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1.

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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2.

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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目次情報: 続きを見る
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:
3.

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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4.

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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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:
5.

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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6.

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:
7.

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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8.

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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9.

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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10.

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
11.

図書

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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12.

図書

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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13.

図書

図書
Abdul-Majid Wazwaz
出版情報: Lisse ; Tokyo : A.A. Balkema, c2002  xi, 459 p. ; 25 cm
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14.

図書

図書
edited by Hildeberto Cabral and Florin Diacu
出版情報: Princeton, N.J. : Princeton University Press, c2002  xviii, 385 p. ; 24 cm
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15.

図書

図書
by Ravi P. Agarwal, Said R. Grace and Donal O'Regan
出版情報: Dordrecht : Kluwer Academic, c2002  xiv, 672 p. ; 25 cm
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Preface
Preliminaries / Chapter 1:
Introduction / 1.0.:
Continuability, Boundedness and Convergence to Zero / 1.1.:
Some Useful Results from Analysis and Fixed Point Theorems / 1.2.:
Notes and General Discussions / 1.3.:
References / 1.4.:
Oscillation and Nonoscillation of Linear Ordinary Differential Equations / Chapter 2:
Sturm Comparison Theorem / 2.0.:
Nonoscillatory Characterizations and Comparison Theorems / 2.2.:
Nonoscillation Criteria / 2.3.:
Oscillation Criteria / 2.4.:
Oscillation Criteria-Integral Averaging / 2.5.:
Oscillation Criteria-Integrable Coefficients / 2.6.:
Forced Oscillations / 2.7.:
Oscillation and Nonoscillation of Half-Linear Differential Equations / 2.8.:
Sturm-Type Comparison Theorems / 3.0.:
Levin-Type Comparison Theorems / 3.3.:
Liapunov's Inequality / 3.4.:
An Oscillation Criterion for Almost-Periodic Sturm-Liouville Equations / 3.5.:
On Zeros of Solutions of a Singular Half-linear Differential Equation / 3.6.:
Nonoscillatory Characterization / 3.7.:
Comparison Theorems / 3.7.2.:
Sufficient Conditions for Nonoscillation of Equation (3.1.1) / 3.7.3.:
Further Results on Nonoscillation of Equation (3.1.1) / 3.7.4.:
Oscillation Theorems for Equation (3.1.1) / 3.8.:
Interval Criteria for the Oscillation of Equation (3.1.1) / 3.9.2.:
The Weighted-Average Oscillation Criteria / 3.9.3.:
Oscillation of Damped and Forced Equations / 3.10.:
Oscillation of Equation (3.11.1) / 3.11.1.:
Oscillation of Equation (3.11.2) / 3.11.2.:
Distance of Zeros of Oscillatory Solutions / 3.12.:
Oscillation and Nonoscillation of Half-linear Equations with Deviating Arguments / 3.13.:
Some Useful Lemmas / 3.13.1.:
Oscillation of Equation (3.13.1) / 3.13.2.:
Some Extensions and More Oscillation Criteria / 3.13.3.:
Classification of Nonoscillatory Solutions / 3.13.4.:
A Comparison Theorem / 3.13.5.:
Oscillation of Equation (3.13.2) / 3.13.6.:
Nonoscillation of Solutions of Equation (3.13.127) / 3.13.7.:
Oscillation Theory for Superlinear Differential Equations / 3.14.:
Superlinear Oscillation Criteria / 4.0.:
Further Results on Superlinear Oscillations / 4.2.:
Existence of Nonoscillatory Solutions and Comparison Results / 4.3.:
A Necessary Condition for Oscillation / 4.3.1.:
Comparison of Nonlinear Equations of the Same Form / 4.3.2.:
Linearization of Oscillation Theorems / 4.3.3.:
Oscillation Criteria for Certain Nonlinear Differential Equations / 4.4.:
Superlinear Forced Oscillations / 4.5.:
Oscillation of Nonlinear Differential Equations with Nonlinear Damping Term / 4.6.:
Damping with Nonlinear Growth-Oscillation Criteria / 4.6.1.:
Damping with Nonlinear Growth-A Nonoscillation Theorem / 4.6.2.:
Oscillation Theory for Sublinear Differential Equations / 4.7.:
Sublinear Oscillation Criteria / 5.0.:
Further Sublinear Oscillation Criteria / 5.2.:
Linearization of Sublinear Oscillation Theorems / 5.3.:
Nonoscillation Theorems for Sublinear Differential Equations / 5.4.:
Further Results on the Oscillation of Differential Equations / 5.5.:
Oscillation Criteria of Olech-Opial-Wazewski Type / 6.0.:
Some Definitions and Notation / 6.1.1.:
Further Results / 6.1.2.:
Oscillation Criteria for Half-linear Differential Equations / 6.2.:
Preliminary Results / 6.2.1.:
Oscillation Criteria via Liapunov's Second Method / 6.2.2.:
Oscillation Results for Differential Systems / 6.3.1.:
Oscillation of Nonlinear Two-dimensional Differential Systems / 7.0.:
Superlinear Case / 7.1.1.:
Sublinear Case / 7.1.2.:
Further Oscillation Criteria / 7.1.3.:
Oscillation Theorems for Linear Differential Systems / 7.2.:
Oscillation Theorems for Differential Systems with Functionally Commutative Matrix Coefficients / 7.3.:
Comparison Theorems for Operator-Valued Linear Differential Equations / 7.4.:
Oscillation Results for Differential Systems with Forcing Terms / 7.5.:
Asymptotic Behavior of Solutions of Certain Differential Equations / 7.6.:
Asymptotic Behavior of Solutions of Nonlinear Differential Equations / 8.0.:
Asymptotic Behavior of Nonoscillatory Solutions / 8.1.1.:
Bounded Asymptotically Linear Solutions / 8.1.2.:
Unbounded Asymptotically Linear Solutions / 8.1.3.:
Further Extensions and Improvements / 8.1.4.:
Asymptotic Behavior of Positive Solutions of Singular Emden-Fowler-Type Equations / 8.2.:
Positive Solutions of Equation (8.2.1) / 8.2.1.:
Positive Decaying Solutions of Equation (8.2.2) / 8.2.2.:
Positive Solutions of Singular Emden-Fowler-Type Systems / 8.2.3.:
Miscellaneous Topics / 8.3.:
Comparison and Nonoscillation Results / 9.0.:
Nonoscillatory Solutions of Forced Differential Equations / 9.2.:
Limit Circle Criteria and Related Properties for Nonlinear Equations / 9.3.:
Properties of Certain Differential Equations / 9.4.:
Nonoscillation Theory for Multivalued Differential Equations / 9.5.:
Differential Inclusions / 10.0.:
Neutral Inclusions / 10.3.:
Subject Index / 10.4.:
Preface
Preliminaries / Chapter 1:
Introduction / 1.0.:
16.

図書

図書
by Radu Precup
出版情報: Dordrecht : Kluwer Academic, c2002  xiv, 218 p. ; 25 cm
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Preface
Notation
Overview / 0:
Fixed Point Methods / I:
Compactness in Metric Spaces / 1:
Hausdorff's Theorem / 1.1:
The Ascoli-Arzela Theorem / 1.2:
The Frechet-Kolmogorov Theorem / 1.3:
Completely Continuous Operators on Banach Spaces / 2:
Completely Continuous Operators / 2.1:
Brouwer's Fixed Point Theorem / 2.2:
Schauder's Fixed Point Theorem / 2.3:
Continuous Solutions of Integral Equations via Schauder's Theorem / 3:
The Fredholm Integral Operator / 3.1:
The Volterra Integral Operator / 3.2:
An Integral Operator with Delay / 3.3:
The Leray-Schauder Principle and Applications / 4:
The Leray-Schauder Principle / 4.1:
Existence Results for Fredholm Integral Equations / 4.2:
Existence Results for Volterra Integral Equations / 4.3:
The Cauchy Problem for an Integral Equation with Delay / 4.4:
Periodic Solutions of an Integral Equation with Delay / 4.5:
Existence Theory in L[superscript p] Spaces / 5:
The Nemytskii Operator / 5.1:
The Fredholm Linear Integral Operator / 5.2:
The Hammerstein Integral Operator / 5.3:
Hammerstein Integral Equations / 5.4:
Volterra-Hammerstein Integral Equations / 5.5:
References: Part I
Variational Methods / II:
Positive Self-Adjoint Operators in Hilbert Spaces / 6:
Adjoint Operators / 6.1:
The Square Root of a Positive Self-Adjoint Operator / 6.2:
Splitting of Linear Operators in L[superscript p] Spaces / 6.3:
The Frechet Derivative and Critical Points of Extremum / 7:
The Frechet Derivative. Examples / 7.1:
Minima of Lower Semicontinuous Functionals / 7.2:
Application to Hammerstein Integral Equations / 7.3:
The Mountain Pass Theorem and Critical Points of Saddle Type / 8:
The Ambrosetti-Rabinowitz Theorem / 8.1:
Flows and Generalized Pseudo-Gradients / 8.2:
Schechter's Bounded Mountain Pass Theorem / 8.3:
Nontrivial Solutions of Abstract Hammerstein Equations / 9:
Nontrivial Solvability of Abstract Hammerstein Equations / 9.1:
Nontrivial Solutions of Hammerstein Integral Equations / 9.2:
A Localization Result for Nontrivial Solutions / 9.3:
References: Part II
Iterative Methods / III:
The Discrete Continuation Principle / 10:
Perov's Theorem / 10.1:
The Continuation Principle for Contractive Maps on Generalized Metric Spaces / 10.2:
Hammerstein Integral Equations with Matrix Kernels / 10.3:
Monotone Iterative Methods / 11:
Ordered Banach Spaces / 11.1:
Fixed Point Theorems for Monotone Operators / 11.2:
Monotone Iterative Technique for Fredholm Integral Equations / 11.3:
Minimal and Maximal Solutions of a Delay Integral Equation / 11.4:
Methods of Upper and Lower Solutions for Equations of Hammerstein Type / 11.5:
Quadratically Convergent Methods / 12:
Newton's Method / 12.1:
Generalized Quasilinearization for an Integral Equation with Delay / 12.2:
References: Part III
Index
Preface
Notation
Overview / 0:
17.

