1.
図書
by E.J. Gumbel
出版情報:
New York : Columbia University Press, 1958 xx, 375 p. ; 24 cm
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目次情報:
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Aims and Tools / Chapter 1：
Aims / 1.0.：
Conditions / 1.0.1.：
History / 1.0.2.：
The Flood Problem / 1.0.3.：
Methodology / 1.0.4.：
Arrangement of Contents / 1.0.5.：
General Tools / 1.1.：
Linear Transformations / 1.1.1.：
Other Transformations / 1.1.2.：
Symmetry / 1.1.3.：
Measures of Dispersion / 1.1.4.：
Moments / 1.1.5.：
Generating Function / 1.1.6.：
Convolution / 1.1.7.：
The Gamma Function / 1.1.8.：
The Logarithmic Normal Distribution / 1.1.9.：
Specific Tools / 1.2.：
Problems / 1.2.0.：
The Intensity Function / 1.2.1.：
The Distribution of Repeated Occurrences / 1.2.2.：
Analysis of Return Periods / 1.2.3.：
"Observed" Distributions / 1.2.4.：
Construction of Probability Papers / 1.2.5.：
The Plotting Problem / 1.2.6.：
Conditions for Plotting Positions / 1.2.7.：
Fitting Straight Lines on Probability Papers / 1.2.8.：
Application to the Normal Distribution / 1.2.9.：
Order Statistics and Their Exceedances / Chapter 2：
Order Statistics / 2.1.：
Distributions / 2.1.0.：
Averages / 2.1.2.：
Distribution of Frequencies / 2.1.3.：
Asymptotic Distribution of mth Central Values / 2.1.4.：
The Order Statistic with Minimum Variance / 2.1.5.：
Control Band / 2.1.6.：
Joint Distribution of Order Statistics / 2.1.7.：
Distribution of Distances / 2.1.8.：
The Distribution of Exceedances / 2.2.：
Introduction / 2.2.0.：
Distribution of the Number of Exceedances / 2.2.1.：
The Median / 2.2.2.：
The Probability of Exceedances as Tolerance Limit / 2.2.4.：
Extrapolation from Small Samples / 2.2.5.：
Normal and Rare Exceedances / 2.2.6.：
Frequent Exceedances / 2.2.7.：
Summary / 2.2.8.：
Exact Distribution of Extremes / Chapter 3：
Averages of Extremes / 3.1.：
Exact Distributions / 3.1.0.：
Return Periods of Largest and Large Values / 3.1.2.：
Quantiles of Extremes / 3.1.3.：
Characteristic Extremes / 3.1.4.：
The Extremal Intensity Function / 3.1.5.：
The Mode / 3.1.6.：
The Maximum of the Mean Largest Value / 3.1.7.：
Extremal Statistics / 3.2.：
Absolute Extreme Values / 3.2.0.：
Exact Distribution of Range / 3.2.2.：
The Mean Range / 3.2.3.：
The Range as Tolerance Limit / 3.2.4.：
The Maximum of the Mean Range / 3.2.5.：
Exact Distribution of the Midrange / 3.2.6.：
Asymptotic Independence of Extremes / 3.2.7.：
The Extremal Quotient / 3.2.8.：
Analytical Study of Extremes / Chapter 4：
The Exponential Type / 4.1.：
Largest Value for the Exponential Distribution / 4.1.0.：
Order Statistics for the Exponential Distribution / 4.1.2.：
L'Hopital's Rule / 4.1.3.：
Definition of the Exponential Type / 4.1.4.：
The Three Classes / 4.1.5.：
The Logarithmic Trend / 4.1.6.：
The Characteristic Product / 4.1.7.：
Extremes of the Exponential Type / 4.2.：
The Logistic Distribution / 4.2.0.：
Normal Extremes, Numerical Values / 4.2.2.：
Analysis of Normal Extremes / 4.2.3.：
Normal Extreme Deviates / 4.2.4.：
Gamma Distribution / 4.2.5.：
Logarithmic Normal Distribution / 4.2.6.：
The Normal Distribution as a Distribution of Extremes / 4.2.7.：
The Cauchy Type / 4.3.：
The Exponential Type and the Existence of Moments / 4.3.0.：
Pareto's Distribution / 4.3.2.：
Definition of the Pareto and the Cauchy Types / 4.3.3.：
