
Harmonic Maps, Conformal Structures and Holomorphic Quadratic Di erentials. TeichmullerÆs Theorem / 4.2:
Fenchel-Nielsen Coordinates. An Alternative Approach to the Topology of Teichmuller Space / 4.3:
Uniformization of Compact Riemann Surfaces / 4.4:
Geometric Structures on Riemann Surfaces / 5:
Preliminaries: Cohomology and Homology Groups / 5.1:
Harmonic and Holomorphic Di erential Forms on Riemann Surfaces / 5.2:
The Periods of Holomorphic and Meromorphic Di erential Forms / 5.3:
Divisors. The Riemann-Roch Theorem / 5.4:
Holomorphic 1-Forms and Metrics on Compact Riemann Surfaces / 5.5:
Divisors and Line Bundles / 5.6:
Projective Embeddings / 5.7:
Algebraic Curves / 5.8:
AbelÆs Theorem and the Jacobi Inversion Theorem / 5.9:
Elliptic Curves / 5.10:
Sources and References
Bibliography
Index of Notation
Index
Preface
Topological Foundations / 1:
Manifolds and Di erentiable Manifolds / 1.1:
21.

図書

図書
Seiki Nishikawa ; translated by Kinetsu Abe
出版情報: Providence, R.I. : American Mathematical Society, c2002  xvii, 209 p. ; 22 cm
シリーズ名: Translations of mathematical monographs ; v. 205
Iwanami series in modern mathematics
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Arc-length of curves and geodesics
First and second variation formulas
Energy of maps and harmonic maps
Existence of harmonic maps
Fundamentals of theory of manifolds and functional analysis
Prospects for contemporary mathematics
Solutions to exercise problems
Bibliography
Books
Index
Copying and reprinting notice
Other titles in this series
Arc-length of curves and geodesics
First and second variation formulas
Energy of maps and harmonic maps
22.

図書

図書
Qing Liu ; translated by Reinie Erné
出版情報: Oxford : Oxford University Press, 2002  xv, 576 p. ; 24 cm
シリーズ名: Oxford graduate texts in mathematics ; 6
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Some topics in commutative algebra / 1:
Tensor products / 1.1:
Tensor product of modules / 1.1.1:
Right-exactness of the tensor product / 1.1.2:
Tensor product of algebras / 1.1.3:
Flatness / 1.2:
Left-exactness: flatness / 1.2.1:
Local nature of flatness / 1.2.2:
Faithful flatness / 1.2.3:
Formal completion / 1.3:
Inverse limits and completions / 1.3.1:
The Artin-Rees lemma and applications / 1.3.2:
The case of Noetherian local rings / 1.3.3:
General properties of schemes / 2:
Spectrum of a ring / 2.1:
Zariski topology / 2.1.1:
Algebraic sets / 2.1.2:
Ringed topological spaces / 2.2:
Sheaves / 2.2.1:
Schemes / 2.2.2:
Definition of schemes and examples / 2.3.1:
Morphisms of schemes / 2.3.2:
Projective schemes / 2.3.3:
Noetherian schemes, algebraic varieties / 2.3.4:
Reduced schemes and integral schemes / 2.4:
Reduced schemes / 2.4.1:
Irreducible components / 2.4.2:
Integral schemes / 2.4.3:
Dimension / 2.5:
Dimension of schemes / 2.5.1:
The case of Noetherian schemes / 2.5.2:
Dimension of algebraic varieties / 2.5.3:
Morphisms and base change / 3:
The technique of base change / 3.1:
Fibered product / 3.1.1:
Base change / 3.1.2:
Applications to algebraic varieties / 3.2:
Morphisms of finite type / 3.2.1:
Algebraic varieties and extension of the base field / 3.2.2:
Points with values in an extension of the base field / 3.2.3:
Frobenius / 3.2.4:
Some global properties of morphisms / 3.3:
Separated morphisms / 3.3.1:
Proper morphisms / 3.3.2:
Projective morphisms / 3.3.3:
Some local properties / 4:
Normal schemes / 4.1:
Normal schemes and extensions of regular functions / 4.1.1:
Normalization / 4.1.2:
Regular schemes / 4.2:
Tangent space to a scheme / 4.2.1:
Regular schemes and the Jacobian criterion / 4.2.2:
Flat morphisms and smooth morphisms / 4.3:
Flat morphisms / 4.3.1:
Etale morphisms / 4.3.2:
Smooth morphisms / 4.3.3:
Zariski's 'Main Theorem' and applications / 4.4:
Coherent sheaves and Cech cohomology / 5:
Coherent sheaves on a scheme / 5.1:
Sheaves of modules / 5.1.1:
Quasi-coherent sheaves on an affine scheme / 5.1.2:
Coherent sheaves / 5.1.3:
Quasi-coherent sheaves on a projective scheme / 5.1.4:
Cech cohomology / 5.2:
Differential modules and cohomology with values in a sheaf / 5.2.1:
Cech cohomology on a separated scheme / 5.2.2:
Higher direct image and flat base change / 5.2.3:
Cohomology of projective schemes / 5.3:
Direct image theorem / 5.3.1:
Connectedness principle / 5.3.2:
Cohomology of the fibers / 5.3.3:
Sheaves of differentials / 6:
Kahler differentials / 6.1:
Modules of relative differential forms / 6.1.1:
Sheaves of relative differentials (of degree 1) / 6.1.2:
Differential study of smooth morphisms / 6.2:
Smoothness criteria / 6.2.1:
Local structure and lifting of sections / 6.2.2:
Local complete intersection / 6.3:
Regular immersions / 6.3.1:
Local complete intersections / 6.3.2:
Duality theory / 6.4:
Determinant / 6.4.1:
Canonical sheaf / 6.4.2:
Grothendieck duality / 6.4.3:
Divisors and applications to curves / 7:
Cartier divisors / 7.1:
Meromorphic functions / 7.1.1:
Inverse image of Cartier divisors / 7.1.2:
Weil divisors / 7.2:
Cycles of codimension 1 / 7.2.1:
Van der Waerden's purity theorem / 7.2.2:
Riemann-Roch theorem / 7.3:
Degree of a divisor / 7.3.1:
Riemann-Roch for projective curves / 7.3.2:
Algebraic curves / 7.4:
Classification of curves of small genus / 7.4.1:
Hurwitz formula / 7.4.2:
Hyperelliptic curves / 7.4.3:
Group schemes and Picard varieties / 7.4.4:
Singular curves, structure of Pic[superscript 0](X) / 7.5:
Birational geometry of surfaces / 8:
Blowing-ups / 8.1:
Definition and elementary properties / 8.1.1:
Universal property of blowing-up / 8.1.2:
Blowing-ups and birational morphisms / 8.1.3:
Normalization of curves by blowing-up points / 8.1.4:
Excellent schemes / 8.2:
Universally catenary schemes and the dimension formula / 8.2.1:
Cohen-Macaulay rings / 8.2.2:
Fibered surfaces / 8.2.3:
Properties of the fibers / 8.3.1:
Valuations and birational classes of fibered surfaces / 8.3.2:
Contraction / 8.3.3:
Desingularization / 8.3.4:
Regular surfaces / 9:
Intersection theory on a regular surface / 9.1:
Local intersection / 9.1.1:
Intersection on a fibered surface / 9.1.2:
Intersection with a horizontal divisor, adjunction formula / 9.1.3:
Intersection and morphisms / 9.2:
Factorization theorem / 9.2.1:
Projection formula / 9.2.2:
Birational morphisms and Picard groups / 9.2.3:
Embedded resolutions / 9.2.4:
Minimal surfaces / 9.3:
Exceptional divisors and Castelnuovo's criterion / 9.3.1:
Relatively minimal surfaces / 9.3.2:
Existence of the minimal regular model / 9.3.3:
Minimal desingularization and minimal embedded resolution / 9.3.4:
Applications to contraction; canonical model / 9.4:
Artin's contractability criterion / 9.4.1:
Determination of the tangent spaces / 9.4.2:
Canonical models / 9.4.3:
Weierstrass models and regular models of elliptic curves / 9.4.4:
Reduction of algebraic curves / 10:
Models and reductions / 10.1:
Models of algebraic curves / 10.1.1:
Reduction / 10.1.2:
Reduction map / 10.1.3:
Graphs / 10.1.4:
Reduction of elliptic curves / 10.2:
Reduction of the minimal regular model / 10.2.1:
Neron models of elliptic curves / 10.2.2:
Potential semi-stable reduction / 10.2.3:
Stable reduction of algebraic curves / 10.3:
Stable curves / 10.3.1:
Stable reduction / 10.3.2:
Some sufficient conditions for the existence of the stable model / 10.3.3:
Deligne-Mumford theorem / 10.4:
Simplifications on the base scheme / 10.4.1:
Proof of Artin-Winters / 10.4.2:
Examples of computations of the potential stable reduction / 10.4.3:
Bibliography
Index
Some topics in commutative algebra / 1:
Tensor products / 1.1:
Tensor product of modules / 1.1.1:
23.

図書

図書
Jiří Matoušek
出版情報: New York : Springer, c2002  xvi, 481 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 212
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24.

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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25.

図書

図書
Klaus Fritzsche, Hans Grauert
出版情報: New York : Springer, c2002  xv, 392 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 213
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26.

図書

図書
Christopher Parker, Peter Rowley
出版情報: London : Springer, c2002  xi, 361 p. ; 24 cm
シリーズ名: Springer monographs in mathematics
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27.

図書

図書
Ken A. Brown, Ken R. Goodearl
出版情報: Basel : Birkhäuser, c2002  ix, 348 p. ; 24 cm
シリーズ名: Advanced courses in mathematics CRM Barcelona
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28.

図書

図書
A. Galves, J.K. Hale, C. Rocha, editors
出版情報: Providence, R.I. : American Mathematical Society, c2002  xiv, 353 p. ; 26 cm
シリーズ名: Fields Institute communications ; 31
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29.

図書

図書
Axel Harnack
出版情報: London ; Edinburgh : Williams and Norgate, 1891  x, 404 p. ; 24 cm
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30.

図書

図書
by C. Howard Hinton
出版情報: London : G. Allen & Unwin, 1906  viii, 270 p. ; 19 cm
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31.

図書

図書
by Ferenc Weisz
出版情報: Dordrecht : Kluwer Academic, c2002  xv, 332 p. ; 25 cm
シリーズ名: Mathematics and its applications ; Vol.541
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Preface
Acknowledgments
Multi-Dimensional Dyadic Hardy Spaces / 1.:
Introduction / 1.1:
Martingales and dyadic Hardy spaces / 1.2:
Inequalities with respect to Hardy spaces / 1.3:
Atomic decomposition / 1.4:
Interpolation between Hardy spaces / 1.5:
Bounded operators on H[subscript p] / 1.6:
Multi-Dimensional Classical Hardy Spaces / 2.:
Distributions and Hardy spaces on R[superscript d] / 2.1:
The atomic decomposition of H[superscript square subscript p] / 2.3:
The atomic decomposition of H[subscript p] / 2.5:
Interpolation between classical Hardy spaces / 2.6:
Hardy spaces on T[superscript d] / 2.7:
Summability of D-Dimensional Walsh-Fourier Series / 3.:
(C, [alpha]) and Riesz summations / 3.1:
Estimations of the (C, [alpha]) and Riesz kernels / 3.3:
The boundedness of the maximal operators on L[subscript p] spaces / 3.4:
The boundedness of the maximal operators on Hardy spaces / 3.5:
Some weak type inequalities for the maximal operators / 3.6:
Marcinkiewicz-Fejer summability of Walsh-Fourier series / 3.7:
Vilenkin system / 3.8:
The D-Dimensional Dyadic Derivative / 4.:
The dyadic derivative and some estimations of the kernel function / 4.1:
The boundedness of I* on L[subscript p] spaces / 4.3:
The boundedness of I[subscript square] and I* on Hardy spaces / 4.4:
Vilenkin derivative / 4.5:
Summability of D-Dimensional Trigonometric-Fourier Series / 5.:
[theta]-summability of Fourier series / 5.1:
Some summability methods / 5.3:
The boundedness of the maximal [theta]-operator on L[subscript p] spaces / 5.4:
The boundedness of the maximal [theta]-operator on Hardy spaces / 5.5:
Marcinkiewicz-Cesaro summability of trigonometric-Fourier series / 5.6:
Summability of D-Dimensional Fourier Transforms / 6.:
[theta]-summability / 6.1:
Marcinkiewicz-[theta]-summability of Fourier transforms / 6.3:
Spline and Ciesielski Systems / 7.:
Hardy spaces and spline systems of higher order / 7.1:
The boundedness of some operators on L[subscript p] spaces / 7.3:
The boundedness of the maximal spline operators on Hardy spaces / 7.4:
Unconditional bases in multi-dimensional Hardy spaces / 7.5:
Bounded Ciesielski systems and Fejer kernels / 7.6:
The boundedness of the maximal Fejer-Ciesielski operators on L[subscript p] spaces / 7.7:
The boundedness of the maximal Fejer-Ciesielski operators on H[subscript p] spaces / 7.8:
References / 7.9:
Index
Preface
Acknowledgments
Multi-Dimensional Dyadic Hardy Spaces / 1.:
32.

図書

図書
editors, Toshikazu Sunada, Polly W Sy, Yang, Lo
出版情報: River Edge, N.J. : World Scientific, c2002  xviii, 613 p. ; 23 cm
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33.

図書

図書
Cho-Ho Chu, Anthony To-Ming Lau
出版情報: Berlin ; Tokyo : Springer-Verlag, c2002  100 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1782
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34.