図書

図書
Michael Brin, Garrett Stuck
出版情報: Cambridge : Cambridge University Press, 2002  xii, 240 p. ; 24 cm
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Introduction
Examples and basic concepts / 1:
Topological dynamics / 2:
Symbolic dynamics / 3:
Ergodic theory / 4:
Hyperbolic dynamics / 5:
Ergodicity of Anosov diffeomorphisms / 6:
Low dimensional dynamics / 7:
Complex dynamics / 8:
Measure theoretic entropy / 9:
Index
Introduction
Examples and basic concepts / 1:
Topological dynamics / 2:
18.

図書

図書
edited by Zhenting Hou, Jerzy A. Filar, Anyue Chen
出版情報: Dordrecht : Kluwer Academic, c2002  x, 511 p. ; 25 cm
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Preface
Markov processes / Part I:
Branching exit Markov system and their applications to partial differential equations / E.B. Dynkin1:
Feller transition functions, resolvent decomposition theorems, and their application in unstable denumerable Markov processes / Anyue Chen ; Hanjun Zhang ; Zhenting Hou2:
Identifying Q-processes with a given finite [mu]-invariant measure / P.K. Pollett3:
Convergence property of standard transition functions / Qixiang Mei ; Xiang Lin4:
Markov skeleton processes / Hou Zhenting ; Liu Zaiming ; Zou Jiezhong ; Chen Xuerong5:
Piecewise deterministic Markov processes and semi-dynamic systems / Guoxin Liu6:
Controlled Markov chains and decision processes / Part II:
Average optimality for adaptive Markov control processes with unbounded costs and unknown disturbance distribution / J. Adolfo Minjarez-Sosa7:
Controlled Markov chains with utility functions / Seiichi Iwamoto ; Takayuki Ueno ; Toshiharu Fujita8:
Classification problems in MDPs / L.C.M. Kallenberg9:
Optimality conditions for CTMDP with average cost criterion / Xianping Guo ; Weiping Zhu10:
Optimal and nearly optimal policies in Markov decision chains with nonnegative rewards and risk-sensitive expected total-reward criterion / Rolando Cavazos-Cadena ; Raul Montes-de-Oca11:
Interval methods for uncertain Markov decision processes / Masami Kurano ; Masami Yasuda ; Jun-ichi Nakagami12:
Constrained discounted semi-Markov decision processes / Eugene A. Feinberg13:
Linear program for communicating MDPs with multiple constraints / Jerzy A. Filar14:
Optimal switching problem for Markov chains / A.A. Yushkevich15:
Approximations of a controlled diffusion model for renewable resource exploitation / Sara Pasquali ; Wolfgang J. Runggaldier16:
Stochastic processes and martingales / Part III:
A Fleming-Viot process with unbounded selection, II / S.N. Ethier ; Tokuzo Shiga17:
Boundary theory for superdiffusions / S.E. Kuznetsov18:
On solutions of backward stochastic differential equations with jumps and stochastic control / Situ Rong19:
Doob's inequality and lower estimation of the maximum of martingales / Li Zhichan20:
The Hausdorff measure of the level sets of Brownian motion on the Sierpinski carpet / Yuan Chenggui21:
Monotonic approximation of the Gittins index / Xikui Wang22:
Applications to finance, control systems and other related fields / Part IV:
Optimal consumption-investment decisions allowing for bankruptcy: A brief survey / Suresh P. Sethi23:
The hedging strategy of an Asian option / Zhaojun Yang ; Jiezhong Zou24:
The pricing of options to exchange one asset for another / Chao Chen25:
Finite horizon portfolio risk models with probability criterion / Yuanlie Lin ; Ke Liu26:
Long term average control of a local time process / Marta S. Mendiondo ; Richard H. Stockbridge27:
Singularly perturbed hybrid control systems approximated by structured linear programs / A. Haurie ; F. Moresino ; J.-P. Vial28:
The effect of stochastic disturbance on the solitary waves / Junping Li ; Weiguo Zhang ; Zaiming Liu29:
Independent candidate for Tierney model of H-M algorithms / Peide Chen30:
How rates of convergence for Gibbs fields depend on the interaction and the kind of scanning used / Yuzhi Cai31:
Expected loss and availability of multistate repairable system / Yubo GE32:
Preface
Markov processes / Part I:
Branching exit Markov system and their applications to partial differential equations / E.B. Dynkin1:
19.

図書

図書
edited by Gisbert Wüstholz
出版情報: Cambridge : Cambridge University Press, 2002  xv, 356 p. ; 24 cm
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Introduction
One century of logarithmic forms / G. Wüstholz1:
Report on p-adic logarithmic forms / Kunrun Yui2:
Recent progress on linear forms in elliptic logarithms / Sinnou David ; Noriko Hirata-Kohno3:
Solving Diophantine equations by Baker's theory / KÃílmÃín Györy4:
Baker's method and modular curves / Yuri F. Bilu5:
Application of the AndréâÇôOort conjecture / Paula B. Cohen ; Gisbert Wüstholz6:
Regular dessins / Jürgen Wolfart7:
Maass cusp forms with integer coefficients / Peter Sarnak8:
Modular forms, elliptic curves and the ABC-conjecture / Dorian Goldfeld9:
On the algebraic independence of numbers / Yu. V. Nesterenko10:
Ideal lattices / Eva Bayer-Fluckiger11:
Integral points and MordellâÇôWeil lattices / Tetsuji Shioda12:
Forty years of effective results in Diophantine theory / Enrico Bombieri13:
Points on subvarieties of tori / Jan-Hendrik Evertse14:
A new application of Diophantine approximations / G. Faltings15:
Search bounds for Diophantine equations / D. W. Masser16:
Regular systems and ubiquity / V. V. Beresnevich ; V. I. Bernik ; M. M. Dodson17:
Diophantine approximation, lattices and flows / Gregory Margulis18:
Baker's constant and Vinogradov's bound / Ming-Chit Liu ; Tianze Wang19:
Powers in arithmetic progression / T. N. Shorey20:
Greatest common divisor / A. Schinzel21:
Heilbronn's exponential sum and transcendence theory / D. R. Heath-Brown22:
Introduction
One century of logarithmic forms / G. Wüstholz1:
Report on p-adic logarithmic forms / Kunrun Yui2:
20.

図書

図書
Robert Gilmore, Marc Lefranc
出版情報: New York : Wiley, c2002  xxiii, 495 p. ; 25 cm
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Preface
Introduction / 1:
Dscrete Dynamical Systems: Maps / 2:
Continuous Dynamical Systems: Flows / 3:
Topological Invariants / 4:
Branched Manifolds / 5:
Topological Analysis Program / 6:
Folding Mechanisms: A2 / 7:
Tearing Mechanisms: A3 / 8:
Unfoldings / 9:
Symmetry / 10:
Flows in Higher Dimensions / 11:
Program for Dynamical Systems Theory / 12:
Determining Templates from Topological Invariants / Appendix A:
References
Topic Index
Preface
Introduction / 1:
Dscrete Dynamical Systems: Maps / 2:
21.

図書

図書
Miklós Bóna
出版情報: River Edge, N.J. : World Scientific, c2002  xvii, 406 p. ; 24 cm
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22.