Extremal Properties / 4.3.4.：
Other Distributions without Moments / 4.3.5.：
The First Asymptotic Distribution / 4.3.6.：
The Three Asymptotes / 5.1.：
Preliminary Derivation / 5.1.0.：
The Stability Postulate / 5.1.2.：
Outline of Other Derivations / 5.1.3.：
Interdependence / 5.1.4.：
The Double Exponential Distribution / 5.2.：
Derivations / 5.2.0.：
The Methods of Cramer and Von Mises / 5.2.2.：
Mode and Median / 5.2.3.：
Generating Functions / 5.2.4.：
Standard and Mean Deviations / 5.2.5.：
Probability Paper and Return Period / 5.2.6.：
Comparison with Other Distributions / 5.2.7.：
Barricelli's Generalization / 5.2.8.：
Extreme Order Statistics / 5.3.：
Distribution of the MTH Extreme / 5.3.0.：
Probabilities of the mth Extreme / 5.3.2.：
Cramer's Distribution of MTH Extremes / 5.3.3.：
Extreme Distances / 5.3.5.：
The Largest Absolute Value and the Two Sample Problem / 5.3.6.：
Uses of the First Asymptote / Chapter 6：
Order Statistics from the Double Exponential Distribution / 6.1.：
Maxima of Largest Values / 6.1.0.：
Minima of Largest Values / 6.1.2.：
Consecutive Modes / 6.1.3.：
Consecutive Means and Variances / 6.1.4.：
Standard Errors / 6.1.5.：
Extension of the Control Band / 6.1.6.：
The Control Curve of Dick and Darwin / 6.1.7.：
Estimation of Parameters / 6.2.：
Exponential and Normal Extremes / 6.2.0.：
Use of Order Statistics / 6.2.2.：
Estimates for Probability Paper / 6.2.3.：
Sufficient Estimation Functions / B. F. Kimball6.2.4.：
Maximum Likelihood Estimations / 6.2.5.：
Approximate Solutions / 6.2.6.：
Asymptotic Variance of a Forecast / 6.2.7.：
Numerical Examples / 6.3.：
Floods / 6.3.0.：
The Design Flood / 6.3.2.：
Meteorological Examples / 6.3.3.：
Application to Aeronautics / 6.3.4.：
Oldest Ages / 6.3.5.：
Breaking Strength / 6.3.6.：
Breakdown Voltage / 6.3.7.：
Applications to Naval Engineering / 6.3.8.：
An Application to Geology / 6.3.9.：
The Second and Third Asymptotes / Chapter 7：
The Second Asymptote / 7.1.：
Frechet's Derivation / 7.1.0.：
Averages and Moments / 7.1.2.：
Estimation of the Parameters / 7.1.4.：
The Increase of the Extremes / 7.1.5.：
Generalization / 7.1.6.：
Applications / 7.1.7.：
The Third Asymptote / 7.1.8.：
The Von Mises Derivation / 7.2.0.：
Other Derivations / 7.2.2.：
Averages and Moments of Smallest Values / 7.2.3.：
Special Cases / 7.2.4.：
The 15 Relations Among the 3 Asymptotes / 7.2.5.：
Applications of the Third Asymptote / 7.3.：
Estimation of the Three Parameters / 7.3.0.：
Estimation of Two Parameters / 7.3.2.：
Analytical Examples / 7.3.3.：
Droughts / 7.3.4.：
Fatigue Failures / 7.3.5.：
The Range / Chapter 8：
Asymptotic Distributions of Range and Midrange / 8.1.：
The Range of Minima / 8.1.0.：
Generating Function of the Range / 8.1.2.：
The Reduced Range / 8.1.3.：
Asymptotic Distribution of the Midrange / 8.1.4.：
A Bivariate Transformation / 8.1.5.：
Asymptotic Distribution of the Range / 8.1.6.：
Boundary Conditions / 8.1.7.：
Extreme Ranges / 8.1.8.：
Extremal Quotient and Geometric Range / 8.1.9.：
Definitions / 8.2.0.：
The Geometric Range / 8.2.2.：
The Midrange / 8.3.：
The Parameters in the Distribution of Range / 8.3.2.：
Normal Ranges / 8.3.3.：
Estimation of Initial Standard Deviation / 8.3.4.：
Climatological Examples / 8.3.5.：
Bibliography
Index
Aims and Tools / Chapter 1：
Aims / 1.0.：
Conditions / 1.0.1.：
2.