図書

図書
Svetlana I. Boyarchenko, Sergei Z. Levendorskiĭ
出版情報: Singapore : World Scientific, c2002  xxi, 398 p. ; 23 cm
シリーズ名: Advanced series on statistical science & applied probability ; v. 9
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図書

図書
edited by Chaohua Jia and Kohji Matsumoto
出版情報: Dordrecht : Kluwer Academic, c2002  xv, 408 p. ; 25 cm
シリーズ名: Developments in mathematics ; v. 6
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Preface
On analytic continuation of multiple L-functions and related zeta-functions / Shigeki Akiyama ; Hideaki Ishikawa1:
On the values of certain q-hypergeometric series II / Masaaki Amou ; Masanori Katsurada ; Keijo Vaananen2:
The class number one problem for some non-normal sextic CM-fields / Gerard Boutteaux ; Stephane Louboutin3:
Ternary problems in additive prime number theory / Jorg Brudern ; Koichi Kawada4:
A generalization of E. Lehmer's congruence and its applications / Tianxin CAI5:
On Chen's theorem / Cai Yingchun ; Lu Minggao6:
On a twisted power mean of L(1, x) / Shigeki Egami7:
On the pair correlation of the zeros of the Riemann zeta function / Akio Fujii8:
Discrepancy of some special sequences / Kazuo Goto ; Yukio Ohkubo9:
Pade approximation to the logarithmic derivative of the Gauss hypergeometric function / Masayoshi Hata ; Marc Huttner10:
The evaluation of the sum over arithmetic progressions for the co-efficients of the Rankin-Selberg series II / Yumiko Ichihara11:
Substitutions, atomic surfaces, and periodic beta expansions / Shunji Ito ; Yuki Sano12:
The largest prime factor of integers in the short interval / Chaohua Jia13:
A general divisor problem in Landau's framework / S. Kanemitsu ; A. Sankaranarayanan14:
On inhomogeneous Diophantine approximation and the Borweins' algorithm, II / Takao Komatsu15:
Asymptotic expansions of double gamma-functions and related remarks / Kohji Matsumoto16:
A note on a certain average of L(1/2 + it, x) / Leo Murata17:
On covering equivalence / Zhi-Wei Sun18:
Certain words, tilings, their non-periodicity, and substitutions of high dimension / Jun-ichi Tamura19:
Determination of all Q-rational CM-points in moduli spaces of polarized abelian surfaces / Atsuki Umegaki20:
On families of cubic Thue equations / Isao Wakabayashi21:
Two examples of zeta-regularization / Masami Yoshimoto22:
A hybrid mean value formula of Dedekind sums and Hurwitz zeta-functions / Zhang Wenpeng23:
Preface
On analytic continuation of multiple L-functions and related zeta-functions / Shigeki Akiyama ; Hideaki Ishikawa1:
On the values of certain q-hypergeometric series II / Masaaki Amou ; Masanori Katsurada ; Keijo Vaananen2:
36.

図書

図書
by R. Beattie and H.-P. Butzmann
出版情報: Dordrecht : Kluwer Academic, c2002  xiii, 264 p. ; 25 cm
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目次情報: 続きを見る
Introduction
Convergence spaces / 1:
Preliminaries / 1.1:
Initial and final convergence structures / 1.2:
Special convergence spaces, modifications / 1.3:
Compactness / 1.4:
The continuous convergence structure / 1.5:
Countability properties and sequences in convergence spaces / 1.6:
Sequential convergence structures / 1.7:
Categorical aspects / 1.8:
Uniform convergence spaces / 2:
Generalities on uniform convergence spaces / 2.1:
Initial and final uniform convergence structures / 2.2:
Complete uniform convergence spaces / 2.3:
The Arzela-Ascoli theorem / 2.4:
The uniform convergence structure of a convergence group / 2.5:
Convergence vector spaces / 3:
Convergence groups / 3.1:
Generalities on convergence vector spaces / 3.2:
Initial and final vector space convergence structures / 3.3:
Projective and inductive limits of convergence vector spaces / 3.4:
The locally convex topological modification / 3.5:
Countability axioms for convergence vector spaces / 3.6:
Boundedness / 3.7:
Notes on bornological vector spaces / 3.8:
Duality / 4:
The dual of a convergence vector space / 4.1:
Reflexivity / 4.2:
The dual of a locally convex topological vector space / 4.3:
An application of continuous duality / 4.4:
Notes / 4.5:
Hahn-Banach extension theorems / 5:
General results / 5.1:
Hahn-Banach spaces / 5.2:
Extending to the adherence / 5.3:
Strong Hahn-Banach spaces / 5.4:
An application to partial differential equations / 5.5:
The closed graph theorem / 5.6:
Ultracompleteness / 6.1:
The main theorems / 6.2:
An application to web spaces / 6.3:
The Banach-Steinhaus theorem / 7:
Equicontinuous sets / 7.1:
Banach-Steinhaus pairs / 7.2:
The continuity of bilinear mappings / 7.3:
Duality theory for convergence groups / 8:
Duality for convergence vector spaces / 8.1:
Subgroups and quotient groups / 8.3:
Topological groups / 8.4:
Groups of unimodular continuous functions / 8.5:
c- and co-duality for topological groups / 8.6:
Bibliography
List of Notations
Index
Introduction
Convergence spaces / 1:
Preliminaries / 1.1:
37.

図書

図書
editors, H. Fujita, S.T. Kuroda, H. Okamoto
出版情報: Tokyo : University of Tokyo Press Production Center [producer] , Tokyo : Yurinsha [distoributor], c2002  viii, 284 p. ; 27 cm
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38.

図書

図書
P.G. Lemarié-Rieusset
出版情報: Boca Raton : Chapman & Hall/CRC, c2002  xii, 395 p. ; 24 cm
シリーズ名: Research notes in mathematics ; 431
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目次情報: 続きを見る
Introduction
What is this book about? / Chapter 1:
Some results of real harmonic analysis / Part 1:
Real interpolation, Lorentz spaces and Sobolev embeddings / Chapter 2:
Besov spaces and Littlewood-Paley decomposition / Chapter 3:
Shift-invariant Banach spaces of distributions and related Besov spaces / Chapter 4:
Vector-valued integrals / Chapter 5:
Complex interpolation, Hardy space and Calderon-Zygmund operators / Chapter 6:
Vector-valued singular integrals / Chapter 7:
A primer to wavelets / Chapter 8:
Wavelets and functional spaces / Chapter 9:
The space BMO / Chapter 10:
A general framework for shift-invariant estimates for the Navier-Stokes equations / Part 2:
Weak solutions for the Navier-Stokes equations / Chapter 11:
Divergence-free vector wavelets / Chapter 12:
The mollified Navier-Stokes equations / Chapter 13:
Classical existence results for the Navier-Stokes equations / Part 3:
The Leray solutions for the Navier-Stokes equations / Chapter 14:
The Kato theory of mild solutions for the Navier-Stokes equations / Chapter 15:
New approaches to mild solutions / Part 4:
The mild solutions of Koch and Tataru / Chapter 16:
Generalization of the L[superscript p] theory: Navier-Stokes and local measures / Chapter 17:
Further results for local measures / Chapter 18:
Regular initial values / Chapter 19:
Besov spaces of negative order / Chapter 20:
Pointwise multipliers of negative order / Chapter 21:
Further adapted spaces for the Navier-Stokes equations / Chapter 22:
Cannone's approach of self-similarity / Chapter 23:
Decay and regularity results for weak and mild solutions / Part 5:
Solutions of the Navier-Stokes equations are space-analytical / Chapter 24:
Space localization and Navier-Stokes equations / Chapter 25:
Time decay for the solutions to the Navier-Stokes equations / Chapter 26:
Uniqueness of L[superscript d] solutions / Chapter 27:
Further results on uniqueness of mild solutions / Chapter 28:
Stability and Lyapunov functionals / Chapter 29:
Local energy inequalities for the Navier-Stokes equations on IR[superscript 3] / Part 6:
The Caffarelli, Kohn, and Nirenberg regularity criterion / Chapter 30:
On the dimension of the set of singular points / Chapter 31:
Local existence (in time) of suitable local square-integrable weak solutions / Chapter 32:
Global existence of suitable local square-integrable weak solutions / Chapter 33:
Leray's conjecture on self-similar singularities / Chapter 34:
Conclusion
Singular initial values / Chapter 35:
References
Bibliography
Author index
Subject index
Introduction
What is this book about? / Chapter 1:
Some results of real harmonic analysis / Part 1:
39.

図書

図書
Paul C. Eklof, Alan H. Mekler
出版情報: Amsterdam : Elsevier, 2002  xxi, 597 p. ; 23 cm
シリーズ名: North-Holland mathematical library ; v. 65
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Algebraic Preliminaries / I:
Homomorphisms and extensions / 1:
Direct sums and products / 2:
Linear topologies / 3:
Set Theory / II:
Ordinary set theory
Filters and large cardinals
Ultraproducts
Clubs and stationary sets / 4:
Games and trees / 5:
utri;-systems and partitions / 6:
Slender Modules / III:
Introduction to slenderness
Examples of slender modules and rings
The Lstrok;os-Eda theorem
Almost Free Modules / IV:
Introduction to aleph; 1 free abelian groups / 0:
kgr;-free modules
aleph; 1 -free abelian groups
Compactness results
Pure Injective Modules / V:
Structure theory
Cotorsion groups
More Set Theory / VI:
Prediction Principles
Models of set theory
L, the constructible universe
MA and PFA
PCF theory and I [lgr;]
Almost Free Modules Revisisted (IV, VI) / VII:
aleph; 1 -free abelian groups revisited
kgr;-free modules revisited
kgr;-free abelian groups
Transversals, lgr;-systems and NPT
Reshuffling lgr;-systems / 3A:
Hereditarily separable groups
NPT and the construction of almost free groups
aleph; 1 -Separable Groups (VI, VII.0,1) / VIII:
Constructions and definitions
aleph; 1 -separable groups under Martin's axiom
aleph; 1 -separable groups under PFA
Quotients Of Products Of Z (III, IV, V) / IX:
Perps and products
Countable products of the integers
Uncountable products of the integers
Radicals and large cardinals
Iterated Sums And Products (III) / X:
The Reid class
Types in the Reid class
Topological Methods (X, IV) / XI:
Inverse and direct limits
Completions
Density and dual bases
Groups of continuous functions
Sheaves of abelian groups
An Analysis Of Ext (VII, VIII.1) / XII:
Ext and Diamond
Ext, MA and Proper forcing
Baer modules
The structure of Ext
The structure of Ext when Hom=0
Uniformization (XII) / XIII:
Whitehead groups and uniformization
The basic construction and its applications
The necessity of uniformization
The diversity of Whitehead groups
Monochromatic uniformization and hereditarily separable groups
The Black Box And Endomorphism Rings(V, VI) / XIV:
Introducing the Black Box
Proof of the Black Box
Endomorphism rings of cotorsion-free groups
Endomorphism rings of separable groups
Weak realizability of endomorphism rings and the Kaplansky Test problems
Some Constructions In ZFC (VII, VIII, XIV) / XV:
A rigid aleph; 1 -free group of cardinality aleph; 1
aleph; n -separable groups with the Corner pathology
Absolutely indecomposable modules
The existence of lgr;-separable groups
Cotorsion Theories, Covers And Splitters(IX, XII.1, XIV) / XVI:
Orthogonal classes and splitters
Cotorsion theories
Almost free splitters
The Black Box and Ext
Dual Groups (IX, XI, XIV) / XVII:
Invariants of dual groups
Tree groups
Criteria for being a dual group
Some non-reflexive groups
Dual groups in L
Algebraic Preliminaries / I:
Homomorphisms and extensions / 1:
Direct sums and products / 2:
40.

図書

図書
Gilberto Bini, Flaminio Flamini
出版情報: Boston : Kluwer Academic, c2002  x, 176 p. ; 25 cm
シリーズ名: The Kluwer international series in engineering and computer science
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41.

図書

図書
edited by Abdelmoujib Benkirane, Abdelfattah Touzani
出版情報: New York : M. Dekker, c2002  viii, 297 p. ; 26 cm
シリーズ名: Lecture notes in pure and applied mathematics ; v. 229
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Preface
Contributors
Nonresonance for a Nonautonomous Elliptic Problem with Respect to the Conical Fucik Spectrum / A. Addou ; B. Bentahar ; O. Chakrone1.:
Maximum and Antimaximum Principles for Some Elliptic Systems Involving Schrodinger Operators / Benedicte Alziary ; Naziha Besbas ; Laure Cardoulis ; Jacqueline Fleckinger2.:
Weak Solutions for Some Reaction-Diffusion Systems with Mass Control and Critical Growth with Respect to the Gradient / N. Alaa ; I. Mounir3.:
Fucik Spectrum for the Neumann Problem with Indefinite Weights / Mohssine Alif4.:
Decay of Mass for a Semilinear Parabolic System / L. Amour ; T. Raoux5.:
Maximum Principle for First Order Nonlinear Elliptic System / A. Anane ; Z. El Allali ; N. Tsouli6.:
Nonresonance Conditions on the Potential for a Neumann Problem / A. Dakkak7.:
Some Remarks on the Antimaximum Principle and the Fucik Spectrum for the p-Laplacian / M. Arias8.:
Existence Result for a Second Order Nonlinear Degenerate Elliptic Equation in Weighted Orlicz-Sobolev Spaces / E. Azroul ; Abdelmoujib Benkirane9.:
Existence of Renormalized Solutions for Some Elliptic Problems Involving Derivatives of Nonlinear Terms in Orlicz Spaces / J. Bennouna10.:
On a Necessary Condition for Some Strongly Nonlinear Elliptic Equations in R[superscript n] / M. Kbiri Alaoui11.:
On the Regularizing Effect of Strongly Increasing Lower Order Terms / Lucio Boccardo12.:
On the Asymptotic Behavior of Solutions of a Damped Oscillator under a Sublinear Friction Term: From the Exceptional to the Generic Behaviors / J. I. Diaz ; A. Linan13.:
Landesman-Lazer Problems for the p-Laplacian / P. Drabek ; S. Robinson14.:
Optimal BMO and [pound superscript p.[lambda] Estimates Near the Boundary for Solutions of a Class of Degenerate Elliptic Problems / A. El Baraka15.:
On the First Eigencurve of the p-Laplacian / A. Elkhalil ; Abdelfattah Touzani16.:
Compactness Results in Inhomogeneous Orlicz-Sobolev Spaces / A. Elmahi17.:
On a Degenerate Parabolic Equation with Nonlocal Reaction Term / Abdelilah Gmira ; Rachid Eloulaimi18.:
Existence of Nontrivial Solutions for Some Elliptic Systems in R[superscript 2] / S. El Manouni19.:
Viscosity Solution for a Degenerate Parabolic Problem / Mohamed Maliki20.:
Remarks on Inhomogeneous Elliptic Eigenvalue Problems / Vesa Mustonen ; Matti Tienari21.:
On the First Curve of the Fucik Spectrum of an Elliptic Operator with Weight / N. Nakbi22.:
Asymptotics of Solutions of Quasilinear Parabolic Equations via the Refined Energy Method and Semiclassical Limit of Schrodinger Operators / Laurent Veron23.:
Preface
Contributors
Nonresonance for a Nonautonomous Elliptic Problem with Respect to the Conical Fucik Spectrum / A. Addou ; B. Bentahar ; O. Chakrone1.:
42.