図書

図書
edited by M. Loss and M.B. Ruskai
出版情報: Berlin : Springer, c2002  ix, 711 p. ; 25 cm
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Commentaries
Inequalities Related to Statistical Mechanics and Condensed Matter / Part I:
Theory of Ferromagnetism and the Ordering of Electronic Energy Levels / D.C. MattisI.1:
Ordering Energy Levels of Interacting Spin Systems / I.2:
Entropy Inequalities / H. ArakiI.3:
A Fundamental Property of Quantum-Mechanical Entropy / M.B. RuskaiI.4:
Proof of the Strong Subadditivity of Quantum-Mechanical Entropy / I.5:
Some Convexity and Subadditivity Properties of Entropy / I.6:
A Refinement of SimonÆs Correlation Inequality / I.7:
Two Theorems on the Hubbard Model / I.8:
Magnetic Properties of Some Itinerant-Electron Systems at T > 0 / M. AizenmanI.9:
Matrix Inequalities and Combinatorics / Part II:
Proofs of Some Conjectures on Permanents / II.1:
Concavity Properties and a Generating Function for Stirling Numbers / II.2:
Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture / II.3:
Some Operator Inequalities of the Schwarz Type / II.4:
Inequalities for Some Operator and Matrix Functions / II.5:
Positive Linear Maps Which Are Order Bounded on C* Subalgebras / E.B. DaviesII.6:
Optimal Hypercontractivity for Fermi Fields and Related Non-Commutative Integration Inequalities / E. CarlenII.7:
Sharp Uniform Convexity and Smoothness Inequalities for Trace Norms / K. BallII.8:
A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy / II.9:
Inequalities Related to the Stability of Matter / Part III:
Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and Their Relation to Sobolev Inequalities / W. ThirringIII.1:
On Semi-Classical Bounds for Eigenvalues of Schrödinger Operators / III.2:
The Number of Bound States of One-Body Schrödinger Operators and the Weyl Problem / III.3:
Improved Lower Bound on the Indirect Coulomb Energy / S. OxfordIII.4:
Density Functionals for Coulomb Systems / III.5:
On Characteristic Exponents in Turbulence / III.6:
Baryon Mass Inequalities in Quark Models / III.7:
Kinetic Energy Bounds and Their Application to the Stability of Matter / III.8:
A Sharp Bound for an Eigenvalue Moment of the One-Dimensional Schrödinger Operator / D. Hundertmark ; L.E. ThomasIII.9:
Coherent States / Part IV:
The Classical Limit of Quantum Spin Systems / IV.1:
Proof of an Entropy Conjecture of Wehrl / IV.2:
Quantum Coherent Operators: A Generalization of Coherent States / J.P. SolovejIV.3:
Coherent States as a Tool for Obtaining Rigorous Bounds / IV.4:
Brunn-Minkowski Inequality and Rearrangements / Part V:
A General Rearrangement Inequality for Multiple Integrals / H.J. Brascamp ; J.M. LuttingerV.1:
Some Inequalities for Gaussian Measures and the Long-Range Order of the One-Dimensional Plasma / V.2:
Best Constants in YoungÆs Inequality, Its Converse and Its Generalization to More than Three Functions / V.3:
On Extensions of the Brunn-Minkowski and Prékopa-Leindler Theorems, Including Inequalities for Log Concave Functions and with an Application to the Diffusion Equation / V.4:
Existence and Uniqueness of the Minimizing Solution of ChoquardÆs Nonlinear Equation / V.5:
Symmetric Decreasing Rearrangement Can Be Discontinuous / F. AlmgrenV.6:
The (Non) Continuity of Symmetric Decreasing Rearrangement / V.7:
On the Case of Equality in the Brunn-Minkowski Inequality for Capacity / L. Cafarelli ; D. JerisonV.8:
General Analysis / Part VI:
An Lp Bound for the Riesz and Bessel Potentials of Orthonormal Functions / VI.1:
A Relation Between Pointwise Convergence of Functions and Convergence of Functionals / H. BrezisVI.2:
Sharp Constants in the Hardy-Littlewood-Sobolev and Related Inequalities / VI.3:
On the Lowest Eigenvalue of the Laplacian for the Intersection of Two Domains / VI.4:
Minimum Action Solutions of Some Vector Field Equations / VI.5:
Sobolev Inequalities with Remainder Terms / VI.6:
Gaussian Kernels Have Only Gaussian Maximizers / VI.7:
Integral Bounds for Radar Ambiguity Functions and Wigner Distributions / VI.8:
Inequalities Related to Harmonic Maps / 11:
Estimations d'énergie pour des applications de R3 a valeurs dans S2 / J-M. CoronVII.1:
Singularities of Energy Minimizing Maps from the Ball to the Sphere / VII.2:
Co-area, Liquid Crystals, and Minimal Surfaces / W. BrowderVII.3:
Counting Singularities in Liquid Crystals / VII.4:
Symmetry of the Ginzburg-Landau Minimizer in a Disc / M. LossVII.5:
Publications of Elliott H. Lieb
Commentaries
Inequalities Related to Statistical Mechanics and Condensed Matter / Part I:
Theory of Ferromagnetism and the Ordering of Electronic Energy Levels / D.C. MattisI.1:
23.

図書

図書
edited by Guy Latouche, Peter Taylor
出版情報: New Jersey : World Scientific, c2002  xiv, 416 p. ; 24 cm
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24.

図書

図書
S. Sitharama Iyengar, E.C. Cho, Vir V. Phoha
出版情報: Boca Raton : Chapman & Hall/CRC, c2002  258 p. ; 25 cm
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Mathematical Preliminaries / I:
Sets / 1.1:
Functions / 1.2:
Sequences and Series / 1.3:
Complex Numbers / 1.4:
Linear Spaces / 1.5:
Matrices / 1.6:
Hilbert Spaces / 1.7:
Topology / 1.8:
Measure and Integral / 1.9:
Fourier Series / 1.10:
Exercises / 1.11:
Wavelets / 2:
Introduction / 2.1:
Dilation and Translation / 2.2:
Inner Product / 2.3:
Haar Wavelet / 2.4:
Multiresolution Analysis / 2.5:
Continuous Wavelet Transform / 2.6:
Discrete Wavelet Transform / 2.7:
Fourier Transform / 2.8:
Discrete Fourier Transform / 2.9:
DFT of Finite Sequences / 2.10:
Convolution / 2.11:
Neural Networks / 2.12:
McCulloch-Pitts Model of Neuron / 3.1:
Optimal Network Structure / 3.1.2:
Single Layer Perceptron / 3.1.3:
Multilayer Perceptrons / 3.2:
Adaptation Procedure of Rosenblatt / 3.2.1:
Backpropagation Learning / 3.2.2:
Hebbian Learning / 3.3:
Hebb's Rule / 3.3.1:
Hebbian Learning Applied to Multiple Input PEs / 3.3.2:
Oja's Rule / 3.3.3:
Sanger's Rule / 3.3.4:
Principal Component Analysis (PCA) / 3.3.5:
Anti-Hebbian Learning / 3.3.6:
Competitive and Kohonen Networks / 3.4:
Competitive Learning / 3.4.1:
Kohonen Self-Organizing Map / 3.4.2:
Grossberg's Instar-Outstar Network / 3.4.3:
Adaptive Resonance Theory (ART) / 3.4.4:
Recurrent Neural Networks / 3.5:
Hopfield Networks / 3.5.1:
Wavelet Networks / 3.6:
What are Wavelet Networks? / 4.1:
Dyadic Wavelet Network / 4.3:
Theory of Wavelet Networks / 4.4:
Wavelet Network Structure / 4.5:
Wavelet Network Algorithm / 4.5.1:
Multidimensional Wavelets / 4.6:
Learning in Wavelet Networks / 4.7:
Initialization of Wavelet Networks / 4.8:
Properties of Wavelet Networks / 4.9:
Scaling at Higher Dimensions
Recurrent Learning / 4.11:
Neural Structures / 5.1:
Learning Problems / 5.2.2:
On-line Learning Approaches: Recurrent Backpropagation / 5.2.3:
Recurrent Wavelets / 5.3:
Wavelets in Function Approximation / 5.3.1:
Recurrent Wavelet Networks / 5.3.2:
Numerical Experiments / 5.4:
Case 1 / 5.4.1:
Case 2 / 5.4.2:
Concluding Remarks / 5.5:
Separating Order from Disorder / 5.6:
Order within Disorder / 6.1:
Wavelet Networks: Trading Advisors / 6.2:
Comparison Results / 6.3:
Conclusions / 6.4:
Radial Wavelet Neural Networks / 6.5:
Data Description and Preparation / 7.1:
Classification Systems / 7.3:
Minimum Distance Classifier / 7.3.1:
Wavelet Neural Network Classifier / 7.3.2:
Results / 7.4:
Predicting Chaotic Time Series / 7.5:
Nonlinear Prediction / 8.1:
Short-Term Prediction / 8.3:
Parameter-Varying Systems / 8.5:
Long-Term Prediction / 8.6:
Appendix / 8.7:
Acknowledgments / 8.9:
Figures / 8.10:
Concept Learning / 8.11:
Background / 9.1:
Preliminaries / 9.2:
PAC Learning / 9.3.1:
Approximation by Wavelet Networks / 9.3.2:
Stochastic Approximation Algorithms / 9.3.3:
Learning Algorithms / 9.4:
Basic Algorithm / 9.4.1:
Batching Algorithm / 9.4.2:
Summary / 9.5:
Bibliography / 9.6:
Index / 10.1:
Mathematical Preliminaries / I:
Sets / 1.1:
Functions / 1.2:
25.

図書

図書
F. P. [i.e. R.] Gantmacher, M. G. Krein
出版情報: Providence, Rhode Island : AMS Chelsea, c2002  viii, 310 p. ; 26 cm
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26.