図書
edited by B.N. Petrov and F. Csáki
出版情報:
Budapest : Akadémiai Kiadó, 1973 451 p. ; 25 cm
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3.
図書
Hans Föllmer, Alexander Schied
目次情報:
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Introduction
Mathematical finance in one period / I：
Arbitrage theory / 1：
Assets, portfolios, and arbitrage opportunities / 1.1：
Absence of arbitrage and martingale measures / 1.2：
Derivative securities / 1.3：
Complete market models / 1.4：
Geometric characterization of arbitrage-free models / 1.5：
Contingent initial data / 1.6：
Preferences / 2：
Preference relations and their numerical representation / 2.1：
Von Neumann-Morgenstern representation / 2.2：
Expected utility / 2.3：
Uniform preferences / 2.4：
Robust preferences on asset profiles / 2.5：
Probability measures with given marginals / 2.6：
Optimality and equilibrium / 3：
Portfolio optimization and the absence of arbitrage / 3.1：
Exponential utility and relative entropy / 3.2：
Optimal contingent claims / 3.3：
Microeconomic equilibrium / 3.4：
Monetary measures of risk / 4：
Risk measures and their acceptance sets / 4.1：
Robust representation of convex risk measures / 4.2：
Convex risk measures on L[infinity] / 4.3：
Value at Risk / 4.4：
Measures of risk in a financial market / 4.5：
Shortfall risk / 4.6：
Dynamic hedging / II：
Dynamic arbitrage theory / 5：
The multi-period market model / 5.1：
Arbitrage opportunities and martingale measures / 5.2：
European contingent claims / 5.3：
Complete markets / 5.4：
The binomial model / 5.5：
Convergence to the Black-Scholes price / 5.6：
American contingent claims / 6：
Hedging strategies for the seller / 6.1：
Stopping strategies for the buyer / 6.2：
Arbitrage-free prices / 6.3：
Lower Snell envelopes / 6.4：
Superhedging / 7：
P-supermartingales and upper Snell envelopes / 7.1：
Uniform Doob decomposition / 7.2：
Superhedging of American and European claims / 7.3：
Superhedging with derivatives / 7.4：
Efficient hedging / 8：
Quantile hedging / 8.1：
Hedging with minimal shortfall risk / 8.2：
Hedging under constraints / 9：
Absence of arbitrage opportunities / 9.1：
Upper Snell envelopes / 9.2：
Superhedging and risk measures / 9.4：
Minimizing the hedging error / 10：
Local quadratic risk / 10.1：
Minimal martingale measures / 10.2：
Variance-optimal hedging / 10.3：
Appendix
Convexity / A.1：
Absolutely continuous probability measures / A.2：
The Neyman-Pearson lemma / A.3：
The essential supremum of a family of random variables / A.4：
Spaces of measures / A.5：
Some functional analysis / A.6：
Introduction
Mathematical finance in one period / I：
Arbitrage theory / 1：
4.
図書
by E.W. Hobson
出版情報:
New York : Dover Publications, 1957 2 v. ; 22 cm
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5.
図書
A. Galindo, P. Pascual ; translated by J.D. García and L. Alvarez-Gaumé
6.