図書

図書
by N.M. Ferrers
出版情報: London : Macmillan, 1890  xiv, 184 p. ; 19 cm
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43.

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
44.

図書

図書
Valery Rubakov ; translated by Stephen S. Wilson
出版情報: Princeton : Princeton University Press, c2002  x, 444 p. ; 24 cm
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Preface
Gauge Principle in Electrodynamics / Part I:
Electromagnetic-field action in vacuum / 1.1:
Gauge invariance / 1.2:
General solution of Maxwell's equations in vacuum / 1.3:
Choice of gauge / 1.4:
Scalar and Vector Fields / Chapter 2:
System of units h = c = 1 / 2.1:
Scalarfield action / 2.2:
Massive vectorfield / 2.3:
Complex scalarfield / 2.4:
Degrees of freedom / 2.5:
Interaction offields with external sources / 2.6:
Interactingfields. Gauge-invariant interaction in scalar electrodynamics / 2.7:
Noether's theorem / 2.8:
Elements of the Theory of Lie Groups and Algebras / Chapter 3:
Groups / 3.1:
Lie groups and algebras / 3.2:
Representations of Lie groups and Lie algebras / 3.3:
Compact Lie groups and algebras / 3.4:
Non-Abelian Gauge Fields / Chapter 4:
Non-Abelian global symmetries / 4.1:
Non-Abelian gauge invariance and gaugefields: the group SU(2) / 4.2:
Generalization to other groups / 4.3:
Field equations / 4.4:
Cauchy problem and gauge conditions / 4.5:
Spontaneous Breaking of Global Symmetry / Chapter 5:
Spontaneous breaking of discrete symmetry / 5.1:
Spontaneous breaking of global U(1) symmetry. Nambu-Goldstone bosons / 5.2:
Partial symmetry breaking: the SO(3) model / 5.3:
General case. Goldstone's theorem / 5.4:
Higgs Mechanism / Chapter 6:
Example of an Abelian model / 6.1:
Non-Abelian case: model with complete breaking of SU(2) symmetry / 6.2:
Example of partial breaking of gauge symmetry: bosonic sector of standard electroweak theory / 6.3:
Supplementary Problems for
The Simplest Topological Solitons / Part II:
Kink / 7.1:
Scale transformations and theorems on the absence of solitons / 7.2:
The vortex / 7.3:
Soliton in a model of n-field in (2 + 1)-dimensional space-time / 7.4:
Elements of Homotopy Theory / Chapter 8:
Homotopy of mappings / 8.1:
The fundamental group / 8.2:
Homotopy groups / 8.3:
Fiber bundles and homotopy groups / 8.4:
Summary of the results / 8.5:
Magnetic Monopoles / Chapter 9:
The soliton in a model with gauge group SU(2) / 9.1:
Magnetic charge / 9.2:
Generalization to other models / 9.3:
The limit mh/mv 0 / 9.4:
Dyons / 9.5:
Non-Topological Solitons / Chapter 10:
Tunneling and Euclidean Classical Solutions in Quantum Mechanics / Chapter 11:
Decay of a metastable state in quantum mechanics of one variable / 11.1:
Generalization to the case of many variables / 11.2:
Tunneling in potentials with classical degeneracy / 11.3:
Decay of a False Vacuum in Scalar Field Theory / Chapter 12:
Preliminary considerations / 12.1:
Decay probability: Euclidean bubble (bounce) / 12.2:
Thin-wall approximation / 12.3:
Instantons and Sphalerons in Gauge Theories / Chapter 13:
Euclidean gauge theories / 13.1:
Instantons in Yang-Mills theory / 13.2:
Classical vacua and 0-vacua / 13.3:
Sphalerons in four-dimensional models with the Higgs mechanism / 13.4:
Fermions in Background Fields / Part III:
Free Dirac equation / 14.1:
Solutions of the free Dirac equation. Dirac sea / 14.2:
Fermions in background bosonicfields / 14.3:
Fermionic sector of the Standard Model / 14.4:
Fermions and Topological External Fields in Two-dimensional Models / Chapter 15:
Charge fractionalization / 15.1:
Level crossing and non-conservation of fermion quantum numbers / 15.2:
Fermions in Background Fields of Solitons and Strings in Four-Dimensional Space-Time / Chapter 16:
Fermions in a monopole backgroundfield: integer angular momentum and fermion number fractionalization / 16.1:
Scattering of fermions off a monopole: non-conservation of fermion numbers / 16.2:
Zero modes in a backgroundfield of a vortex: superconducting strings / 16.3:
Preface
Gauge Principle in Electrodynamics / Part I:
Electromagnetic-field action in vacuum / 1.1:
45.

図書

図書
Seiichi Kamada
出版情報: Providence, R.I. : American Mathematical Society, c2002  xiii, 313 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; v. 95
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46.

図書

図書
by David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
出版情報: Dordrecht : Kluwer Academic, c2002  xvi, 643 p. ; 25 cm
シリーズ名: Mathematics and its applications ; Vol.543
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Preface
Acknowledgments
Basic notation
Hardy-Type Operators / 1.:
Boundedness and compactness in BFS / 1.1:
An extension of the Hardy transform / 1.2:
Estimates for approximation numbers / 1.3:
Norms of positive operators / 1.4:
Notes and comments on Chapter 1 / 1.5:
Fractional Integrals on the Line / 2.:
Fractional integrals / 2.1:
Two-weight problems / 2.2:
Trace inequalities ("Diagonal case"). Examples / 2.3:
Weak-type inequalities. Examples / 2.4:
Integral transforms with power- logarithmic kernels / 2.5:
Erdelyi-Kober operators / 2.6:
Integral transforms with positive kernels / 2.7:
Extended Erdelyi-Kober operators / 2.8:
Generalized one-sided potentials / 2.9:
One-sided potentials on the half-space / 2.10:
Weighted criteria in Lorentz spaces / 2.11:
Applications to Abel's integral equations / 2.12:
On some Volterra-type integral equations / 2.13:
Application to the existence of positive solutions of nonlinear integral equations / 2.14:
Notes and comments on Chapter 2 / 2.15:
One-Sided Maximal Functions / 3.:
One-sided maximal functions / 3.1:
Mapping properties of potentials on the line / 3.2:
Potentials T[subscript gamma] on the line (the case 0 [less than sign] [gamma] [less than sign] 1/p) / 3.3:
Weak-type inequalities / 3.4:
Potentials on bounded intervals / 3.5:
Two-weight criteria for fractional maximal functions / 3.6:
Generalized one-sided maximal functions / 3.7:
Potentials with power-logarithmic kernels / 3.8:
Multiple potentials / 3.9:
One-sided Hormander-type maximal functions / 3.10:
Notes and comments on Chapter 3 / 3.11:
Ball Fractional Integrals / 4.:
Boundedness criteria / 4.1:
Compactness criteria / 4.2:
The measure of non-compactness / 4.3:
Mapping properties in Lorentz spaces / 4.4:
Notes and comments on Chapter 4 / 4.5:
Potentials on R[superscript N] / 5.:
Truncated potentials / 5.1:
Two-weight compactness conditions for Riesz potentials / 5.2:
Integral transforms with radial kernels / 5.3:
Notes and comments on Chapter 5 / 5.4:
Fractional Integrals on Measure Spaces / 6.:
Integral transforms on nonhomogeneous spaces / 6.1:
Theorems of Adams type / 6.2:
Truncated potentials on SHT / 6.3:
Riesz potentials in the half-space / 6.4:
Truncated potentials in the half-space / 6.5:
Two-weight (p, p) type inequalities / 6.6:
Theorems of Koosis type / 6.7:
Fractional maximal functions on SHT / 6.8:
Weighted estimates in Lorentz spaces / 6.9:
Notes and comments on Chapter 6 / 6.10:
Singular Numbers / 7.:
Volterra integral operators / 7.1:
Riemann-Liouville-type operators / 7.2:
Potential-type operators / 7.3:
Hardy-type operators / 7.4:
Asymptotic behaviour of singular and entropy numbers / 7.5:
Notes and comments on Chapter 7 / 7.6:
Singular Integrals / 8.:
Two-weight strong-type estimates / 8.1:
Weak-type estimates / 8.2:
Singular integrals on nonhomogeneous spaces / 8.3:
Two-weight inequalities for the Hilbert transform / 8.4:
Estimates in Lorentz spaces / 8.5:
Cauchy-Szego projection / 8.6:
Singular integrals via Clifford analysis / 8.7:
Notes and comments on Chapter 8 / 8.8:
Multipliers of Fourier Transforms / 9.:
Weighted Triebel-Lizorkin spaces / 9.1:
Two-weight multipliers in Triebel-Lizorkin spaces / 9.2:
(F[superscript q, theta] [subscript beta, omega] F[superscript p,theta] [subscript beta, upsilon]) multipliers. The case 1 [less than sign] q [less than or equal] p [less than sign] [infinity] / 9.3:
Multipliers in weighted spaces with mixed norms / 9.4:
Examples / 9.5:
Notes and comments on Chapter 9 / 9.6:
Problems / 10.:
References
Index
Preface
Acknowledgments
Basic notation
47.

図書

図書
Burger, Marc ; Iozzi, Alessandra
出版情報: Berlin ; Tokyo : Springer-Verlag, c2002  492 p. ; 24 cm
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48.

図書

図書
Vladas Sidoravicius, editor
出版情報: Boston : Birkhäuser, c2002  vi, 472 p. ; 25 cm
シリーズ名: Progress in probability / series editors, Thomas Liggett, Charles Newman, Loren Pitt ; v. 51
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49.

図書

図書
Simon Thomas, editor
出版情報: Providence, RI : American Mathematical Society, c2002  xi, 160 p. ; 27 cm
シリーズ名: DIMACS series in discrete mathematics and theoretical computer science ; v. 58
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Containment does not imply Borel reducibility / S. Adams
Hajnal's contributions to combinatorial set theory and the partition calculus / J. E. Baumgartner
Multicolored graphs on countable ordinals of finite exponent / C. Darby ; J. A. Larson
On $D$-spaces and discrete families of sets / M. Dzamonja
Analytic Hausdorff gaps / I. Farah
Stationary sets, Chang's conjecture and partition theory / M. D. Foreman
A consistent example of a hereditarily $\mathfrak{c}$-Lindelof first countable space of size $>\mathfrak{c}$ / I. Juhasz ; L. Soukup ; Z. Szentmiklossy
Subgraph chromatic number / P. Komjath
Superatomic Boolean algebras: Maximal rigidity / S. Shelah
Some applications of superrigidity to Borel equivalence relations / S. Thomas
Localized reflection and fragments of PFA / S. Todorcevic
The basis problem for CCC posets / B. Velickovic
Containment does not imply Borel reducibility / S. Adams
Hajnal's contributions to combinatorial set theory and the partition calculus / J. E. Baumgartner
Multicolored graphs on countable ordinals of finite exponent / C. Darby ; J. A. Larson
50.

図書

図書
C. Rogers, W.K. Schief
出版情報: Cambridge : Cambridge University Press, 2002  xvii, 413 p. ; 23-24 cm
シリーズ名: Cambridge texts in applied mathematics
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51.

図書

図書
Gabor Toth
出版情報: New York : Springer, c2002  xxii, 450 p., [4] p. of plates ; 25 cm
シリーズ名: Undergraduate texts in mathematics ; . Reading in mathematics
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"A Number is a multitude composed of units" (Euclid)
"..there are no irrational numbers at all" (Kronecker)
Rationality, Elliptic Curves and Fermat's Last Theorem
Algebraic or Transcendential?
Complex Arithmetic
Quadratic, Cubic, and Quartic Equations
Stereographic Projection
Proof of the Fundamental Theorem of Algebra
Symmetries of Regular Polygons
Discrete Subgroups of Iso(R^2)
Mobius Geometry
Complex Linear Fractional Transformations
"Out of nothing I have created a new universe" (Bolyai)
Fuchsian Groups
Riemann Surfaces
General Surfaces
The Five Platonic Solids
Finite Mobius Groups
Detour in Topology: Euler-Poincare Characteristic
Detour in Graph Theory: Euler, Hamilton and the Four Color Theorem
Dimension Leap
Quaternions
Back to R^3!
Invariants
The Icosahedron and the Unsolvable Quintic
The Fourth Dimension
Appendices
Solutions for 100 Selected Problems
Index
"A Number is a multitude composed of units" (Euclid)
"..there are no irrational numbers at all" (Kronecker)
Rationality, Elliptic Curves and Fermat's Last Theorem
52.

図書

図書
Harm Derksen, Gregor Kemper
出版情報: Berlin ; Tokyo : Springer, c2002  x, 268 p. ; 24 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 130 . Invariant theory and algebraic transformation groups ; 1
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53.