図書

図書
István Gaą́l
出版情報: Boston : Birkhäuser, c2002  xiii, 184 p. ; 24 cm
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Preface
Acknowledgements
Introduction
Auxiliary Results, Tools
Auxiliary Equations
Index Form Equations in General
Cubic Fields
Quartic Fields
Quintic Fields
Sextic Fields
Relative Power Integral Bases
Some Higher Degree Fields
Tables
References
Author Index
Subject Index
Preface
Acknowledgements
Introduction
27.

図書

図書
Prem K. Kythe, Pratap Puri
出版情報: Boston : Birkhäuser, c2002  xviii, 508 p. ; 25 cm
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28.

図書

図書
Paul S. Addison
出版情報: Bristol : Institute of Physics Pub., c2002  xiii, 353 p., [8] p. of plates. ; 25 cm
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Preface
Getting started / 1:
Introduction / 1.1:
The wavelet transform / 1.2:
Reading the book / 1.3:
The continuous wavelet transform / 2:
The wavelet / 2.1:
Requirements for the wavelet / 2.3:
The energy spectrum of the wavelet / 2.4:
Identification of coherent structures / 2.5:
Edge detection / 2.7:
The inverse wavelet transform / 2.8:
The signal energy: wavelet-based energy and power spectra / 2.9:
The wavelet transform in terms of the Fourier transform / 2.10:
Complex wavelets: the Morlet wavelet / 2.11:
The wavelet transform, short time Fourier transform and Heisenberg boxes / 2.12:
Adaptive transforms: matching pursuits / 2.13:
Wavelets in two or more dimensions / 2.14:
The CWT: computation, boundary effects and viewing / 2.15:
Endnotes / 2.16:
Chapter keywords and phrases / 2.16.1:
Further resources / 2.16.2:
The discrete wavelet transform / 3:
Frames and orthogonal wavelet bases / 3.1:
Frames / 3.2.1:
Dyadic grid scaling and orthonormal wavelet transforms / 3.2.2:
The scaling function and the multiresolution representation / 3.2.3:
The scaling equation, scaling coefficients and associated wavelet equation / 3.2.4:
The Haar wavelet / 3.2.5:
Coefficients from coefficients: the fast wavelet transform / 3.2.6:
Discrete input signals of finite length / 3.3:
Approximations and details / 3.3.1:
The multiresolution algorithm--an example / 3.3.2:
Wavelet energy / 3.3.3:
Alternative indexing of dyadic grid coefficients / 3.3.4:
A simple worked example: the Haar wavelet transform / 3.3.5:
Everything discrete / 3.4:
Discrete experimental input signals / 3.4.1:
Smoothing, thresholding and denoising / 3.4.2:
Daubechies wavelets / 3.5:
Filtering / 3.5.1:
Symmlets and coiflets / 3.5.2:
Translation invariance / 3.6:
Biorthogonal wavelets / 3.7:
Two-dimensional wavelet transforms / 3.8:
Adaptive transforms: wavelet packets / 3.9:
Fluids / 3.10:
Statistical measures / 4.1:
Moments, energy and power spectra / 4.2.1:
Intermittency and correlation / 4.2.2:
Wavelet thresholding / 4.2.3:
Wavelet selection using entropy measures / 4.2.4:
Engineering flows / 4.3:
Jets, wakes, turbulence and coherent structures / 4.3.1:
Fluid-structure interaction / 4.3.2:
Two-dimensional flow fields / 4.3.3:
Geophysical flows / 4.4:
Atmospheric processes / 4.4.1:
Ocean processes / 4.4.2:
Other applications in fluids and further resources / 4.5:
Engineering testing, monitoring and characterization / 5:
Machining processes: control, chatter, wear and breakage / 5.1:
Rotating machinery / 5.3:
Gears / 5.3.1:
Shafts, bearings and blades / 5.3.2:
Dynamics / 5.4:
Chaos / 5.5:
Non-destructive testing / 5.6:
Surface characterization / 5.7:
Other applications in engineering and further resources / 5.8:
Impacting / 5.8.1:
Data compression / 5.8.2:
Engines / 5.8.3:
Miscellaneous / 5.8.4:
Medicine / 6:
The electrocardiogram / 6.1:
ECG timing, distortions and noise / 6.2.1:
Detection of abnormalities / 6.2.2:
Heart rate variability / 6.2.3:
Cardiac arrhythmias / 6.2.4:
ECG data compression / 6.2.5:
Neuroelectric waveforms / 6.3:
Evoked potentials and event-related potentials / 6.3.1:
Epileptic seizures and epileptogenic foci / 6.3.2:
Classification of the EEG using artificial neural networks / 6.3.3:
Pathological sounds, ultrasounds and vibrations / 6.4:
Blood flow sounds / 6.4.1:
Heart sounds and heart rates / 6.4.2:
Lung sounds / 6.4.3:
Acoustic response / 6.4.4:
Blood flow and blood pressure / 6.5:
Medical imaging / 6.6:
Ultrasonic images / 6.6.1:
Magnetic resonance imaging, computed tomography and other radiographic images / 6.6.2:
Optical imaging / 6.6.3:
Other applications in medicine / 6.7:
Electromyographic signals / 6.7.1:
Sleep apnoea / 6.7.2:
DNA / 6.7.3:
Fractals, finance, geophysics and other areas / 6.7.4:
Fractals / 7.1:
Exactly self-similar fractals / 7.2.1:
Stochastic fractals / 7.2.2:
Multifractals / 7.2.3:
Finance / 7.3:
Geophysics / 7.4:
Properties of subsurface media / 7.4.1:
Surface feature analysis / 7.4.2:
Climate, clouds, rainfall and river levels / 7.4.3:
Other areas / 7.5:
Astronomy / 7.5.1:
Chemistry and chemical engineering / 7.5.2:
Plasmas / 7.5.3:
Electrical systems / 7.5.4:
Sound and speech / 7.5.5:
Useful books, papers and websites / 7.5.6:
Useful books and papers
Useful websites
References
Index
Preface
Getting started / 1:
Introduction / 1.1:
29.

図書

図書
John E. Jayne and C. Ambrose Rogers
出版情報: Princeton, NJ : Princeton University Press, c2002  xiv, 167 p. ; 24 cm
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Preface
Introduction
Classical results / Chapter 1:
Michael's Continuous Selection Theorem / 1.1:
Results of Kuratowski and Ryll-Nardzewski / 1.2:
Remarks / 1.3:
Functions that are constant on the sets of a disjoint discretely o-decomposable family of F s -sets / Chapter 2:
Discretely o-Decomposable Partitions of a Metric Space / 2.1:
Functions of the First Borel and Baire Classes / 2.2:
When is a Function of the First Borel Class also of the First Baire Class? / 2.3:
Selectors for upper semi-continuous functions with non-empty compact values / 2.4:
A General Theorem / 3.1:
Special Theorems / 3.2:
Minimal Upper Semi-continuous Set-valued Maps / 3.3:
Selectors for compact sets / 3.4:
A Sp ial Theorem / 4.1:
A Ge ral Theorem / 4.2:
Applications / 4.3:
Monotone Maps and Maximal Monotone Maps / 5.1:
Subdifferential Maps / 5.2:
Attainment Maps from X* to X / 5.3:
Attainment Maps from X to X* / 5.4:
Metric Projections or Nearest Point Maps / 5.5:
Some Selections into Families of Convex Sets / 5.6:
Example / 5.7:
Selectors for upper semi-continuous set-valued maps with nonempty values that are otherwise arbitrary / 5.8:
Diagonal Lemmas / 6.1:
Selection Theorems / 6.2:
A Selection Theorem for Lower Semi-continuous Set-valued Maps / 6.3:
Further applications / 6.4:
Duals of Asplund Spaces / 7.1tBoundary Lemmas:
A Partial Converse to Theorem 5.4 / 7.3:
Bibliography / 7.4:
Index
Preface
Introduction
Classical results / Chapter 1:
30.

図書

図書
by Alexander V. Mikhalev and Günter F. Pilz [editors]
出版情報: Dordrecht : Kluwer Academic Publishers, c2002  xvi, 618 p. ; 25 cm
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31.

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図書
edited by Ngaiming Mok
出版情報: Hong Kong : Dept. of Mathematics, University of Hong Kong, c2001  415 p. ; 22 cm
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32.

図書

図書
Thomas Fiedler
出版情報: Dordrecht ; Boston : Kluwer Academic Pub., c2001  xvi, 412 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 532
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33.

図書

図書
M. Aslam Chaudhry, Syed M. Zubair
出版情報: Boca Raton : Chapman & Hall/CRC, c2002  xi, 493 p. ; 24 cm
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34.

図書

図書
Tadeusz Iwaniec and Gaven Martin
出版情報: Oxford : Clarendon Press , New York : Oxford University Press, 2001  xv, 552 p. ; 25 cm
シリーズ名: Oxford mathematical monographs
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35.

