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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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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
William E. Hartnett
出版情報: New York : J. Wiley, c1964  xiv, 154 p. ; 22 cm
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4.

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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5.

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:
6.

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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7.

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:
8.

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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9.

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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10.

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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11.

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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12.

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
13.

図書

図書
by I. Todhunter
出版情報: London : Macmillan, 1867  vi, 318 p. ; 20 cm
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14.

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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15.

図書

図書
出版情報: Pisa : Scuola normale superiore, 1999  287 p.
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16.

図書

図書
by Charles Smith
出版情報: London : Macmillan, 1904  vi, 259 p. ; 19 cm
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17.

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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18.

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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19.

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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20.

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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21.

図書

図書
par Alfred Henry ; traduit de l'anglais par A. Sallin
出版情報: Paris : Hermann et cie, 1932  210 p. ; 25 cm
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22.

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.:
23.

図書

図書
J.S. MacNerney
出版情報: [Chapell Hill] : [University of North Carolina], 1960  v, 108 leaves ; 28 cm
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24.

図書

図書
by Radu Precup
出版情報: Dordrecht : Kluwer Academic, c2002  xiv, 218 p. ; 25 cm
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目次情報: 続きを見る
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:
25.

図書

図書
by George Boole
出版情報: London : Macmillan, 1877  xv, 496 p. ; 20 cm
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26.

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:
27.

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:
28.

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:
29.

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:
30.

図書

図書
von Ernst Roeser
出版情報: München : R. Oldenbourg, 1957  233 p. ; 24 cm
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31.

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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32.

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:
33.

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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34.

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:
35.

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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36.

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
37.

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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38.

図書

図書
by J. Harkness and F. Marley
出版情報: London : Macmillan, 1898  xv, 336 p. ; 23 cm
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39.

図書

図書
by I. Todhunter
出版情報: Cambridge [Eng.] : Macmillan, 1861  xii, 532 p., [1] leaf of plates ; 23 cm
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40.

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:
41.

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:
42.

図書

図書
平田巧[ほか]編
出版情報: 東京 : 東洋館出版社, 1968.1  979 p. ; 22cm
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43.

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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44.

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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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45.

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図書
von Hans Hermann Bock
出版情報: Göttingen : Vandenhoeck und Ruprecht, 1974  480 p. ; 24 cm
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46.

図書

図書
by Florian Cajori
出版情報: New York : Macmillan, 1924, c1919  viii, 516 p. ; 22 cm
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47.

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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48.

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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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49.

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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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50.

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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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