図書

図書
S. S. Vinogradov, P. D. Smith, E. D. Vinogradova
出版情報: Boca Raton, Fla. : Chapman & Hall/CRC, c2002  xii, 503 p. ; 25 cm
シリーズ名: Chapman & Hall/CRC monographs and surveys in pure and applied mathematics ; 127 . Canonical problems in scattering and potential theory ; pt. 2
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Preface
Mathematical Aspects of Wave Scattering / 1:
The Equations of Acoustic and Electromagnetic Waves / 1.1:
Solution of the Helmholtz Equation: Separation of Variables / 1.2:
Fields of Elementary Sources. Green's Functions / 1.3:
Representations of Incident Electromagnetic Waves / 1.4:
Formulation of Wave Scattering Theory for Structures with Edges / 1.5:
Single- or Double-Layer Surface Potentials and Dual Series Equations / 1.6:
A Survey of Methods for Scattering / 1.7:
Acoustic Diffraction from a Circular Hole in a Thin Spherical Shell / 2:
Plane Wave Diffraction from a Soft or Hard Spherical Cap / 2.1:
Rigorous Theory of the Spherical Helmholtz Resonator / 2.2:
Quasi-Eigenoscillations: Spectrum of the Open Spherical Shell / 2.3:
Total and Sonar Cross-Sections / 2.4:
Rayleigh Scattering / 2.4.1:
Resonance Region / 2.4.2:
High Frequency Regime / 2.4.3:
The Mechanical Force Factor / 2.5:
The Focal Region of a Spherical Reflector Antenna / 2.6:
The Transmitting Spherical Reflector Antenna / 2.7:
Complex Point Source / 2.7.1:
Regularised Solution and Far-Field Characteristics / 2.7.2:
Numerical Results / 2.7.3:
Acoustic Diffraction from Various Spherical Cavities / 3:
The Hard Spherical Barrel and Soft Slotted Spherical Shell / 3.1:
The Soft Spherical Barrel and Hard Slotted Spherical Shell / 3.2:
Helmholtz Resonators: Barrelled or Slotted Spherical Shells / 3.3:
Quasi-Eigenoscillations of the Spherical Cavity / 3.4:
Total and Sonar Cross-Sections; Mechanical Force Factor / 3.5:
Electromagnetic Diffraction from a Metallic Spherical Cavity / 4:
Electric or Magnetic Dipole Excitation / 4.1:
The Vertical Electric Dipole (TM Case) / 4.1.1:
The Vertical Magnetic Dipole (TE Case) / 4.1.2:
Plane Wave Diffraction from a Circular Hole in a Thin Metallic Sphere / 4.2:
Reflectivity of Open Spherical Shells / 4.3:
The Focal Region of a Receiving Spherical Reflector Antenna / 4.4:
The Complex-Point Huygens Source: Debye Potentials / 4.5:
Excitation of the Reflector by a CPHS / 4.5.2:
Electromagnetic Diffraction from Various Spherical Cavities / 4.5.3:
EM Plane Wave Scattering by Two Concentric Spherical Shells / 5.1:
Dipole Excitation of a Slotted Sphere / 5.2:
The Vertical Electric Dipole / 5.2.1:
The Vertical Magnetic Dipole / 5.2.2:
Dipole Excitation of Doubly-Connected Spherical Shells / 5.3:
Plane Wave Diffraction: Perfectly Conducting Slotted Spherical Shell / 5.4:
Magnetic Dipole Excitation of an Open Spherical Resonator / 5.5:
Open Resonators Composed of Spherical and Disc Mirrors / 5.6:
Spherical Cavities with Spherical Dielectric Inclusions / 6:
Resonant Cavity Heating of a Small Lossy Dielectric Sphere / 6.1:
Reflectivity of a Partially Screened Dielectric Sphere / 6.2:
The Luneberg Lens Reflector / 6.3:
Diffraction from Spheroidal Cavities / 7:
Regularisation in Spheroidal Coordinates / 7.1:
Acoustic Scattering by a Rigid Spheroidal Shell with a Circular Hole / 7.2:
Rigorous Theory of the Spheroidal Helmholtz Resonator / 7.3:
Axial Electric Dipole Excitation of a Metallic Spheroidal Cavity / 7.4:
Axial Magnetic Dipole Excitation of a Metallic Spheroidal Cavity / 7.5:
Axial Electric Dipole Excitation of a Spheroidal Barrel / 7.6:
The Series Equations with Odd Index Coefficients / 7.6.1:
The Series Equations with Even Index Coefficients / 7.6.2:
Impedance Loading of the Spheroidal Barrel / 7.6.3:
Spheroid Embedded in a Spheroidal Cavity with Two Holes / 7.8:
Wave Scattering Problems for Selected Structures / 8:
Plane Wave Diffraction from Infinitely Long Strips / 8.1:
Axially Slotted Infinitely Long Circular Cylinders / 8.2:
Axially Slotted Cylinders of Arbitrary Profile / 8.3:
Diffraction from Circular Discs / 8.4:
Diffraction from Elliptic Plates / 8.5:
Wave Scattering Problems for Hollow Finite Cylinders / 8.6:
Wave Scattering Problems for Periodic Structures / 8.7:
Periodic Linear Array of Strips / 8.7.1:
Periodic Linear Array of Hollow Finite Cylinders / 8.7.2:
Shielded Microstrip Lines / 8.8:
References
Index
Preface
Mathematical Aspects of Wave Scattering / 1:
The Equations of Acoustic and Electromagnetic Waves / 1.1:
54.

図書

図書
Béla Bollobás (ed.)
出版情報: Berlin : Springer , Budapest : János Bolyai Mathematical Society, 2002  301 p. ; 25 cm
シリーズ名: Bolyai Society mathematical studies ; 10
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55.

図書

図書
A.Yu. Kitaev, A.H. Shen, M.N. Vyalyi ; [translated from the Russian by Lester J. Senechal]
出版情報: Providence, R.I. : American Mathematical Society, c2002  xiii, 257 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 47
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56.

図書

図書
edited by Kenji Fukaya, Seiki Nishikawa and Joel Spruck
出版情報: Tokyo : Mathematical Society of Japan, c2002  259 p. ; 24 cm
シリーズ名: Advanced studies in pure mathematics ; 34
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57.

図書

図書
Yu.Ya. Belov
出版情報: Utrecht : VSP, 2002  viii, 211 p. ; 25 cm
シリーズ名: Inverse and ill-posed problems series
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58.

図書

図書
S.G. Pyatkov
出版情報: Utrecht : VSP, 2002  ix, 346 p. ; 25 cm
シリーズ名: Inverse and ill-posed problems series
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59.

図書

図書
editors V. F. Kolchin ... [et. al.]
出版情報: Utrecht : VSP, c2002  x, 389 p. ; 25 cm
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60.

図書

図書
Rüdiger Seydel
出版情報: Berlin : Tokyo : Springer, c2002  xiv, 224 p. ; 24 cm
シリーズ名: Universitext
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目次情報: 続きを見る
Prefaces
Contents
Notation
Modeling Tools for Financial Options / Chapter 1:
Options / 1.1:
Model of the Financial Market / 1.2:
Numerical Methods / 1.3:
The Binomial Method / 1.4:
Risk-Neutral Valuation / 1.5:
Stochastic Processes / 1.6:
Wiener Process / 1.6.1:
Stochastic Integral / 1.6.2:
Stochastic Differential Equations / 1.7:
Ito Process / 1.7.1:
Application to the Stock Market / 1.7.2:
Ito Lemma and Implications / 1.8:
Jump Processes / 1.9:
Notes and Comments
Exercises
Generating Random Numbers with Specified Distributions / Chapter 2:
Pseudo-Random Numbers / 2.1:
Linear Congruential Generators / 2.1.1:
Random Vectors / 2.1.2:
Fibonacci Generators / 2.1.3:
Transformed Random Variables / 2.2:
Inversion / 2.2.1:
Transformation in IR[superscript 1] / 2.2.2:
Transformation in IR[superscript n] / 2.2.3:
Normally Distributed Random Variables / 2.3:
Method of Box and Muller / 2.3.1:
Variant of Marsaglia / 2.3.2:
Correlated Random Variables / 2.3.3:
Sequences of Numbers with Low Discrepancy / 2.4:
Monte Carlo Integration / 2.4.1:
Discrepancy / 2.4.2:
Examples of Low-Discrepancy Sequences / 2.4.3:
Numerical Integration of Stochastic Differential Equations / Chapter 3:
Approximation Error / 3.1:
Stochastic Taylor Expansion / 3.2:
Examples of Numerical Methods / 3.3:
Intermediate Values / 3.4:
Monte Carlo Simulation / 3.5:
The Basic Version / 3.5.1:
Variance Reduction / 3.5.2:
Finite Differences and Standard Options / Chapter 4:
Preparations / 4.1:
Foundations of Finite-Difference Methods / 4.2:
Difference Approximation / 4.2.1:
The Grid / 4.2.2:
Explicit Method / 4.2.3:
Stability / 4.2.4:
Implicit Method / 4.2.5:
Crank-Nicolson Method / 4.3:
Boundary Conditions / 4.4:
American Options as Free Boundary-Value Problems / 4.5:
Free Boundary-Value Problems / 4.5.1:
Black-Scholes Inequality / 4.5.2:
Obstacle Problems / 4.5.3:
Linear Complementarity for American Put Options / 4.5.4:
Computation of American Options / 4.6:
Discretization with Finite Differences / 4.6.1:
Iterative Solution / 4.6.2:
Algorithm for Calculating American Options / 4.6.3:
On the Accuracy / 4.7:
Finite-Element Methods / Chapter 5:
Weighted Residuals / 5.1:
The Principle of Weighted Residuals / 5.1.1:
Examples of Weighting Functions / 5.1.2:
Examples of Basis Functions / 5.1.3:
Galerkin Approach with Hat Functions / 5.2:
Hat Functions / 5.2.1:
A Simple Application / 5.2.2:
Application to Standard Options / 5.3:
Error Estimates / 5.4:
Classical and Weak Solutions / 5.4.1:
Approximation on Finite-Dimensional Subspaces / 5.4.2:
Cea's Lemma / 5.4.3:
Pricing of Exotic Options / Chapter 6:
Exotic Options / 6.1:
Asian Options / 6.2:
The Payoff / 6.2.1:
Modeling in the Black-Scholes Framework / 6.2.2:
Reduction to a One-Dimensional Equation / 6.2.3:
Discrete Monitoring / 6.2.4:
Numerical Aspects / 6.3:
Convection-Diffusion Problems / 6.3.1:
Von Neumann Stability Analysis / 6.3.2:
Upwind Schemes and Other Methods / 6.4:
Upwind Scheme / 6.4.1:
Dispersion / 6.4.2:
High-Resolution Methods / 6.5:
The Lax-Wendroff Method / 6.5.1:
Total Variation Diminishing / 6.5.2:
Numerical Dissipation / 6.5.3:
Appendices
Financial Derivatives / A1:
Essentials of Stochastics / A2:
The Black-Scholes Equation / A3:
Iterative Methods for Ax = b / A4:
Function Spaces / A6:
Complementary Formula / A7:
References
Index
Prefaces
Contents
Notation
61.

図書

図書
Ingo Lieb, Joachim Michel
出版情報: Braunschweig : Vieweg, 2002  x, 362 p. ; 25 cm
シリーズ名: Aspects of mathematics = Aspekte der Mathematik ; v. E34
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62.

図書

図書
edited by N. Kenmochi, M. Niezgódka, M. Ôtani
出版情報: Tokyo : Gakkōtosho, c2002  396 p. ; 27 cm
シリーズ名: GAKUTO international series ; . Mathematical sciences and applications ; vol. 17
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63.

図書

図書
editors, V.G. Gurzadyan, A.G. Sedrakian
出版情報: Singapore : World Scientific, c2002  viii, 317 p. ; 23 cm
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64.

図書

図書
Alain Bensoussan, Jens Frehse
出版情報: Berlin ; Tokyo : Springer-Verlag, c2002  xii, 440 p. ; 24 cm
シリーズ名: Applied mathematical sciences ; v. 151
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65.

図書

図書
Y. Eliashberg, N. Mishachev
出版情報: Providence, R.I. : American Mathematical Society, c2002  xvii, 206 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 48
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Intrigue Holonomic approximation: Jets and holonomy
Thom transversality theorem Holonomic approximation
Applications Differential relations and Gromov's $h$-principle: Differential relations
Homotopy principle Open Diff $V$-invariant differential relations
Applications to closed manifolds
The homotopy principle in symplectic geometry: Symplectic and contact basics
Symplectic and contact structures on open manifolds
Symplectic and contact structures on closed manifolds
Embeddings into symplectic and contact manifolds
Microflexibility and holonomic $\mathcal{R}$-approximation
First applications of microflexibility
Microflexible $\mathfrak{U}$-invariant differential relations
Further applications to symplectic geometry
Convex integration: One-dimensional convex integration
Homotopy principle for ample differential relations
Directed immersions and embeddings
First order linear differential operators Nash-Kuiper theorem
Bibliography
Index
Intrigue Holonomic approximation: Jets and holonomy
Thom transversality theorem Holonomic approximation
Applications Differential relations and Gromov's $h$-principle: Differential relations
66.

図書

図書
Ingrid Bauer ... [et al.] (editors)
出版情報: Berlin ; Tokyo : Springer, c2002  xxii, 340 p. ; 24 cm
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67.