図書

図書
Larry C. Grove
出版情報: Providence, R.I. : American Mathematical Society, c2002  x, 169 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 39
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36.

図書

図書
Jean-Pierre Otal ; translated by Leslie D. Kay
出版情報: Providence, R.I. : American Mathematical Society , [Paris] : Société Mathématique de France, c2001  xiv, 126 p., [1] p. of plates ; 26 cm
シリーズ名: SMF/AMS texts and monographs ; v. 7
Astérisque ; no. 235, 1996
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Teichmuller spaces and Kleinian groups
Real trees and degenerations of hyperbolic structures
Geodesic laminations and real trees
Geodesic laminations and the Gromov topology
The double limit theorem
The hyperbolization theorem for fibered manifolds
Sullivan's theorem
Actions of surface groups on real trees
Two examples of hyperbolic manifolds that fiber over the circle
Geodesic laminations
Bibliography
Index
Teichmuller spaces and Kleinian groups
Real trees and degenerations of hyperbolic structures
Geodesic laminations and real trees
37.

図書

図書
Jie Xiao
出版情報: Berlin : Springer, c2001  viii, 112 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1767
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38.

図書

図書
Markus J. Pflaum
出版情報: Berlin ; Tokyo : Springer, c2001  viii, 230 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1768
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Introduction
Notation
Stratified Spaces and Functional Structures / 1:
Decomposed spaces / 1.1:
Stratifications / 1.2:
Smooth Structures / 1.3:
Local Triviality and the Whitney conditions / 1.4:
The sheaf of Whitney functions / 1.5:
Rectifiable curves and regularity / 1.6:
Extension theory for Whitney functions on regular spaces / 1.7:
Differential Geometric Objects on Singular Spaces / 2:
Stratified tangent bundles and Whitney's condition (A) / 2.1:
Derivations and vector fields / 2.2:
Differential forms and stratified cotangent bundle / 2.3:
Metrics and length space structures / 2.4:
Differential Operators / 2.5:
Poisson structures / 2.6:
Control Theory / 3:
Tubular neighborhoods / 3.1:
Cut point distance and maximal tubular neighborhoods / 3.2:
Curvature moderate submanifolds / 3.3:
Geometric implications of the Whitney conditions / 3.4:
Existence and uniqueness theorems / 3.5:
Tubes and control data / 3.6:
Controlled vector fields and integrability / 3.7:
Extension theorems on controlled spaces / 3.8:
Thom's first isotopy lemma / 3.9:
Cone spaces / 3.10:
Orbit Spaces / 4:
Differentiable <$>\cal {G}<$>-Manifolds / 4.1:
Proper Group Actions / 4.2:
Stratification of the Orbit Space / 4.3:
Functional Structure / 4.4:
DeRham-Cohomology / 5:
The deRham complex on Singular Spaces / 5.1:
DeRham cohomology on <$>\cal {C}^\infty<$>-cone Spaces / 5.2:
DeRham theorems on orbit spaces / 5.3:
DeRham cohomology of Whitney functions / 5.4:
Homology of Algebras of Smooth Functions / 6:
Topological algebras and their modules / 6.1:
Homological algebra for topological modules / 6.2:
Continuous Hochschild homology / 6.3:
Hochschild homology of algebras of smooth functions / 6.4:
Supplements from linear algebra and functional analysis / A:
The vector space distance / A.1:
Polar decomposition / A.2:
Topological tensor products / A.3:
Kahler diflferentials / B:
The space of Kähler differentials / B.1:
Topological version / B.2:
Application to locally ringed Spaces / B.3:
Jets, Whitney functions and a few <$>\cal {C}^\infty<$>-mappings / C:
Fréchet topologies for <$>\cal {C}^\infty<$>-functions / C.1:
Jets / C.2:
Whitney functions / C.3:
Smoothing of the angle / C.4:
Introduction
Notation
Stratified Spaces and Functional Structures / 1:
39.

図書

図書
by Wilfried Hazod and Eberhard Siebert
出版情報: Dordrecht : Kluwer Academic Publishers, c2001  xvii, 612 p. ; 25 cm
シリーズ名: Mathematics and its applications ; vol. 531
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Preface
Introduction
Probabilities on vector spaces / I:
Preparations: Linear operators on finite-dimensional vector spaces / 1.1:
Notations (in particular for Chapter I)
Discrete one-parameter groups of operators / II:
Continuous one-parameter groups of operators / III:
Linear groups / IV:
Full probability measures and convergence of types / 1.2:
Operator-semistable laws and operator-stable laws / 1.3:
Definition and Levy-Khinchin representation
Annexe: More on infinitely divisible laws
Levy measures of operator- (semi-) stable laws / 1.4:
Levy measures of operator-semistable laws
Levy measures of operator-stable laws
Algebraic characterization of operator- (semi-) stability / 1.5:
The structure of Lin ([mu])
Subordination and (semi-) stability
A randomized characterization of operator-stability
Operator- (semi-) stable laws as limit distributions / 1.6:
Domains of operator- (semi-) attraction
Annexe: More on limits of infinitely divisible laws
More on domains of operator semi-attraction
Properties of operator- (semi-) stable laws / 1.7:
Exponents of operator-stable laws / 1.8:
Elliptical symmetry and large symmetry groups / 1.9:
Elliptically symmetric operator- (semi-) stable laws
Large symmetry groups
Domains of normal operator attraction / 1.10:
Stable laws
Remarks on operator-semistable laws
Moments and domains of attraction
The existence of commuting normalizations / 1.11:
More on the structure of the decomposability group Lin([mu]) / 1.12:
Semistability and strict semistability
Jordan decomposition and spectrum of normalizing operators
Marginal distributions of operator (semi-) stable laws
More on convergence of types theorems / 1.13:
Types and transformation groups
Applications of the convergence of types theorem
Finite-dimensional vector spaces
A method to construct full measures, given B
Some examples / V:
Stochastic compactness and regular variation properties / VI:
Probabilities with idempotent type. [Gamma]-stable and completely stable measures / 1.14:
Examples and counterexamples / 1.15:
Operator-stable laws on V = R[superscript 2] and R[superscript 3]
Subordination of stable laws
Probabilities with discrete symmetry group on V = R[superscript 2]
Marginal distributions of operator stable laws
Convergence of types and idempotent types
Limit laws and domains of attraction
Commuting normalizations / VII:
References and comments for Chapter I / 1.16:
Probabilities on simply connected nilpotent Lie groups
Probabilities on locally compact groups: Some fundamental theorems / 2.0:
Continuous convolution semigroups and the structure of generating functionals
Convergence of continuous convolution semigroups
Discrete convolution semigroups
Embedding theorems
Annexe: Supports of convolution semigroups
Discrete and continuous convolution semigroups: The translation procedure / 2.1:
Automorphisms and contractible Lie groups. Some basic facts
Some examples of contractible Lie groups
Convergence of types and full measures / 2.2:
Simply connected nilpotent Lie groups
Some generalizations
Semistable and stable continuous convolution semigroups on simply connected nilpotent Lie groups / 2.3:
Levy measures of stable and semistable laws / 2.4:
Levy measures of semistable laws
Levy measures of stable laws
Algebraic characterization of (semi-) stability / 2.5:
The structure of Lin([mu])
The structure of Inv([mu]), resp. Inv(A)
Subordination and semistability
(Semi-) stable laws as limit distributions / 2.6:
Limit theorems and uniqueness of embedding for semistable laws
Domains of (semi-) attraction
Properties of (semi-) stable laws / 2.7:
Absolute continuity and purity laws
Gaussian and Bochner stable measures
Holomorphic convolution semigroups
Moments of (semi-) stable laws
Exponents of stable laws / 2.8:
Elliptical symmetry and large invariance groups / 2.9:
Domains of normal attraction / 2.10:
Stable and semistable laws
Probabilities with idempotent type: [Gamma]-stable and completely stable measures / 2.11:
Idempotent (infinitesimal) [Gamma]-types and [Gamma]-stable laws
Complete stability
Marginals and complete stability
Intrinsic definitions of semistability
Domains of partial attraction and random limit theorems on groups and vector spaces / 2.12:
The existence of universal laws (Doeblin laws)
Stochastic compactness
Random limit theorems: Independent random times
Geometric (semi-) stability / 2.13:
Geometric convolutions
Properties of geometric and exponential distributions
Characterization of geometric convolutions and exponential mixtures
Geometric semistability
Geometric domains of attraction
Illustrations and examples for vector spaces G = V
More arithmetic properties of geometric convolutions
Remarks on self-decomposable laws on vector spaces and on groups / 2.14:
The decomposability semigroup D([mu])
Self-decomposability
Cocycle equations, background driving processes and generalized Ornstein-Uhlenbeck processes
Stable hemigroups and self-similar processes
Space-time processes
Processes on G and on V
Background driving processes with logarithmic moments
Full self-decomposable distributions and limit laws / VIII:
Generalizations and examples / IX:
More limit theorems on G and V: Mixing properties and dependent random times / 2.15:
A theorem of H. Cramer
Limit theorems for mixing arrays of random variables
Random limit theorems in the domain of attraction of (semi-) stable laws: Dependent random times
References and comments for Chapter II / 2.16:
(Semi-) stability and limit theorems on general locally compact groups
Contractive automorphisms on locally compact groups / 3.1:
Contractive automorphisms and contractible groups
Totally disconnected contractible groups
The structure theorem for contractible groups
Contractive one-parameter automorphism groups
Some more structure theorems for discrete automorphism groups
Automorphisms contracting modulo a compact subgroup K / 3.2:
Contraction mod K
The structure theorem: C[subscript K]([tau]) = C([tau])[middle dot]K for discrete automorphism groups acting on a Lie group
Borel cross-sections for the action of C([tau]) on C[subscript K]([tau]) (discrete automorphism groups)
Continuous automorphism groups
The structure theorem: C[subscript K](T) = C(T) [times sign, right closed] K for continuous automorphism groups
The structure of C[subscript K]([tau]) for p-adic Lie groups
Examples, counterexamples and some more structure theory / 3.3:
Contractible and K-contractible Lie groups
Automorphisms of compact groups
Infinite-dimensional tori and solenoidal groups
Retopologization of C([tau]): Intrinsic topologies of contractible groups
(Semi-) stable convolution semigroups with trivial idempotents / 3.4:
General definitions of strictly (semi-) stable convolution semigroups
(Semi-) stable continuous convolution semigroups with trivial idempotents
Some examples and further remarks
(Semi-) stable convolution semigroups with nontrivial idempotents / 3.5:
Semistable convolution semigroups on Lie groups with nontrivial idempotents
Stable convolution semigroups with nontrivial idempotents
Semistable submonogeneous semigroups on Lie groups
Semistable convolution semigroups with nontrivial idempotents on p-adic Lie groups
More on probabilities on contractible groups / 3.6:
Domains of partial attraction on contractible groups
The existence of Doeblin laws on contractible groups
A translation procedure for contractible locally compact groups
Point processes on groups and continuous convolution semigroups
Limit laws and convergence of types theorems. A survey / 3.7:
Limits of discrete convolution semigroups with nontrivial idempotents
Convergence of types theorems
Applications to semistability
Limit laws on compact extensions of contractible groups N [times sign, right closed] K
References and comments for Chapter III / 3.8:
Epilogue
Bibliography
List of Symbols
Index
Preface
Introduction
Probabilities on vector spaces / I:
40.