図書
Luis Ribes, Pavel Zalesskii
目次情報:
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Preface
Inverse and Direct Limits / 1：
Inverse or Projective Limits / 1.1：
Direct or Inductive Limits / 1.2：
Notes, Comments and Further Reading / 1.3：
Profinite Groups / 2：
Pro- <$>{\cal C}<$> Groups / 2.1：
Basic Properties of Pro- <$>{\cal C}<$> Groups / 2.2：
Existence of Sections
Exactness of Inverse Limits of Profinite Groups
The Order of a Profinite Group and Sylow Subgroups / 2.3：
Generators / 2.4：
Finitely Generated Profinite Groups / 2.5：
Generators and Chains of Subgroups / 2.6：
Procyclic Groups / 2.7：
The Frattini Subgroup of a Profinite Group / 2.8：
Pontryagin Duality for Profinite Groups / 2.9：
Pullbacks and Pushouts / 2.10：
Profinite Groups as Galois Groups / 2.11：
Free Profinite Groups / 2.12：
Profinite Topologies / 3.1：
The Pro-<$>{\cal C}<$> Completion / 3.2：
The Completion Functor
Free Pro-<$>{\cal C}<$> Groups / 3.3：
Free Pro - <$>{\cal C}<$> Group on a Set Converging to 1
Maximal Pro- <$>{\cal C}<$> Quotient Groups / 3.4：
Characterization of Free Pro-<$>{\cal C}<$> Groups / 3.5：
Open Subgroups of Free Pro-<$>{\cal C}<$> Groups / 3.6：
Some Special Profinite Groups / 3.7：
Powers of Elements with Exponents from <$>\hat {\rm Z}<$> / 4.1：
Subgroups of Finite Index in a Profinite Group / 4.2：
Profinite Abelian Groups / 4.3：
Automorphism Group of a Profinite Group / 4.4：
Automorphism Group of a Free Pro-p Group / 4.5：
Profinite Frobenius Groups / 4.6：
Torsion in the Profinite Completion of a Group / 4.7：
Discrete and Profinite Modules / 4.8：
Profinite Rings and Modules / 5.1：
Duality Between Discrete and Profinite Modules
Free Profinite Modules / 5.2：
G-modules and Complete Group Algebras / 5.3：
The Complete Group Algebra
Projective and Injective Modules / 5.4：
Complete Tensor Products / 5.5：
Profinite G-spaces / 5.6：
Free Profinite <$$$>[[RG]]-modules / 5.7：
Diagonal Actions / 5.8：
Homology and Cohomology of Profinite Groups / 5.9：
Review of Homological Algebra / 6.1：
Right and Left Derived Functors
Bifunctors
The Ext Functors
The Tor Functors
Cohomology with Coefficients in DMod(<$$$>[[RG]]) / 6.2：
Standard Resolutions
Homology with Coefficients in PMod(<$$$>[[RG]]) / 6.3：
Cohomology Groups with Coefficients in DMod(G) / 6.4：
The Functorial Behavior of Hn (G, A) and Hn (G, A) / 6.5：
The Inflation Map
Hn (G,A) as Derived Functors on DMod(G) / 6.6：
Special Mappings / 6.7：
The Restriction Map in Cohomology
The Corestriction Map in Cohomology
The Corestriction Map in Homology
The Restriction Map in Homology
Homology and Cohomology Groups in Low Dimensions / 6.8：
H2 (G, A) and Extensions of Profinite Groups
Extensions of Profinite Groups with Abelian Kernel / 6.9：
Induced and Coinduced Modules / 6.10：
The Induced Module <$>{\rm Ind}_H^G<$> (B) for H Open / 6.11：
Cohomological Dimension / 6.12：
Basic Properties of Dimension / 7.1：
The Lyndon-Hochschild-Serre Spectral Sequence / 7.2：
Cohomological Dimension of Subgroups / 7.3：
Cohomological Dimension of Normal Subgroups and Quotients / 7.4：