図書

図書
Veli-Matti Hokkanen, Gheorghe Moroșanu
出版情報: Boca Raton, Fla. : Chapman & Hall/CRC, c2002  xiii, 243 p. ; 24 cm
シリーズ名: Research notes in mathematics ; 432
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Introduction
Preliminaries / 1:
Function and distribution spaces / 1.1:
Monotone operators, convex functions, and subdifferentials / 1.2:
Some elements of spectral theory / 1.3:
Linear evolution equations and semigroups / 1.4:
Nonlinear evolution equations / 1.5:
Elliptic boundary value problems / 2:
Nondegenerate elliptic boundary value problems / 2.1:
Degenerate elliptic boundary value problems / 2.2:
Parabolic problems with algebraic boundary conditions / 3:
Homogeneous boundary conditions / 3.1:
Nonhomogeneous boundary conditions / 3.2:
Higher regularity of solutions / 3.3:
Parabolic problems with algebraic-differential boundary conditions / 4:
Homogeneous algebraic boundary conditions / 4.1:
Nonhomogeneous algebraic boundary condition / 4.2:
Hyperbolic problems with algebraic boundary conditions / 4.3:
Existence, uniqueness, and long-time behavior of solutions / 5.1:
Hyperbolic problems with algebraic-differential boundary conditions / 5.2:
The Fourier method for abstract differential equations / 6.1:
First order linear equations / 7.1:
Semilinear first order equations / 7.2:
Second order linear equations / 7.3:
Semilinear second order equations / 7.4:
The semigroup approach for abstract differential equations / 8:
Hyperbolic partial differential systems with nonlinear boundary conditions / 8.1:
Nonlinear nonautonomous abstract differential equations / 9:
First order differential and functional equations containing subdifferentials / 9.1:
An application / 9.2:
Implicit nonlinear differential equations / 10:
Existence of solution / 10.1:
Uniqueness of solution / 10.2:
Continuous dependence of solution / 10.3:
Existence of periodic solutions / 10.4:
Index
Introduction
Preliminaries / 1:
Function and distribution spaces / 1.1:
68.

図書

図書
Susumu Ariki
出版情報: Providence, R.I. : American Mathematical Society, c2002  vii, 158 p. ; 26 cm
シリーズ名: University lecture series ; 26
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Introduction
The Serre relations Kac-Moody Lie algebras
Crystal bases of $U_v$-modules
The tensor product of crystals
Crystal bases of $U_v^-$
The canonical basis
Existence and uniqueness (part I)
Existence and uniqueness (part II)
The Hayashi realization Description of the crystal graph of $V(\Lambda)$
An overview of the application to Hecke algebras
The Hecke algebra of type $G(m,1,n)$
The proof of Theorem 12.5
Reference guide
Bibliography
Index
Introduction
The Serre relations Kac-Moody Lie algebras
Crystal bases of $U_v$-modules
69.

図書

図書
by W.W. Rouse Ball
出版情報: London : Macmillan, 1888  xxiii, 464 p. ; 20 cm
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70.

図書

図書
Adrian I. Ban & Sorin G. Gal
出版情報: New Jersey : World Scientific, c2002  xi, 352 p. ; 23 cm
シリーズ名: Series on concrete and applicable mathematics ; vol. 5
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71.

図書

図書
edited by Sever S. Dragomir and Themistocles M. Rassias
出版情報: Dordrecht : Kluwer, c2002  xix, 481 p. ; 25 cm
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List of Figures
List of Tables
Preface
Symbols List
Generalisations of the Ostrowski Inequality and Applications / Sever S. Dragomir ; Themistocles M. Rassias1:
Introduction
Generalisations for Functions of Bounded Variation / 2:
Some Inequalities / 2.1:
A General Quadrature Formula / 2.2:
Particular Inequalities / 2.3:
Particular Quadrature Formulae / 2.4:
Generalisations for Functions whose Derivatives are in L[subscript infinity] / 3:
Generalisation for Functions whose Derivatives are in L[subscript p] / 3.1:
General Quadrature Formulae / 4.1:
Generalisations in Terms of L[subscript 1]-norm / 4.3:
Integral Inequalities for n-Times Differentiable Mappings / Anthony Sofo5.1:
Integral Identities
Integral Inequalities
The Convergence of a General Quadrature Formula
Gruss Type Inequalities
Some Particular Integral Inequalities / 6:
Applications for Numerical Integration / 7:
Concluding Remarks / 8:
Three Point Quadrature Rules / Pietro Cerone
Bounds Involving at most a First Derivative
Inequalities Involving the First Derivative
Application in Numerical Integration
A Generalized Ostrowski-Gruss Inequality Using Cauchy-Schwartz
A Generalized Ostrowski Gruss Inequality Via a New Identity
Inequalities for which the First Derivative Belongs to L[subscript 1] [a, b] / 2.5:
Gruss-type Inequalities for Functions whose First Derivative Belongs to L[subscript 1] [a, b] / 2.6:
Inequalities for which the First Derivative Belongs to L[subscript p] [a, b] / 2.7:
Gruss-type Inequalities for Functions whose First Derivative Belongs to L[subscript p] [a, b] / 2.8:
Three Point Inequalities for Mappings of Bounded Variation, Lipschitzian or Monotonic / 2.9:
Conclusion and Discussion / 2.10:
Bounds for n--Time Differentiable Functions
Some Integral Identities
Perturbed Rules Through Gruss Type Inequalities
Perturbed Rules From Premature Inequalities / 3.5:
Applications in Numerical Integration / 3.6:
Product Branched Peano Kernels and Numerical Integration / 3.7:
Fundamental Results
Simpson Type Formulae
Perturbed Results
More Perturbed Results Using [Delta] - Seminorms
Ostrowski Type Inequalities for Multiple Integrals / Neil S. Barnett
An Ostrowski Type Inequality for Double Integrals
Some Inequalities in Terms of [double vertical line] . [double vertical line subscript infinity]--Norm
Applications for Cubature Formulae
Some Inequalities in Terms of [double vertical line] . [double vertical line subscript p]--Norm
Applications For Cubature Formulae
Some Inequalities in Terms of [double vertical line] . [double vertical line subscript 1]--Norm
Other Ostrowski Type Inequalities
Some Identities
Some Bounds
Ostrowski's Inequality for Holder Type Functions
The Unweighted Case
The Weighted Case
Results for Double Integrals Based on an Ostrowski Type Inequality / George Hanna
Techniques for Two Dimensional Integrals
Mappings Whose First Derivative Belongs to L[subscript infinity a, b] / 1.1:
Application to Cubature Formulae / 1.3:
Mappings Whose First Derivative Belongs to L[subscript p a, b] / 1.4:
Mappings Whose First Derivative Belongs to L[subscript 1](a, b) / 1.5:
Numerical Results / 1.7:
A General Ostrowski Type Inequality for Double Integrals
Some Integral Inequalities
Applications to Numerical Integration
Product Inequalities and Weighted Quadrature / John Roumeliotis
Weight Functions
Interior Point Inequalities
Two Interior Points
Some Weighted Integral Inequalities
Uniform (Legendre) / 3.2.1:
Logarithm / 3.2.2:
Jacobi / 3.2.3:
Chebyshev / 3.2.4:
Laguerre / 3.2.5:
Hermite / 3.2.6:
Weighted Boundary Point (Lobatto) Integral Inequalities
Development of a Product-Trapezoidal Like Quadrature Rule
Numerical Experiment
Some Particular Weighted Integral Inequalities
Weighted Three Point Integral Inequalities / 4.3.1:
Development of a Quadrature Rule
Application of Gruss Type Inequalities / 5.1.1:
Gruss-type Inequalities for Some Weight Functions
Legendre / 5.3.1:
Some Inequalities for the Riemann-Stieltjes Integral / 5.3.2:
Some Trapezoid Like Inequalities for Riemann-Stieltjes Integral
A Trapezoid Formula for the Riemann-Stieltjes Integral
Approximation of the Riemann-Stieltjes Integral
Another Trapezoid Like Inequality
A Generalisation of the Trapezoid Inequality
Approximating the Riemann-Stieltjes Integral
Inequalities of Ostrowski Type for the Riemann-Stieltjes Integral
Another Inequality of Ostrowski Type for the Riemann-Stieltjes Integral
Some Inequalities of Gruss Type for the Riemann-Stieltjes Integral
A Numerical Quadrature Formula for the Riemann-Stieltjes Integral
Quadrature Methods for the Riemann-Stieltjes Integral of Continuous Mappings
Index
List of Figures
List of Tables
Preface
72.

図書

図書
Tobin A. Driscoll, Lloyd N. Trefethen
出版情報: Cambridge : Cambridge University Press, 2002  xvi, 132 p. ; 24 cm.
シリーズ名: Cambridge monographs on applied and computational mathematics ; 8
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Preface
Introduction / 1:
Essentials / 2:
Numerical methods / 3:
Variations / 4:
Applications / 5:
Using the SC toolbox
Preface
Introduction / 1:
Essentials / 2:
73.

図書

図書
V.G. Romanov
出版情報: Utrecht : VSP, 2002  xii, 280 p. ; 25 cm
シリーズ名: Inverse and ill-posed problems series
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74.

図書

図書
V.E. Nazaikinskii, B.-W. Schulze, B.Yu. Sternin
出版情報: London : Taylor & Francis, 2002  xii, 356 p. ; 26 cm
シリーズ名: Differential and integral equations and their applications ; v. 3
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Semiclassical Quantization
Quantization and Microlocalization
Quantization by the Wave Packet Transform
Maslov's Canonical Operator and Hormander's Oscillatory Integrals
Topological Aspects of Quantization Conditions
The Schrodinger Equation
The Maxwell Equations
Equations with Trapping Hamiltonians
Quantization by the Method of Ordered Operators (Noncommutative Analysis)
Noncommutative Analysis: Main Ideas, Definitions, and Theorems
Exactly Soluble Commutation Relations
Semiclassical Quantization
Quantization and Microlocalization
Quantization by the Wave Packet Transform
75.

図書

図書
Joel Feldman, Horst Knörrer, Eugene Trubowitz
出版情報: Providence : American Mathematical Society, c2002  vii, 115 p. ; 26 cm
シリーズ名: CRM monograph series ; v. 16
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Fermionic functional integrals Fermionic expansions
Infinite-dimensional Grassman algebras / Appendix A:
Pfaffians / Appendix B:
Propagator bounds / Appendix C:
Problem solutions / Appendix D:
Bibliography
Fermionic functional integrals Fermionic expansions
Infinite-dimensional Grassman algebras / Appendix A:
Pfaffians / Appendix B:
76.

図書

図書
by Alfred North Whitehead
出版情報: Cambridge : Cambridge University Press, 1898  xxvi, 586 p. ; 28 cm
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77.

図書

図書
by I. Todhunter
出版情報: London : Macmillan, 1867  vi, 318 p. ; 20 cm
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78.

図書

図書
Carlos Castillo-Chavez ... [et al.], editors
出版情報: New York ; Tokyo : Springer, c2002  v. ; 25 cm
シリーズ名: The IMA volumes in mathematics and its applications ; v. 125-126
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New directions in the mathematics of infectious diseases
Fred Brauer
Kenneth Cooke
Maximal prevalence and the basic reproduction number in simple epidemics
The transition through stages with arbitrary length distributions, and applications in epidemics
Measles outbreaks are not chaotic
Epidemics among a population of households
Infection transmission dynamics and vaccination program effectiveness as a function of vaccine effects in individuals
The influence of different forms of cross-protective immunity on the population dynamics of antigenetically diverse pathogens
Dynamics of multiple strains of infectious agents coupled by cross-immunity
Virulence evolution in macro-parasites
Mathematical models for schistosomiasis with delays and multiple definitive hosts
Infectious disease models with chronological age structure and epidemiological age structure
Effects of genetic heterogeneity on HIV transmission in homosexual populations
Age-structured core group model and its impact on STD dynamics
Global dynamics of tuberculosis models with density dependent demography
Global stability in some SEIR epidemic models
The global stability analysis for an SIS model with age and infection age structures
Endemic threshold and stability in an evolutionary epidemic model
Epilogue
New directions in the mathematics of infectious disease
Kenneth L. Cooke
Basic ideas of mathematical epidemiology
Extensions of the basic models
New vaccination strategies for pertussis
Time delay in epidemic models
Nonlocal response in a simple epidemiological model
Discrete-time S-I-S models with simple and complex population dynamics
Intraspecific competition, dispersal, and disease dynamics in discrete-time patchy environments
The impact of long-range dispersal on the rate of spread in population and epidemic models
Endemicity, persistence, and quasi-stationarity
On the computation of Ro and its role in global stability
Nonlinear mating models for populations with discrete generations
Center manifolds and normal forms in epidemic models
Remarks on modeling host-viral dynamics and treatment
A multiple compartment model for the evolution of HIV-1 after highly active antiretroviral therapy
Modeling cancer as an infectious disease
Frequency dependent risk of infection and the spread of infectious diseases
Long-term dynamics and emergence of tuberculosis
New directions in the mathematics of infectious diseases
Fred Brauer
Kenneth Cooke
79.

図書

図書
[by] Shwu-Yeng T. Lin [and] You-Feng Lin
出版情報: Boston : Houghton Mifflin, c1974  ix, 164 p ; 24 cm
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80.

図書

図書
Lluís Puig
出版情報: Berlin : Springer, c2002  213 p. ; 25 cm
シリーズ名: Springer monographs in mathematics
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Introduction / I:
Lifting idempotents / II:
Points of the O-algebras and multiplicity of the points / III:
Divisors on N-interior G-algebras / IV:
Restriction and induction of divisors / V:
Local pointed groups on N-interior G-algebras / VI:
On Green's indecomposability theorem / VII:
Fusions in N-interior G-algebras / VIII:
N-interior G-algebras through G-interior algebras / IX:
The group algebra / X:
Fusion Z-algebra of a block / XI:
Source algebras of blocks / XII:
Local structure of the hyperfocal subalgebra / XIII:
Uniqueness of the hyperfocal subalgebra / XIV:
Existence of the hyperfocal subalgebra / XV:
On the exponential and logarithmic functions in O-algebras / XVI:
Introduction / I:
Lifting idempotents / II:
Points of the O-algebras and multiplicity of the points / III:
81.