図書

図書
Luis Barreira, Yakov B. Pesin
出版情報: Providence, RI : American Mathematical Society, c2002  xii, 151 p. ; 26 cm
シリーズ名: University lecture series ; 23
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Introduction
Lyapunov stability theory of differential equations
Elements of nonuniform hyperbolic theory
Examples of nonuniformly hyperbolic systems
Local manifold theory
Ergodic properties of smooth hyperbolc measures
Bibliography
Index
Introduction
Lyapunov stability theory of differential equations
Elements of nonuniform hyperbolic theory
41.

図書

図書
A.M. Vinogradov ; [translated from the original Russian manuscript by Joseph Krasilʹshchik]
出版情報: Providence, R.I. : American Mathematical Society, c2001  xv, 247 p. ; 27 cm
シリーズ名: Translations of mathematical monographs ; v. 204
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42.

図書

図書
edited by Eiichi Bannai ... [et al.]
出版情報: Tokyo : Mathematical Society of Japan, c2001  474 p. ; 24 cm
シリーズ名: Advanced studies in pure mathematics ; 32
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43.

図書

図書
Bruce C. Berndt, Robert A. Rankin, editors
出版情報: [Providence, R.I.] : American Mathematical Society , [London] : London Mathematical Society, c2001  xvi, 347 p. ; 26 cm
シリーズ名: History of mathematics ; v. 22
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44.

図書

図書
Brian Conrad, Karl Rubin, editors
出版情報: Providence, R.I. : American Mathematical Society , [Princeton] : Institute for Advanced Study, c2001  xiv, 569 p. ; 26 cm
シリーズ名: IAS/Park City mathematics series / [Dan Freed, series editor] ; v. 9
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Preface
Introduction
Elliptic Curves, Modular Forms, and Applications / Joe P. Buhler
Elliptic Curves / Lecture 1.:
Curves in the affine plane
Projective curves
The group operation
Rational maps
Genus
Weierstrass form and the group law via divisors
Points on Elliptic Curves / Lecture 2.:
Finding points
Minimal discriminants
Reduction
The p-adic filtration
Elliptic Curves Over C / Lecture 3.:
Fundamental isomorphisms
The j invariant of an elliptic curve
Elliptic curves via lattices
Lattices via the upper half-plane
Modular Forms of Level 1 / Lecture 4.:
Weak modular forms
Modular Forms
Dimensions of spaces of modular forms
Hecke operators
L-series; Modular Forms of Higher Level / Lecture 5.:
Dirichlet series
L-functions of modular forms of level 1
Forms of higher level
L-series of elliptic curves
L-adic Representations / Lecture 6.:
Galois representations
One-dimensional representations
Galois representations coming from elliptic curves
The conductor
The Rank of Elliptic Curves Over Q / Lecture 7.:
Mordell-Weil
The Weak Mordell-Weil Theorem
The analytic rank
Applications of Elliptic Curves / Lecture 8.:
Primality
Factoring
Cryptography
Bibliography
Open Questions in Arithmetic Algebraic Geometry / Alice Silverberg
Overview / Chapter 1.:
Elliptic curves
Abelian varieties
Mordell-Weil groups
Torsion subgroups
Ranks
Looking ahead
Suggested reading
Torsion Subgroups / Chapter 2.:
Torsion subgroups for elliptic curves
A quick look at modular curves
Conjectures
Other results for elliptic curves
Abelian varieties over number fields
Abelian varieties over other fields
Digression on complex multiplication
Examples / Chapter 3.:
Unboundedness/boundedness
Vary the field
Quadratic twists
Average ranks
Distribution of ranks
Conjectures of Birch and Swinnerton-Dyer / Chapter 4.:
The L-function of an elliptic curve
Modularity
BSD I
The Congruent Number Problem
Evidence for BSD I
BSD II
Evidence for BSD II
Selmer groups
Examples--descents
ABC and Related Conjectures / Chapter 5.:
ABC Conjectures
ABC Conjectures for function fields
Szpiro Conjecture
Goldfeld-Szpiro Conjecture
de Weger Conjectures
Additional remarks
Some Other Conjectures / Chapter 6.:
Integral points on elliptic curves
Bounds on numbers of rational points on curves
Conductors of elliptic curves
Abelian varieties, Shimura varieties, and open questions
Lectures on Serre's Conjectures / Kenneth A. Ribet ; William A. Stein
Introduction to Serre's Conjecture
The weak conjecture of Serre
The strong conjecture
Representations arising from an elliptic curve
Background material
The cyclotomic character
Frobenius elements
Modular forms
Tate curves
Mod l modular forms
Optimizing the Weight
Representations arising from forms of low weight
The ordinary case
The supersingular case and fundamental characters
Representations of high weight
The supersingular case
Systems of mod l eigenvalues
The supersingular case revisited
Distinguishing between weights 2 and l + 1
Geometric construction of Galois representations
Representations arising from elliptic curves
Frey curves
Companion forms
Optimizing the Level
Reduction to weight 2
Geometric realization of Galois representations
Multiplicity one
Multiplicity one representations
Multiplicity one theorems
Multiplicity one for mod 2 representations
The key case
Approaches to level optimization in the key case
Some commutative algebra
Aside: Examples in characteristic two
III applies but I and II do not
II applies but I and III do not
Aside: Sketching the spectrum of the Hecke algebra
Mazur's principle
Level optimization using a pivot
Shimura curves
Character groups
Proof
Level optimization with multiplicity one
Exercises
Solutions
Appendix by Brian Conrad: The Shimura Construction in Weight 2
Analytic preparations
Algebraic preliminaries
Proof of Theorem 5.12
Appendix by Kevin Buzzard: A Mod l Multiplicity One Result
Deformations of Galois Representations / Fernando Q. Gouvea
Galois Groups and Their Representations
Galois groups of infinite algebraic extensions
The galois group of Q
Restricting the ramification
Complements to Lecture 1
Deformations of Representations
Why deform Galois representations?
The deformation functor
Universal deformations: why representable functors are nice
Representable functors and fiber products
The tangent space
Complements to Lecture 2
The Universal Deformation: Existence
Schlessinger's criteria
Universal Deformations exist
Absolutely irreducible representations
Example: the case n = 1
Extra Problems
Complements of Lecture 3
The Universal Deformation: Properties
Functorial properties
Tangent spaces and cohomology groups
Tangent spaces and extensions of modules
Obstructed and unobstructed deformation problems
Explicit Deformations
The basic setup
Group theory
Pro-p-extensions
Tame representations
Deformations With Prescribed Properties
Deformation conditions
Deformations with fixed determinant
Categorical deformation conditions
Ordinary deformations
Deformation conditions for global Galois representations
Representations that are ordinary at p
Complements to Lecture 6
Modular Deformations
Classical modular forms and their representations
p-adic modular forms
Imposing deformation conditions
p-adic Families and Infinite Ferns
The slope of an eigenform
p-old and p-new
p-adic families of modular forms
Infinite ferns
A Criterion for Existence of a Universal Deformation Ring / Mark DickinsonAppendix 1.:
An Overview of a Theorem of Flach / Tom WestonAppendix 2.:
Unobstructed deformation problems
Galois modules and the calculus of Tate twists
First reductions
The L-function of Sym[superscript 2] T[subscript l]
Kolyvagin's theory of Euler systems
The Flach map
The geometry of modular curves
Some modular units
Local behavior of the c[subscript r]
On the local Galois invariants of E[l] [multiply sign in circle] E[l] / Appendix A:
The definition of the Flach map / Appendix B:
An Introduction to the p-adic Geometry of Modular Curves / Matthew EmertonAppendix 3.:
The curve X[subscript 0](2)
Canonical subgroups of elliptic curves over C[subscript 2]
The parameter q
The Hasse invariant
Return to X[subscript 0](2)
The theory for arbitrary primes p
Guide to the literature
Introduction to Iwasawa Theory for Elliptic Curves / Ralph Greenberg
Mordell-Weil Groups
Selmer Groups
A-Modules
Mazur's Control Theorem
Galois Cohomology / John Tate
Group modules
Cohomology
Characterization of H[superscript r] (G, -)
Kummer theory
Functor of pairs (G, A)
The Shafarevich group
The inflation-restriction sequence
Cup products
G-pairing
Duality for finite modules
Local Fields
The Arithmetic of Modular Forms / Wen-Ching Winnie Li
Introduction to Elliptic Curves, Modular Forms, and Calabi-Yau Varieties
Classical modular forms
Zeta functions
Calabi-Yau varieties
The arithmetic of modular forms
Eisenstein series
The structure of C(k, N, x)- The theory of newforms
Connections Among Modular Forms, Elliptic Curves, and Representations of Galois Groups
Functional equations
Connections with elliptic curves
Connections with representations of the Galois group over Q
Comparisons with automorphic forms of GL[subscript 2] over function fields
Arithmetic of Certain Calabi-Yau Varieties and Mirror Symmetry / Noriko Yui
Acknowledgements
The Modularity Conjecture for Rigid Calabi-Yau Threefolds over the Field of Rational Numbers
Definition of Calabi-Yau varieties
The mirror symmetry conjecture
Rigid Calabi-Yau threefolds over Q
The modularity conjecture for rigid Calabi-Yau threefolds over Q
Evidence for the modularity conjecture
Strategy for establishing the modularity conjecture
The intermediate Jacobian of a Calabi-Yau threefold
The order of vanishing of L-series at s = 2
The conjecture of Beilinson and Bloch
Arithmetic of Orbifold Calabi-Yau Varieties Over Number Fields
Fermat hypersurfaces and their deformations
Orbifold Calabi-Yau varieties
Sketch of proof of Theorem 2.2
The L-series of orbifold Calabi-Yau varieties
Sketch of proof of Theorem 4.2
The Tate conjecture
Construction of Mirror Calabi-Yau varieties
Problems
K3 Surfaces, Mirror Moonshine Phenomenon
Mirror Moonshine phenomena
K3 surfaces
The K3 lattice
Lattice polarized K3 surfaces
Moduli space of lattice polarized K3 surfaces
Picard-Fuchs differential equations for one-parameter families of K3 surfaces
Mirror maps
Generalizations and open problems
Preface
Introduction
Elliptic Curves, Modular Forms, and Applications / Joe P. Buhler
45.