Groups G with cdp (G) ≤ 1 / 7.5：
Projective Profinite Groups / 7.6：
Free Pro-p Groups and Cohomological Dimension / 7.7：
Generators and Relators for Pro-p Groups / 7.8：
Cup Products / 7.9：
Normal Subgroups of Free Pro - <$>{\cal C}<$> Groups / 7.10：
Normal Subgroup Generated by a Subset of a Basis / 8.1：
The S-rank / 8.2：
Accessible Subgroups / 8.3：
Accessible Subgroups H with w0 (F/H) < rank(F) / 8.4：
Homogeneous Pro- <$>{\cal C}<$> Groups / 8.5：
Normal Subgroups / 8.6：
Proper Open Subgroups of Normal Subgroups / 8.7：
The Congruence Kernel of SL2 (Z) / 8.8：
Sufficient Conditions for Freeness / 8.9：
Characteristic Subgroups of Free Pro- <$>{\cal C}<$> Groups / 8.10：
Free Constructions of Profinite Groups / 8.11：
Free Pro- <$>{\cal C}<$> Products / 9.1：
Amalgamated Free Pro- <$>{\cal C}<$> Products / 9.2：
Cohomological Characterizations of Amalgamated Products / 9.3：
Pro- <$>{\cal C}<$> HNN extensions / 9.4：
Open Questions / 9.5：
Appendix
Spectral Sequences / A1：
Positive Spectral Sequences / A2：
Spectral Sequence of a Filtered Complex / A3：
Spectral Sequences of a Double Complex / A4：
Bibliography / A5：
Index of Symbols
Index of Authors
Index of Terms
Preface
Inverse and Direct Limits / 1：
Inverse or Projective Limits / 1.1：
7.
図書
von Helmut Hasse
出版情報:
Würzburg ; Wien : Physica-Verlag, 1965 2 v ; 25 cm
子書誌情報:
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目次情報:
T. 1/1a. Klassenkörpertheorie/Beweise zu Teil 1
T. 2. Reziprozitätsgesetz
T. 1/1a. Klassenkörpertheorie/Beweise zu Teil 1
T. 2. Reziprozitätsgesetz
8.
図書
N. Bourbaki
9.
図書
David Gilbarg, Neil S. Trudinger
目次情報:
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Introduction / Chapter 1：
Linear Equations / Part I：
Laplace''s Equation / Chapter 2：
The Mean Value Inequalities / 2.1：
Maximum and Minimum Principle / 2.2：
The Harnack Inequality / 2.3：
Green''s Representation / 2.4：
The Poisson Integral / 2.5：
Convergence Theorems / 2.6：
Interior Estimates of Derivatives / 2.7：
The Dirichlet Problem; the Method of Subharmonic Functions / 2.8：
CapacityProblems / 2.9：
The Classical Maximum Principle / Chapter 3：
The Weak Maximum Principle / 3.1：
The Strong Maximum Principle / 3.2：
Apriori Bounds / 3.3：
Gradient Estimates for Poisson''s Equation / 3.4：
A Harnack Inequality / 3.5：
Operators in Divergence FormNotesProblems / 3.6：
Poisson''s Equation and Newtonian Potential / Chapter 4：
H+ lder Continuity / 4.1：
The Dirichlet Problem for Poisson''s Equation / 4.2：
H+ lder Estimates for the Second Derivatives / 4.3：
Estimates at the Boundary / 4.4：
H+ lder Estimates for the First DerivativesNotes Problems / 4.5：
Banach and Hilbert Spaces / Chapter 5：
The Contraction Mapping / 5.1：
The Method of Cintinuity / 5.2：
The Fredholm Alternative / 5.3：
Dual Spaces and Adjoints / 5.4：
Hilbert Spaces / 5.5：
The Projection Theorem / 5.6：
The Riesz Representation Theorem / 5.7：
The Lax-Milgram Theorem / 5.8：
The Fredholm Alternative in Hilbert Spaces / 5.9：
Weak CompactnessNotesProblems / 5.10：