図書

図書
L.H. Eliasson ... [et al.] ; editors, S. Marmi, J.-C. Yoccoz
出版情報: Berlin ; Tokyo : Springer, c2002  viii, 198 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1784 . Fondazione C.I.M.E.
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Perturbations of linear quasi-periodic system / L. H. Eliasson
Introduction / 1:
Covariance and normal form matrices / 2:
Block splitting / 3:
Quadratic convergence / 4:
Block clustering / 5:
Transversality of resultants / 6:
A Perturbation theorem / 7:
Applications / 8:
Appendix A / A:
Appendix B / B:
KAM-persistence of finite-gap solutions / Sergei B. Kuksin
Some analysis in Hilbert spaces and scales
Symplectic structures and Hamiltonian equations
Lax-integrable Hamiltonian equations and their integrable subsystems
Finite-gap manifolds and theta-formulas
Linearised equations and their Floquet solutions
Linearised Lax-integrable equations
Normal form
The KAM theorem
Examples / 9:
Analytic linearization of circle diffeomorphisms / Jean-Christophe Yoccoz
Arithmetics
The Cr theory for r ≥ 0
Analytic case
Appendix: Estimates of moduli of annular domains
Some open problems related to small divisors / S. Marmi ; J.-C. Yoccoz
One-Dimensional Small Divisor Problems (On Holomorphic Germs and Circle Diffeomorphisms) / 0:
Finite-Dimensional Small Divisor Problems
KAM Theory and Hamiltonian Systems
Linear Quasiperiodic Skew-Products, Spectral Theory and Hamil- tonian Partial Differential Equations
Perturbations of linear quasi-periodic system / L. H. Eliasson
Introduction / 1:
Covariance and normal form matrices / 2:
82.

図書

図書
edited by J. C. Fields, with the collaboration of an editorial committee
出版情報: Nendeln/Liechtenstein : Kraus Reprint, 1967  2 v. ; 25 cm
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目次情報:
v. 1.Report of the congress. Lectures. Communications to sections 1 and 2
v. 2.Communications to sections 3-6.
v. 1.Report of the congress. Lectures. Communications to sections 1 and 2
v. 2.Communications to sections 3-6.
83.

図書

図書
V.S. Vladimirov
出版情報: London : Taylor & Francis, 2002  xiv, 311 p. ; 26 cm
シリーズ名: Analytical methods and special functions ; v. 6
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Preface
Symbols and Definitions
Generalized Functions and their Properties / Chapter 1.:
Test and Generalized Functions / 1.:
Introduction / 1.1.:
The space of test functions D(O) / 1.2.:
The space of generalized functions D'(O) / 1.3.:
The completeness of the space of generalized functions D'(O) / 1.4.:
The support of a generalized function / 1.5.:
Regular generalized functions / 1.6.:
Measures / 1.7.:
Sochozki formulae / 1.8.:
Change of variables in generalized functions / 1.9.:
Multiplication of generalized functions / 1.10.:
Differentiation of Generalized Functions / 2.:
Derivatives of generalized functions / 2.1.:
The antiderivative (primitive) of a generalized function / 2.2.:
Examples / 2.3.:
The local structure of generalized functions / 2.4.:
Generalized functions with compact support / 2.5.:
Generalized functions with point support / 2.6.:
Generalized functions P([pi subscript v vertical bar]x[vertical bar superscript alpha-1]) / 2.7.:
Direct Product of Generalized Functions / 3.:
The definition of a direct product / 3.1.:
The properties of a direct product / 3.2.:
Some applications / 3.3.:
Generalized functions that are smooth with respect to some of the variables / 3.4.:
The Convolution of Generalized Functions / 4.:
The definition of convolution / 4.1.:
The properties of a convolution / 4.2.:
The existence of a convolution / 4.3.:
Cones in R[superscript n] / 4.4.:
Convolution algebras D'([Gamma]+) and D'([Gamma]) / 4.5.:
Mean functions of generalized functions / 4.6.:
Convolution as a continuous linear translation-invariant operator / 4.7.:
Tempered Generalized Functions / 4.9.:
The space S of test (rapidly decreasing) functions / 5.1.:
The space S' of tempered generalized functions / 5.2.:
Examples of tempered generalized functions and elementary operations in S' / 5.3.:
The structure of tempered generalized functions / 5.4.:
The direct product of tempered generalized functions / 5.5.:
The convolution of tempered generalized functions / 5.6.:
Homogeneous generalized functions / 5.7.:
Integral Transformations of Generalized Functions / Chapter 2.:
The Fourier Transform of Tempered Generalized Functions / 6.:
The Fourier transform of test functions in S / 6.1.:
The Fourier transform of tempered generalized functions / 6.2.:
Properties of the Fourier transform / 6.3.:
The Fourier transform of generalized functions with compact support / 6.4.:
The Fourier transform of a convolution / 6.5.:
The Mellin transform / 6.6.:
Fourier Series of Periodic Generalized Functions / 7.:
The definition and elementary properties of periodic generalized functions / 7.1.:
Fourier series of periodic generalized functions / 7.2.:
The convolution algebra D'[subscript T] / 7.3.:
Positive Definite Generalized Functions / 7.4.:
The definition and elementary properties of positive definite generalized functions / 8.1.:
The Bochner-Schwartz theorem / 8.2.:
The Laplace Transform of Tempered Generalized Functions / 8.3.:
Definition of the Laplace transform / 9.1.:
Properties of the Laplace transform / 9.2.:
The Cauchy Kernel and the Transforms of Cauchy-Bochner and Hilbert / 9.3.:
The space H[subscript s] / 10.1.:
The Cauchy kernel K[subscript C](z) / 10.2.:
The Cauchy-Bochner transform / 10.3.:
The Hilbert transform / 10.4.:
Holomorphic functions of the class H[superscript (s) subscript a] (C) / 10.5.:
The generalized Cauchy-Bochner representation / 10.6.:
Poisson Kernel and Poisson Transform / 11.:
The definition and properties of the Poisson kernel / 11.1.:
The Poisson transform and Poisson representation / 11.2.:
Boundary values of the Poisson integral / 11.3.:
Algebras of Holomorphic Functions / 12.:
The definition of the H[subscript +] (C) and H (C) algebras / 12.1.:
Isomorphism of the algebras S'(C* +) - H[subscript +] (C) and S'(C*) - H (C) / 12.2.:
The Paley-Wiener-Schwartz theorem and its generalizations / 12.3.:
The space H[subscript a](C) is the projective limit of the spaces H[subscript a'](C') / 12.4.:
The Schwartz representation / 12.5.:
A generalization of the Phragmen-Lindelof theorem / 12.6.:
Equations in Convolution Algebras / 13.:
Divisors of unity in the H[subscript +] (C) and H(C) algebras / 13.1.:
On division by a polynomial in the H(C) algebra / 13.2.:
Estimates for holomorphic functions with nonnegative imaginary part in T[subscript C] / 13.3.:
Divisors of unity in the algebra W(C) / 13.4.:
Example / 13.5.:
Tauberian Theorems for Generalized Functions / 14.:
Preliminary results / 14.1.:
General Tauberian theorem / 14.2.:
One-dimensional Tauberian theorems / 14.3.:
Tauberian and Abelian theorems for nonnegative measures / 14.4.:
Tauberian theorems for holomorphic functions of bounded argument / 14.5.:
Some Applications in Mathematical Physics / Chapter 3.:
Differential Operators with Constant Coefficients / 15.:
Fundamental solutions in D' / 15.1.:
Tempered fundamental solutions / 15.2.:
A descent method / 15.3.:
A comparison of differential operators / 15.4.:
Elliptic and hypoelliptic operators / 15.6.:
Hyperbolic operators / 15.7.:
The sweeping principle / 15.8.:
The Cauchy Problem / 16.:
The generalized Cauchy problem for a hyperbolic equation / 16.1.:
Wave potential / 16.2.:
Surface wave potentials / 16.3.:
The Cauchy problem for the wave equation / 16.4.:
A statement of the generalized Cauchy problem for the heat equation / 16.5.:
Heat potential / 16.6.:
Solution of the Cauchy problem for the heat equation / 16.7.:
Holomorphic Functions with Nonnegative Imaginary Part in T[subscript C] / 17.:
Preliminary remarks / 17.1.:
Properties of functions of the class P[subscript +](T[superscript C]) / 17.2.:
Estimates of the growth of functions of the class H[subscript +](T[superscript C]) / 17.3.:
Smoothness of the spectral function / 17.4.:
Indicator of growth of functions of the class P[subscript +](T[superscript C]) / 17.5.:
An integral representation of functions of the class H[subscript +](T[superscript C]) / 17.6.:
Holomorphic Functions with Nonnegative Imaginary Part in T[superscript n] / 18.:
Lemmas / 18.1.:
Functions of the classes H[subscript +](T[superscript 1]) and P[subscript +](T[superscript 1]) / 18.2.:
Functions of the class P[subscript +](T[superscript n]) / 18.3.:
Functions of the class H[subscript +](T[superscript n]) / 18.4.:
Positive Real Matrix Functions in T[superscript C] / 19.:
Positive real functions in T[superscript C] / 19.1.:
Positive real matrix functions in T[superscript C] / 19.2.:
Linear Passive Systems / 20.:
Corollaries to the condition of passivity / 20.1.:
The necessary and sufficient conditions for passivity / 20.3.:
Multidimensional dispersion relations / 20.4.:
The fundamental solution and the Cauchy problem / 20.5.:
What differential and difference operators are passive operators? / 20.6.:
Quasiasymptotics of the solutions of equations in convolutions / 20.7.:
Abstract Scattering Operator / 21.:
The definition and properties of an abstract scattering matrix / 21.1.:
A description of abstract scattering matrices / 21.2.:
The relationship between passive operators and scattering operators / 21.3.:
Bibliography
Index
Preface
Symbols and Definitions
Generalized Functions and their Properties / Chapter 1.:
84.

図書

図書
Nikolai Saveliev
出版情報: Berlin ; Tokyo : Springer, c2002  xii, 223 p. ; 24 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 140 . Low-dimensional topology / R.V. Gamkrelidze, V.A. Vassiliev (eds.) ; 1
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Homology 3-Spheres / 1:
Integral Homology 3 Spheres / 1.1:
Homotopy 3-Spheres / 1.1.1:
Poincaré Homology Sphere / 1.1.2:
Brieskorn Homology Spheres / 1.1.3:
Seifert Fibered Homology Spheres / 1.1.4:
Dehn Surgery on Knots / 1.1.5:
Surgery on Links / 1.1.6:
Connected Sums and Splicing / 1.1.7:
Splice Decomposition / 1.1.8:
Plumbing / 1.1.9:
Links of Singularities / 1.1.10:
Mutations / 1.1.11:
Branched Covers / 1.1.12:
Heegaard Splittings of Homology Spheres / 1.1.13:
Rational Homology Spheres / 1.2:
Spherical Space Forms / 1.2.1:
Dehn Surgery / 1.2.2:
Seifert Fibered Manifolds / 1.2.3:
Rokhlin Invariant / 1.2.4:
The Rokhlin Theorem / 2.1:
Definition of the Rokhlin Invariant / 2.2:
Properties of the Rokhlin Invariant / 2.3:
Surgery Formula for the Rokhlin Invariant / 2.3.1:
Surgery on Algebraically Split Links / 2.3.2:
Splicing and Mutation / 2.3.3:
Rokhlin Invariant of Branched Coverings / 2.3.4:
Birman-Craggs Homomorphisms / 2.3.5:
Homology Cobordism Invariance / 2.3.6:
Seifert Fibered and Graph Homology Spheres / 2.4:
The Algorithm / 2.4.1:
The Formula / 2.4.2:
Casson Invariant / 3:
Definition of the Casson Invariant / 3.1:
Construction of the Casson Invariant / 3.2:
SU(2)-Represcntation Spaces / 3.2.1:
The Intersection Theory / 3.2.2:
Orientations / 3.2.3:
Independence of Heegaard Splitting / 3.2.4:
Casson Invariant for Knots and Property (1) / 3.2.5:
The Difference Cycle / 3.2.6:
Casson Invariant for Boundary Links and Property (2) / 3.2.7:
Casson Invariant of a Trefoil and Property (0) / 3.2.8:
Comments and Ramifications / 3.3:
Pillowcase / 3.3.1:
Perturbations / 3.3.2:
The Connected Sum Formula / 3.3.3:
The Integrality of λ(Σ) / 3.3.4:
Casson Invariant of Algebraically Split Links / 3.3.5:
Properties of the Casson Invariant / 3.4:
Splicing Additivity / 3.4.1:
Mutation Invariance / 3.4.2:
Casson Invariant of Branched Coverings / 3.4.3:
Casson Invariant of Fibered Knots / 3.4.4:
Finite Type Invariants / 3.4.5:
Further Properties of the Casson Invariant / 3.4.6:
Casson Invariant of Σ(p, q, r) / 3.5:
Casson Invariant of Σ(a1, …, an) / 3.5.2:
The Neumann-Wahl Conjecture / 3.5.3:
Applications of the Casson Invariant / 3.6:
Triangulating Topological 4-Manifolds / 3.6.1:
Arnphicheiral Homology Spheres / 3.6.2:
Property P for Knots / 3.6.3:
Invariants of Walker and Lescop / 4:
Definition of the Walker Invariant / 4.1:
Construction of the Walker Invariant / 4.2:
SU(2)-Representation Varieties / 4.2.1:
The Surgery Formula / 4.2.2:
Combinatorial Definition of the Walker Invariant / 4.2.4:
The Lescop Invariant / 4.3:
Properties of the Walker and Lescop Invariants / 4.4:
The Gluing Formula / 4.4.1:
Casson Type Invariants from Other Lie Groups / 4.4.2:
Casson Invariant and Gauge Theory / 5:
Gauge Theory in Dimension 3 / 5.1:
Chern-Simons Function / 5.2:
The Casson Invariant from Gauge Theory / 5.3:
Morse Theory and Euler Characteristic / 5.3.1:
Critical Points of cs and Spectral Flow / 5.3.2:
Non-degenerate Case / 5.3.3:
Morse type Perturbations / 5.3.4:
Casson Invariant and Seiberg-Witten Equations / 5.3.6:
Casson-type Invariants of Knots / 5.4:
Representation Varieties of Knot Groups / 5.4.1:
The Invariants / 5.4.2:
Equivariant Casson Invariant / 5.5:
Equivariant Gauge Theory / 5.5.1:
Definition of the Invariants / 5.5.2:
Equivariant Casson and Knot Signatures / 5.5.3:
Applications / 5.5.4:
The SU(3) Casson Invariant / 5.6:
Some SU(3)-Gauge Theory / 5.6.1:
Definition of the Invariant / 5.6.2:
Properties and Computations / 5.6.3:
Instanton Floer Homology / 6:
Gauge Theory in Dimension 4 / 6.1:
Gauge Theory on Closed 4-Manifolds / 6.1.1:
Gauge Theory on Open 4-Manifolds / 6.1.2:
Linear Analysis / 6.1.3:
Non-linear Analysis / 6.1.4:
Definition of the Floer Homology / 6.2:
Review of the Morse Theory / 6.2.1:
Floer Homology of Integral Homology Spheres / 6.2.2:
Functoriality with Respect to Cobordisms / 6.2.3:
Spectral Flow Formulas / 6.3:
The Atiyah-Patodi-Singer Formula / 6.3.1:
The Splitting Formula / 6.3.2:
The Kirk-Klassen Formula / 6.3.3:
The Closed Form Formula / 6.4:
Graph Homology Spheres / 6.4.3:
Properties of the Floer Homology / 6.5:
Orientation Reversal / 6.5.1:
Floer Homology of Homology Handles / 6.5.2:
The Floer Exact Triangle / 6.5.3:
Special Boundary Maps / 6.5.4:
The u-map in Floer Homology / 6.5.5:
Integer Graded Floer Homology / 6.5.6:
Floer Homology of Connected Sums / 6.5.7:
Functoriality with Respect to Diffeornorphisms / 6.5.8:
Floer Homology in Donaldson Theory / 6.5.9:
Donaldson Invariants of Closed 4-Manifolds / 6.6.1:
Relative Donaldson Polynomials / 6.6.2:
Extending Floer Homology / 6.6.3:
Equivariant Floer Homology / 6.7.1:
Fukaya-Floer Homology / 6.7.2:
Floer's Category and Functor / 6.7.3:
The Atiyah-Floer Conjecture / 6.7.4:
Floer Homology of Knots / 6.7.5:
Seiberg-Witten Floer Homology / 6.7.6:
The Homology Cobordism Group / 7:
Homology Cobordisms / 7.1:
Mazur Homology Spheres / 7.1.1:
Knot Cobordisms and Homology Cobordisms / 7.1.2:
Ribbon Concordances and Ribbon Knots / 7.1.3:
Branched Coverings / 7.1.4:
The Structure of <$>\Theta_{\op Z}^3<$> / 7.2:
A Classical Approach to <$>\Theta_{\op Z}^3<$> / 7.2.1:
Infinite Order Elements in <$>\Theta_{\op Z}^3<$> / 7.2.2:
The <$>\bar \mu<$>-Invariant / 7.2.3:
The Fukumoto-Furuta Invariants / 7.2.4:
The Group <$>\Theta_{\op Z}^3<$> is Infinitely Generated / 7.2.5:
Applications of the Homology Cobordism Group / 7.3:
Triangulating Topological Manifolds / 7.3.1:
Knot Concordance Group / 7.3.2:
PL-discs in Contractible 4-Manifolds / 7.3.3:
Constructing Smooth Manifolds / 7.3.4:
References
Index
Homology 3-Spheres / 1:
Integral Homology 3 Spheres / 1.1:
Homotopy 3-Spheres / 1.1.1:
85.