図書

図書
Henrik Gadegaard Spalk
出版情報: Aarhus, Denmark : University of Aarhus, Department of Mathematics, 2001  91 p. ; 21 cm
シリーズ名: Lecture notes series ; no. 67
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46.

図書

図書
editor, Jeffery D. McNeal
出版情報: Berlin : Walter de Gruyter, 2001  191 p. ; 25 cm
シリーズ名: Ohio State University Mathematical Research Institute publications ; 9
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Preface
Points in general position in real-analytic submanifolds in C[superscript N] and applications / M. S. Baouendi ; Linda Preiss Rothschild ; Dmitri Zaitsev
Holomorphic motion of circles through affine bundles / David E. Barrett
Weighted estimates for the [partial differential]-equation / Bo Berndtsson
Hypoellipticity in the infinitely degenerate regime / Michael Christ
Spiraling and nonhypoellipticity
Positivity conditions for real-analytic functions / John P. D'Angelo
On a generalized reflection principle in C[superscript 2] / Peter Ebenfelt ; Xiaojun Huang
Compactness in the [partial differential]-Neumann problem / Siqi Fu ; Emil J. Straube
Hypoellipticity at non-subelliptic points / Joseph J. Kohn
Very ampleness part of Fujita's conjecture and multiplier ideal sheaves of Kohn and Nadel / Yum-Tong Siu
Preface
Points in general position in real-analytic submanifolds in C[superscript N] and applications / M. S. Baouendi ; Linda Preiss Rothschild ; Dmitri Zaitsev
Holomorphic motion of circles through affine bundles / David E. Barrett
47.

図書

図書
edited by Flávio Ulhoa Coelho, Héctor A. Merklen
出版情報: New York : M. Dekker, c2002  xvii, 282 p. ; 26 cm
シリーズ名: Lecture notes in pure and applied mathematics ; v. 224
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Preface
Contributors
Invited Talks
Participants
On the Existence of Left and Right Almost Split Morphisms / Lidia Angeleri-Hugel1.:
Actions of Hopf Algebras on Quantum Polynomials / Vyacheslav A. Artamonov2.:
Strongly Simply Connected Derived Tubular Algebras / Ibrahim Assem3.:
H[superscript 1] and Presentations of Finite Dimensional Algebras / Michael J. Bardzell ; Eduardo N. Marcos4.:
Tame Tilted Algebras with Almost Regular Connecting Components / Grzegorz Bobinski5.:
Reflexive Modules Are Not Closed under Submodules / Gabriella D'Este6.:
Fibre Sum Functors and the Bimodule Ext / Peter Draxler7.:
Smooth Automorphism Group Schemes / Daniel R. Farkas ; Christof Geiss8.:
A Combinatorial Characterization of Hereditary Categories Containing Simple Objects / Dieter Happel ; Idun Reiten9.:
Symmetric Quasi-Schurian Algebras / Octavio Mendoza Hernandez10.:
On Lattices at the Ends of Connected Components of the Auslander-Reiten Quiver / Alfredo Jones11.:
Factorisations of Morphisms for Wild Hereditary Algebras / Otto Kerner12.:
A Note on Concealed-Canonical Artin Algebras / Dirk Kussin ; Zygmunt Pogorzaly13.:
Koszul Algebras and the Gorenstein Condition / Roberto Martinez-Villa14.:
Some Remarks about the "Double Extension" Algebra of a Finite Poset / Teresita Noriega15.:
Coil Algebras that Are Derived-Tame / Jose Antonio de la Pena ; Bertha Tome16.:
One-Point Extensions of Quasitilted Algebras by Modules on Stable Tubes / Sonia E. Trepode17.:
Combinatorial Partial Tilting Complexes for the Brauer Star Algebras / Mary Schaps ; Evelyne Zakay-Illouz18.:
Almost Split Sequences in Categories of Representations of Quivers II / Sverre O. Smalo19.:
Cotilting Objects and Dualities / Robert Wisbauer20.:
Coherent Components of Auslander-Reiten Quivers whose DTr-Orbits Are Finite / Hailou Yao21.:
Twisted Hopf Algebras / Pu Zhang ; Li-Bin Li22.:
Preface
Contributors
Invited Talks
48.

図書

図書
edited by Gennady Lyubeznik
出版情報: New York : M. Dekker, c2002  ix, 342 p. ; 26 cm
シリーズ名: Lecture notes in pure and applied mathematics ; v. 226
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Preface
Contributors
The Minicourses
Local Cohomology in Equivariant Topology / J. P. C. Greenlees1.:
Lectures on Local Cohomology and Duality / Joseph Lipman2.:
Other Papers
Cohomological Invariants of Coherent Sheaves over Projective Schemes: A Survey / Markus Brodmann3.:
A Partial Survey of Local Cohomology / Gennady Lyubeznik4.:
p-Torsion Elements in Local Cohomology Modules II / Anurag K. Singh5.:
Algorithms for Associated Primes, Weyl Closure, and Local Cohomology of D-Modules / Harrison Tsai6.:
Computing Local Cohomology in Macaulay 2 / Anton Leykin7.:
Squarefree Modules and Local Cohomology Modules at Monomial Ideals / Kohji Yanagawa8.:
Graded Greenlees-May Duality and the Cech Hull / Ezra Miller9.:
Residue Methods in Combinatorial Analysis / I-Chiau Huang10.:
Preface
Contributors
The Minicourses
49.