図書

図書
Brian J. Cantwell
出版情報: Cambridge : Cambridge University Press, 2002  xli, 612 p. ; 24 cm
シリーズ名: Cambridge texts in applied mathematics
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Author's Preface
Historical Preface
Rise of the Academies
Abel and Galois
Lie and Klein
1870
Lie's Arrest
Gauss, Riemann, and the New Geometry
The Erlangen Program
Lie's Career at Leipzig
A Falling Out
Lie's Final Return to Norway
After 1900
The Ariadne Thread
Suggested Reading
Introduction to Symmetry / 1:
Symmetry in Nature / 1.1:
Some Background / 1.2:
The Discrete Symmetries of Objects / 1.3:
The Principle of Covariance / 1.4:
Continuous Symmetries of Functions and Differential Equations / 1.5:
Some Notation Conventions / 1.6:
Concluding Remarks / 1.7:
Exercises / 1.8:
References
Dimensional Analysis / 2:
Introduction / 2.1:
The Two-Body Problem in a Gravitational Field / 2.2:
The Drag on a Sphere / 2.3:
The Drag on a Sphere in High-Speed Gas Flow / 2.4:
Buckingham's Pi Theorem--The Dimensional-Analysis Algorithm / 2.5:
Systems of ODEs and First-Order PDEs; State-Space Analysis / 2.6:
Autonomous Systems of ODEs in the Plane / 3.1:
Characteristics / 3.2:
First-Order Ordinary Differential Equations / 3.3:
Thermodynamics; The Legendre Transformation / 3.4:
Incompressible Flow in Two Dimensions / 3.5:
Fluid Flow in Three Dimensions--The Dual Stream Function / 3.6:
Nonlinear First-Order PDEs--The Method of Lagrange and Charpit / 3.7:
Characteristics in n Dimensions / 3.8:
State-Space Analysis in Two and Three Dimensions / 3.9:
Classical Dynamics / 3.10:
Hamilton's Principle / 4.1:
Hamilton's Equations / 4.3:
The Hamilton--Jacobi Equation / 4.4:
Examples / 4.5:
Introduction to One-Parameter Lie Groups / 4.6:
The Symmetry of Functions / 5.1:
An Example and a Counterexample / 5.2:
One-Parameter Lie Groups / 5.3:
Invariant Functions / 5.4:
Infinitesimal Form of a Lie Group / 5.5:
Lie Series, the Group Operator, and the Infinitesimal Invariance Condition for Functions / 5.6:
Solving the Characteristic Equation X [psi] [x] = 0 / 5.7:
Reconstruction of a Group from Its Infinitesimals / 5.8:
Multiparameter Groups / 5.9:
Lie Algebras / 5.10:
Solvable Lie Algebras / 5.11:
Some Remarks on Lie Algebras and Vector Spaces / 5.12:
Invariant Families / 5.13:
Invariance Condition for a Family / 6.2:
First-Order ODEs; The Integrating Factor / 6.3:
Using Groups to Integrate First-Order ODEs / 6.4:
Canonical Coordinates / 6.5:
Invariant Solutions / 6.6:
Elliptic Curves / 6.7:
Criterion for a First-Order ODE to Admit a Given Group / 6.8:
Differential Functions and Notation / 6.9:
Contact Conditions / 7.1:
Ordinary Differential Equations / 7.3:
Extension of Lie Groups in the Plane / 8.1:
Expansion of an ODE in a Lie Series; The Invariance Condition for ODEs / 8.2:
Group Analysis of Ordinary Differential Equations / 8.3:
Failure to Solve for the Infinitesimals That Leave a First-Order ODE Invariant / 8.4:
Construction of the General First-Order ODE That Admits a Given Group--The Ricatti Equation / 8.5:
Second-Order ODEs and the Determining Equations of the Group / 8.6:
Higher-Order ODEs / 8.7:
Reduction of Order by the Method of Canonical Coordinates / 8.8:
Reduction of Order by the Method of Differential Invariants / 8.9:
Successive Reduction of Order; Invariance under a Multiparameter Group with a Solvable Lie Algebra / 8.10:
Group Interpretation of the Method of Variation of Parameters / 8.11:
Partial Differential Equations / 8.12:
Finite Transformation of Partial Derivatives / 9.1:
Expansion of a PDE in a Lie Series--Invariance Condition for PDEs / 9.2:
Invariant Solutions and the Characteristic Function / 9.3:
Impulsive Source Solutions of the Heat Equation / 9.4:
A Modified Problem of an Instantaneous Heat Source / 9.5:
Nonclassical Symmetries / 9.6:
Laminar Boundary Layers / 9.7:
Background / 10.1:
The Boundary-Layer Formulation / 10.2:
The Blasius Boundary Layer / 10.3:
Temperature Gradient Shocks in Nonlinear Diffusion / 10.4:
Boundary Layers with Pressure Gradient / 10.5:
The Falkner--Skan Boundary Layers / 10.6:
Incompressible Flow / 10.7:
Invariance Group of the Navier--Stokes Equations / 11.1:
Frames of Reference / 11.2:
Two-Dimensional Viscous Flow / 11.3:
Viscous Flow in a Diverging Channel / 11.4:
Transition in Unsteady Jets / 11.5:
Elliptic Curves and Three-Dimensional Flow Patterns / 11.6:
Classification of Falkner--Skan Boundary Layers / 11.7:
Compressible Flow / 11.8:
Invariance Group of the Compressible Euler Equations / 12.1:
Isentropic Flow / 12.2:
Sudden Expansion of a Gas Cloud into a Vacuum / 12.3:
Propagation of a Strong Spherical Blast Wave / 12.4:
Compressible Flow Past a Thin Airfoil / 12.5:
Similarity Rules for Turbulent Shear Flows / 12.6:
Reynolds-Number Invariance / 13.1:
Group Interpretation of Reynolds-Number Invariance / 13.3:
Fine-Scale Motions / 13.4:
Application: Experiment to Measure Small Scales in a Turbulent Vortex Ring / 13.5:
The Geometry of Dissipating Fine-Scale Motion / 13.6:
Lie--Backlund Transformations / 13.7:
Lie--Backlund Transformations--Infinite Order Structure / 14.1:
Lie Contact Transformations / 14.2:
Equivalence Classes of Transformations / 14.3:
Applications of Lie--Backlund Transformations / 14.4:
Recursion Operators / 14.5:
Variational Symmetries and Conservation Laws / 14.6:
Backlund Transformations and Nonlocal Groups / 15.1:
Two Classical Examples / 16.1:
Symmetries Derived from a Potential Equation; Nonlocal Symmetries / 16.2:
Review of Calculus and the Theory of Contact / 16.3:
Differentials and the Chain Rule / A1.1:
The Theory of Contact / A1.2:
Invariance of the Contact Conditions under Lie Point Transformation Groups / Appendix 2:
Preservation of Contact Conditions--One Dependent and One Independent Variable / A2.1:
Preservation of the Contact Conditions--Several Dependent and Independent Variables / A2.2:
Infinite-Order Structure of Lie--Backlund Transformations / Appendix 3:
Lie Point Groups / A3.1:
Lie--Backlung Groups / A3.2:
Higher-Order Tangent Transformation Groups / A3.3:
One Dependent Variable and One Independent Variable / A3.5:
Infinite-Order Structure / A3.6:
Reference
Symmetry Analysis Software / Appendix 4:
Summary of the Theory / A4.1:
The Program / A4.2:
Timing, Memory and Saving Intermediate Data / A4.3:
Author Index
Subject Index
Author's Preface
Historical Preface
Rise of the Academies
86.

図書

図書
Q.I. Rahman and G. Schmeisser
出版情報: Oxford : Clarendon Press, 2002  xiv, 742 p. ; 24 cm
シリーズ名: London Mathematical Society monographs ; new ser., 26
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Introduction / 1:
The fundamental theorem of algebra / 1.1:
Symmetric polynomials / 1.2:
The continuity theorem / 1.3:
Orthogonal polynomials: general properties / 1.4:
The classical orthogonal polynomials / 1.5:
Harmonic and subharmonic functions / 1.6:
Tools from matrix analysis / 1.7:
Notes / 1.8:
Critical Points in Terms of Zeros / I:
Fundamental results on critical points / 2:
Convex hulls and the Gauss-Lucas theorem / 2.1:
Extensions of the Gauss-Lucas theorem / 2.2:
Average distances from a line or a point / 2.3:
Real polynomials and Jensen's theorem / 2.4:
Extensions of Jensen's theorem / 2.5:
More sophisticated methods / 2.6:
Circular domains and polar derivative / 3.1:
Laguerre's theorem, its variants, and applications / 3.2:
Apolarity / 3.3:
Grace's theorem and equivalent forms / 3.4:
More specific results on critical points / 3.5:
Products and quotients of polynomials / 4.1:
Derivatives of reciprocals of polynomials / 4.2:
Complex analogues of Rolle's theorem / 4.3:
Bounds for some of the critical points / 4.4:
Converse results / 4.5:
Applications to compositions of polynomials / 4.6:
Linear combination of rational functions / 5.1:
Complex analogues of the intermediate-value theorem / 5.2:
Linear combination of derivatives: Walsh's approach / 5.3:
Linear combination of derivatives: recursive approach / 5.4:
Multiplicative composition: Schur-Szego approach / 5.5:
Multiplicative composition: Laguerre's approach / 5.6:
Multipliers preserving the reality of zeros / 5.7:
Polynomials with real zeros / 5.8:
The span of a polynomial / 6.1:
Largest zero and largest critical point / 6.2:
Interlacing and the Hermite-Biehler theorem / 6.3:
Consecutive zeros and critical points / 6.4:
Refinement of Rolle's theorem / 6.5:
Conjectures and solutions / 6.6:
A conjecture of Popoviciu / 7.1:
A conjecture of Smale / 7.2:
The conjecture of Sendov / 7.3:
Zeros in Terms of Coefficients / 7.4:
Inclusion of all zeros / 8:
The Cauchy bound and its estimates / 8.1:
Various refinements / 8.2:
Multipliers and the Enestrom-Kakeya theorem / 8.3:
More general expansions / 8.4:
Orthogonal expansions with real coefficients / 8.5:
Alternative approach by matrix methods / 8.6:
Inclusion of some of the zeros / 8.7:
Inclusions in terms of a norm / 9.1:
Pellet's theorem and its consequences / 9.2:
Bounds in terms of some of the coefficients / 9.3:
The Landau-Montel problem / 9.4:
Number of zeros in an interval / 9.6:
The Budan-Fourier theorem and Descartes' rule / 10.1:
Exact count under a side condition / 10.2:
Extensions to pairs of conjugate zeros / 10.3:
Exact count by Sturm sequences / 10.4:
Exact count via quadratic forms / 10.6:
Number of zeros in a domain / 10.7:
General principles / 11.1:
Number of zeros in a sector / 11.2:
Number of zeros in a half-plane / 11.3:
The Routh--Hurwitz problem / 11.4:
Number of zeros in a disc / 11.5:
Distribution of zeros / 11.6:
Extremal Properties / 11.7:
Growth estimates / 12:
The Bernstein--Walsh lemma / 12.1:
The convolution method / 12.2:
The method of functionals / 12.3:
Local behaviour / 12.4:
Extensions to functions of exponential type / 12.6:
Mean values / 12.7:
Mean values on circles / 13.1:
A class of linear operators / 13.2:
Mean values on the unit interval / 13.3:
Derivative estimates on the unit disc / 13.4:
Bernstein's inequality and generalizations / 14.1:
Refinements / 14.2:
Conditions on the coefficients / 14.3:
Conditions on the zeros / 14.4:
Some special operators / 14.5:
Inequalities involving mean values / 14.6:
Derivative estimates on the unit interval / 14.7:
Inequalities of S. Bernstein and A. Markov / 15.1:
Extensions to higher-order derivatives / 15.2:
Two other extensions / 15.3:
Dependence of the bounds on the zeros / 15.4:
Some special classes / 15.5:
L[superscript p] analogues of Markov's inequality / 15.6:
Coefficient estimates / 15.7:
Polynomials on the unit circle / 16.1:
Coefficients of real trigonometric polynomials / 16.2:
Polynomials on the unit interval / 16.3:
References / 16.4:
List of notation
Index
Introduction / 1:
The fundamental theorem of algebra / 1.1:
Symmetric polynomials / 1.2:
87.

図書

図書
Dang Dinh Ang ... [et al.]
出版情報: Berlin ; Tokyo : Springer, c2002  viii, 183 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1792
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Introduction
Mathematical preliminaries / 1:
Banach spaces / 1.1:
Hilbert spaces / 1.2:
Some useful function spaces / 1.3:
Spaces of continuous functions / 1.3.1:
Spaces of integrable functions / 1.3.2:
Sobolev spaces / 1.3.3:
Analytic functions and harmonic functions / 1.4:
Fourier transform and Laplace transform / 1.5:
Regularization of moment problems by truncated expansion and by the Tikhonov method / 2:
Method of truncated expansion / 2.1:
A construction of regularized solutions / 2.1.1:
Convergence of regularized solutions and error estimates / 2.1.2:
Error estimates using eigenvalues of the Laplacian / 2.1.3:
Method of Tikhonov / 2.2:
Case 1: exact solutions in L2(Ω) / 2.2.1:
Case 2: exact solutions in Lα* (Ω), 1 < α&infinity; < 8 / 2.2.2:
Case 3: exact solutions in H1(Ω) / 2.2.3:
Notes and remarks / 2.3:
Backus-Gilbert regularization of a moment problem / 3:
Backus-Gilbert solutions and their stability / 3.1:
Definition of the Backus-Gilbert solutions / 3.2.1:
Stability of the Backus-Gilbert solutions / 3.2.2:
Regularization via Backus-Gilbert solutions / 3.3:
Definitions and notations / 3.3.1:
Main results / 3.3.2:
The Hausdorff moment problem: regularization and error estimates / 4:
Finite moment approximation of (4.1) / 4.1:
Proof of Theorem 4.1 / 4.1.1:
Proof of Theorem 4.2 / 4.1.2:
A moment problem from Laplace transform / 4.2:
Analytic functions: reconstruction and Sinc approximations / 4.3:
Reconstruction of functions in H2(U): approximation by polynomials / 5.1:
Reconstruction of an analytic function: a problem of optimal recovery / 5.2:
Cardinal series representation and approximation: reformulation of moment problems / 5.3:
Two-dimensional Sinc theory / 5.3.1:
Approximation theorems / 5.3.2:
Regularization of some inverse problems in potential theory / 6:
Analyticity of harmonic functions / 6.1:
CauchyÆs problem for the Laplace equation / 6.2:
Surface temperature determination from borehole measurements (steady case) / 6.3:
Regularization of some inverse problems in heat conduction147 / 7:
The backward heat equation / 7.1:
Surface temperature determination from borehole measurements: a two-dimensional problem / 7.2:
An inverse two-dimensional Stefan problem: identification of boundary values / 7.3:
Epilogue / 7.4:
References
Index
Introduction
Mathematical preliminaries / 1:
Banach spaces / 1.1:
88.

図書

図書
Yorck Sommerhäuser
出版情報: Berlin : Springer, c2002  157 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1789
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89.

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図書
R.M. Dudley
出版情報: Cambridge : Cambridge University Press, 2002  x, 555 p. ; 23 cm
シリーズ名: Cambridge studies in advanced mathematics ; 74
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Foundations: set theory / 1:
General topology / 2:
Measures / 3:
Integration / 4:
Lp spaces: introduction to functional analysis / 5:
Convex sets and duality of normed spaces / 6:
Measure, topology, and differentiation / 7:
Introduction to probability theory / 8:
Convergence of laws and central limit theorems / 9:
Conditional expectations and martingales / 10:
Convergence of laws on separable metric spaces / 11:
Stochastic processes / 12:
Measurability: Borel isomorphism and analytic sets / 13:
Appendixes
Axiomatic set theory / A:
Complex numbers, vector spaces, and Taylor's theorem with remainder
The problem of measure
Rearranging sums of nonnegative terms
Pathologies of compact nonmetric spaces
Indices
Foundations: set theory / 1:
General topology / 2:
Measures / 3:
90.

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図書
Andrea Braides
出版情報: Oxford : Oxford University Press, 2002  xii, 218 p. ; 25 cm
シリーズ名: Oxford lecture series in mathematics and its applications ; 22
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91.

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図書
出版情報: Pisa : Scuola normale superiore, 1999  287 p.
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92.

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図書
by Charles Smith
出版情報: London : Macmillan, 1904  vi, 259 p. ; 19 cm
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93.

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図書
L.Š. Grinblat ; [translated from an original Russian manuscript by A. Stoyanovskiǐ ; translation edited by A.B. Sossinsky]
出版情報: Providence, R.I. : American Mathematical Society, c2002  vi, 256 p. ; 26 cm
シリーズ名: Translations of mathematical monographs ; v. 214
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94.

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図書
edited by Michael Sh. Birman ... [et al.]
出版情報: New York : Kluwer Academic/Plenum, c2002  v. ; 24 cm
シリーズ名: International mathematical series
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Area Formulas for [sigma]-Harmonic Mappings / Giovanni Alessandrini ; Vincenzo Nesi
On a Variational Problem Connected with Phase Transitions of Means in Controllable Dynamical Systems / Vladimir I. Arnold
A Priori Estimates for Starshaped Compact Hypersurfaces with Prescribed mth Curvature Function in Space Forms / J. Lucas M. Barbosa ; Jorge H. S. Lira ; Vladimir I. Oliker
Elliptic Variational Problems with Nonstandard Growth / Michael Bildhauer ; Martin Fuchs
Existence and Regularity of Solutions of d[omega] = f with Dirichlet Boundary Conditions / Bernard Dacorogna
A Singular Perturbation Property of Capillary Surfaces / Robert Finn
On Solutions with Fast Decay of Nonstationary Navier-Stokes System in the Half-Space / Yoshiko Fujigaki ; Tetsuro Miyakawa
Strong Solutions to the Problem of Motion of a Rigid Body in a Navier-Stokes Liquid under the Action of Prescribed Forces and Torques / Giovanni P. Galdi ; Ana L. Silvestre
The Partially Free Boundary Problem for Parametric Double Integrals / Stefan Hildebrandt ; Heiko von der Mosel
On Evolution Laws Forcing Convex Surfaces to Shrink to a Point / Nina M. Ivochkina
Existence of a Generalized Green Function for Integro-Differential Operators of Fractional Order / Moritz Kassmann ; Mark Steinhauer
L[subscript q]-Estimates of the First-Order Derivatives of Solutions to the Nonstationary Stokes Problem / Herbert Koch ; Vsevolod A. Solonnikov
Two Sufficient Conditions for the Regularity of Lateral Boundary for the Heat Equation / Nicolai V. Krylov
Bound State Asymptotics for Elliptic Operators with Strongly Degenerated Symbols / Ari Laptev ; Oleg Safronov ; Timo Weidl
Nonlocal Problems for Quasilinear Parabolic Equations / Gary M. Lieberman
Boundary Feedback Stabilization of a Vibrating String with an Interior Point Mass / Walter Littman ; Stephen W. Taylor
On Direct Lyapunov Method in Continuum Theories / Mariarosaria Padula
The Fourier Coefficients of Stokes' Waves / Pavel I. Plotnikov ; John F. Toland
A Geometric Regularity Estimate via Fully Nonlinear Elliptic Equations / Reiner Schatzle
On the Eigenvalue Estimates for the Weighted Laplacian on Metric Graphs / Michael Solomyak
Potential Theory for Nonstationary Stokes Problem in Nonconvex Domains
Stability of Axially Symmetric Solutions to the Navier-Stokes Equations in Cylindrical Domains / Wojciech M. Zajaczkowski
Nonhomogeneous Navier-Stokes Equations with Integrable Low Regularity Data / H. Amann
On the Rectiability of Defect Measures Arising in a Micromagnetics Model / L. Ambrosio ; B. Kirchheim ; M. Lecumberry ; T. Riviere
Vorticity and Smoothness in Viscous Flows / H. Beirao da Veiga
Absolute Continuity of the Spectrum of the Periodic Operator of Elasticity
Theory for Constant Shear Modulus / M.Sh. Birman ; T.A. Suslina
Some Properties of Solutions of Fully Nonlinear Partial Differential Inequalities / I. Capuzzo Dolcetta
On Time Discretizations for Generalized Newtonian Fluids / L. Diening ; A. Prohl ; M. Ruzicka
A Stokes Like-System for Mixtures / J. Frehse ; S. Goj ; J. Malek
Real Processes and Realizability of a Stabilization
Method for Navier Stokes Equations / A.V. Fursikov
On the Inelastic Boltzmann Equation with Diffusive Forcing / I.M. Gamba ; V. Panferov ; C. Villani
On Problems in Continuum Mechanics with the Maxwell Viscosity / S.K. Godunov
Uniqueness of Recovery of Some Systems of Quasilinear Elliptic and Parabolic Partial Differential Equations / V. Isakov
Global Solution of Coupled Kuramoto Sivashinsky and Ginzburg-Landau Equations / V.K. Kalantarov
On Skyrme's Model / L. Kapitanski
Linear and Nonlinear Ultraparabolic Equations of Kolmogorov Type Arising in Diffusion Theory and in Finance / E. Lanconelli ; A. Pascucci ; S. Polidoro
On the Dimension of the Global Attractor for the Modifed Navier-Stokes Equations / D. Prazak
The Diffusion Velocity Method as a Tool for General Diffusion Equations / S. Mas-Gallic
Harnack Inequalities on Scale Irregular Sierpinski Gaskets / U. Mosco
Mean Value Theorems and Harnack Inequalities / M. Safonov
The Navier-Stokes Equations and Backward Uniqueness / G. Seregin ; V. Sverak
Hessian Equations on Compact Riemannian Manifolds / J. Urbas
Index
Area Formulas for [sigma]-Harmonic Mappings / Giovanni Alessandrini ; Vincenzo Nesi
On a Variational Problem Connected with Phase Transitions of Means in Controllable Dynamical Systems / Vladimir I. Arnold
A Priori Estimates for Starshaped Compact Hypersurfaces with Prescribed mth Curvature Function in Space Forms / J. Lucas M. Barbosa ; Jorge H. S. Lira ; Vladimir I. Oliker
95.

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図書
Paul Newton, Philip Holmes, Alan Weinstein, editors
出版情報: New York : Springer, c2002  xvii, 571 p. ; 25 cm
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96.

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図書
editors Olga Gil-Medrano, Vicente Miquel
出版情報: New Jersey : World Scientific, c2002  xii, 310 p. ; 23 cm
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97.

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図書
Grigor A. Barsegian
出版情報: London : Taylor & Francis, c2002  ix, 176 p. ; 25 cm
シリーズ名: Asian mathematics series / edited by Chung-Chun Yang ; vol. 5
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Preface
Tangent Variation Principle
Satellite Principles
Modification of Length-area Principle
Estimates for collections of Gamma-Lines
Estimates of lengths of Gamma-Lines for angular-quasiconformal mappings
Remarks on applying of estimates of L (D, Gamma)
Nevanlinna and Ahilfors Theories
Additions
Basic concepts and outcomes of Nevanlinna Value Distribution theory and Ahlfors theory of covering surfaces
Geometric deficient values
On some
Preface
Tangent Variation Principle
Satellite Principles
98.

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Abdul-Majid Wazwaz
出版情報: Lisse ; Tokyo : A.A. Balkema, c2002  xi, 459 p. ; 25 cm
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99.

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M.S. Howe
出版情報: Cambridge, U.K. : Cambridge University Press, 2003  xiv, 216 p. ; 23 cm
シリーズ名: Cambridge texts in applied mathematics
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Preface
Introduction / 1:
Lighthill's theory / 2:
The compact Green's function / 3:
Vorticity / 4:
Vortex sound / 5:
Vortex-surface interaction noise in two-dimensions / 6:
Problems in three-dimensions / 7:
Further worked examples / 8:
Bibliography
Preface
Introduction / 1:
Lighthill's theory / 2:
100.

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by Lord Kelvin and Peter Guthrie Tait
出版情報: Cambridge : At the University Press, 1879-1883  v. ; 23 cm
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