図書

図書
M.C. Delfour, J.-P. Zolésio
出版情報: Philadelphia : Society for Industrial and Applied Mathematics, c2001  xvii, 482 p. ; 26 cm
シリーズ名: Advances in design and control / editor-in-chief, John A. Burns
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List of Figures
Preface
Introduction / 1:
Geometry as a Variable
Shape Analysis / 2:
Geometric Measure Theory / 3:
Distance Functions, Smoothness, Curvatures / 4:
Shape Optimization / 5:
Shape Derivatives / 6:
Shape Calculus and Tangential Differential Calculus / 7:
Shape Analysis in This Book / 8:
Overview of the Book / 9:
Analysis, Shape Spaces, and Optimization / 9.1:
Continuity, Derivatives, Shape Calculus, and Tangential Differential Calculus / 9.2:
Classical Descriptions and Properties of Domains
Notation and Definitions
Basic Notation / 2.1:
Continuous and C[superscript k] Functions / 2.2:
Holder and Lipschitz Continuous Functions / 2.3:
Smoothness of Domains, Boundary Integral, Boundary Curvatures
C[superscript k] and Holderian Sets / 3.1:
Boundary Integral, Canonical Density, and Hausdorff Measures / 3.2:
Fundamental Forms and Principal Curvatures / 3.3:
Domains as Level Sets of a Function
Domains as Local Epigraphs
Sets That Are Locally Lipschitzian Epigraphs / 5.1:
Local Epigraphs and Sets of Class C[superscript k,e] / 5.2:
Boundary Integral from the Graph of a Function / 5.3:
Volume and Surface Measures of the Boundary / 5.4:
Convex Sets / 5.5:
Nonhomogeneous Neumann and Dirichlet Problems / 5.6:
Uniform Cone Property for Lispchitzian Domains
Segment Property and C[superscript 0]-Epigraphs
Courant Metric Topology on Images of a Domain
The Complete Metric Group of Diffeomorphisms F[superscript k subscript 0] / 8.1:
The Courant Metric on the Images / 8.2:
Perturbations of the Identity / 8.3:
The Generic Framework of Micheletti
B[superscript k] (R[superscript N], R[superscript N])-Mappings
Lipschitzian Mappings
The Murat-Simon Approach / 9.2.1:
The Micheletti Approach / 9.2.2:
B[superscript k] (D, R[superscript N])- and C[superscript k subscript 0] (D, R[superscript N])-Mappings / 9.3:
Domains in a Closed Submanifold of R[superscript N] / 10:
Relaxation to Measurable Domains
Characteristic Functions in L[superscript p]-Topologies
Strong Topologies and C[superscript [infinity]-Approximations
Weak Topologies and Microstructures
Nice or Measure Theoretic Representative
The Family of Convex Sets / 2.4:
Sobolev Spaces for Measurable Domains / 2.5:
Some Compliance Problems with Two Materials
Transmission Problem and Compliance
The Original Problem of Cea and Malanowski
Relaxation and Homogenization
Buckling of Columns
Caccioppoli or Finite Perimeter Sets
Finite Perimeter Sets
Decomposition of the Integral along Level Sets
Domains of Class W[superscript [varepsilon],p] (D), 0 [less than or equal] [varepsilon] [ 1/p, p [greater than or equal] 1
Compactness and Uniform Cone Property
Existence for the Bernoulli Free Boundary Problem
An Example: Elementary Modeling of the Water Wave / 6.1:
Existence for a Class of Free Boundary Problems / 6.2:
Weak Solutions of Some Generic Free Boundary Problems / 6.3:
Problem without Constraint / 6.3.1:
Constraint on the Measure of the Domain [Omega] / 6.3.2:
Weak Existence with Surface Tension / 6.4:
Continuity of the Dirichlet Boundary Value Problem
Continuity of Transmission Problems / 7.1:
Approximation by Transmission Problems / 7.2:
Continuity of the Dirichlet Problem / 7.3:
Topologies Generated by Distance Functions
Hausdorff Metric Topologies
The Family of Distance Functions C[subscript d](D)
Hausdorff Metric Topology
Hausdorff Complementary Metric Topology and C[superscript c subscript d](D)
Projection, Skeleton, Crack, and Differentiability
W[superscript 1,p]-Topology and Characteristic Functions
Sets of Bounded and Locally Bounded Curvature
Definitions and Properties
Examples
Characterization of Convex Sets
Federer's Sets of Positive Reach
Compactness Theorems
Global Conditions on D
Local Conditions in Tubular Neighborhoods
Oriented Distance Function and Smoothness of Sets
Uniform Metric Topology
The Family of Oriented Distance Functions C[subscript b](D)
Projection, Skeleton, and Differentiability of b[subscript A]
Boundary Smoothness and Smoothness of b[subscript A]
W[superscript 1,p](D)-Topology and the Family C[superscript 0 subscript b](D)
Definitions and Main Properties
Examples and Limits of the Tubular Norms as h Goes to Zero
(m,p)-Sobolev Domains (or W[superscript m,p]-Domains)
Characterization of Convex and Semiconvex Sets
Compactness Theorems for Sets of Bounded Curvature
Compactness and Uniform Cusp Property / 11:
Optimization of Shape Functions
Introduction and Generic Examples
Embedding of H[superscript 1 subscript 0]([Omega]) into H[superscript 1 subscript 0](D) and First Eigenvalue
Hausdorff Complementary Topology
Continuity of u[subscript [Omega] with Respect to [Omega] for the Dirichlet Problem
Continuity of the Neumann Problem
Optimization over Families of Lipschitzian or Convex Domains
Minimization of an Objective Function under State Equation Constraint
Optimization of the First Eigenvalue
Elements of Capacity Theory
Definition and Basic Properties
Quasi-Continuous Representative and H[superscript 1]-Functions
Transport of Sets of Zero Capacity
Continuity under Capacity Constraints
Flat Cone Condition and the Compact Family O[subscript c,r](D)
Examples with a Constraint on the Gradient
Transformations versus Flows of Velocities
Shape Functions and Choice of Shape Derivatives
Families of Transformations of Domains
C[infinity]-Domains
C[superscript k]-Domains
Cartesian Graphs
Polar Coordinates / 3.4:
Level Sets / 3.5:
Unconstrained Families of Domains
Equivalence between Velocities and Transformations / 4.1:
Equivalence for Special Families of Velocities / 4.2:
Constrained Families of Domains
Transformation of Condition (V2[subscript D]) into a Linear Constraint
Continuity of Shape Functions
Courant Metrics and Flows of Velocities
Shape Continuity and Velocity Method
Shape Derivatives and Calculus, and Tangential Differential Calculus
Review of Differentiation in Banach Spaces
Definitions of Semiderivatives and Derivatives
Locally Lipschitz Functions
Chain Rule for Semiderivatives
Semiderivatives of Convex Functions
Conditions for Frechet Differentiability
Hadamard Semiderivative and Velocity Method / 2.6:
First-Order Semiderivatives and Shape Gradient
Perturbations of the Identity and Frechet Derivative
Shape Gradient and Structure Theorem
Elements of Shape Calculus
Basic Formula for Domain Integrals
Basic Formula for Boundary Integrals
Examples of Shape Derivative
Volume of [Omega] and Area of [Gamma] / 4.3.1:
H[superscript 1]([Omega])-Norm / 4.3.2:
Normal Derivative / 4.3.3:
Elements of Tangential Calculus
Intrinsic Definition of the Tangential Gradient
First-Order Derivatives
Second-Order Derivatives
A Few Useful Formulae and the Chain Rule
The Stokes and Green Formulae
Relation between Tangential and Covariant Derivatives
Back to the Example of Section 4.3.3 / 5.7:
Second-Order Semiderivative and Shape Hessian
Second-Order Derivative of the Domain Integral
Nonautonomous Case
Autonomous Case
Decomposition of d[superscript 2] J([Omega]; V(0), W(0)) / 6.5:
Shape Gradients under a State Equation Constraint
Min Formulation
An Illustrative Example and a Shape Variational Principle
Function Space Parametrization
Differentiability of a Minimum with Respect to a Parameter
Application of the Theorem
Domain and Boundary Integral Expressions of the Shape Gradient
Eigenvalue Problems
Transport of H[superscript k subscript 0]([Omega]) by W[superscript k,[infinity]-Transformations of R[superscript N]
Laplacian and Bi-Laplacian
Linear Elasticity
Saddle Point Formulation and Function Space Parametrization
An Illustrative Example
Saddle Point Formulation
Differentiability of a Saddle Point with Respect to a Parameter
Domain and Boundary Expressions for the Shape Gradient
Multipliers and Function Space Embedding
The Nonhomogeneous Dirichlet Problem
A Saddle Point Formulation of the State Equation
Saddle Point Expression of the Objective Function
Verification of the Assumptions of Theorem 5.1
Elements of Bibliography
Index of Notation
Index
List of Figures
Preface
Introduction / 1:
50.

図書

図書
Ken'ichi Ohshika ; translated by Ken'ichi Ohshika
出版情報: Providence, R.I. : American Mathematical Society, c2002  x, 193 p. ; 22 cm
シリーズ名: Translations of mathematical monographs ; v. 207
Iwanami series in modern mathematics
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