Classical Solutions; the Schauder Approach / Chapter 6：
The Schauder Interior Estimates / 6.1：
Boundary and Global Estimates / 6.2：
The Dirichlet Problem / 6.3：
Interior and Boundary Regularity / 6.4：
An Alternative Approach / 6.5：
Non-Uniformly Elliptic Equations / 6.6：
Other Boundary Conditions; the Obliue Derivative Problem / 6.7：
Appendix 1: Interpolation Inequalities / 6.8：
Appendix 2: Extension LemmasNotesProblems / 6.9：
Sobolev Spaces / Chapter 7：
L^p spaces / 7.1：
Regularization and Approximation by Smooth Functions / 7.2：
Weak Derivatives / 7.3：
The Chain Rule / 7.4：
The W^(k,p) Spaces / 7.5：
Density Theorems / 7.6：
Imbedding Theorems / 7.7：
Potential Estimates and Imbedding Theorems / 7.8：
The Morrey and John-Nirenberg Estimes / 7.9：
Compactness Results / 7.10：
Difference Quotients / 7.11：
Extension and InterpolationNotesProblems / 7.12：
Generalized Solutions and Regularity / Chapter 8：
Solvability of the Dirichlet Problem / 8.1：
Diferentiability of Weak Solutions / 8.3：
Global Regularity / 8.4：
Global Boundedness of Weak Solutions / 8.5：
Local Properties of Weak Solutions / 8.6：
Local Estimates at the Boundary / 8.7：
H+ lder Estimates for the First Derivatives / 8.11：
The Eigenvalue ProblemNotesProblems / 8.12：
Strong Solutions / Chapter 9：
Maximum Princiles for Strong Solutions / 9.1：
L^p Estimates: Preliminary Analysis / 9.2：
The Marcinkiewicz Interpolation Theorem / 9.3：
The Calderon-Zygmund Inequality / 9.4：
L^p Estimates / 9.5：
A Local Maximum Principle / 9.6：
H+ lder and Harnack Estimates / 9.8：
Local Estimates at the BoundaryNotesProblems / 9.9：
Quasilinear Equations / Part II：
Maximum and Comparison Principles / Chapter 10：
The Comparison Principle / 10.1：
Maximum Principles / 10.2：
A Counterexample / 10.3：
Comparison Principles for Divergence Form Operators / 10.4：
Maximum Principles for Divergence Form Operators Notes Problems / 10.5：
Topological Fixed Point Theorems and Their Application / Chapter 11：
The Schauder Fixes Point Theorem / 11.1：
The Leray-Schauder Theorem: a Special Case / 11.2：
An Application / 11.3：
The Leray-Schauder Fixed Point Theorem / 11.4：
Variational ProblemsNotes / 11.5：
Equations in Two Variables / Chapter 12：
Quasiconformal Mappings / 12.1：
h+ lder Gradient Estimates for Linear Equations / 12.2：
The Dirichlet Problem for Uniformly Elliptic Equations / 12.3：
Non-Uniformly Elliptic EquationsNotesProblems / 12.4：
H+ lder Estimates for the Gradient / Chapter 13：
Equations of Divergence Form / 13.1：
Equations of General Form; the Interior Estimate / 13.2：
Equations of General Form; the Boundary Estimate / 13.4：
Application to the Dirichlet ProblemNotes / 13.5：
Boundary Gradient Estimates / Chapter 14：
General Domains / 14.1：
Convex Domains / 14.2：
Boundary Curvature Conditions / 14.3：
Non-Existence Results / 14.4：
Continuity Estimates / 14.5：
Appendix: Boundary Curvature and the Distance FunctionNotesProblems / 14.6：
Introduction / Chapter 1：
Linear Equations / Part I：
Laplace''s Equation / Chapter 2：
10.
図書
by V.S. Varadarajan
11.
図書
F.R. Gantmacher ; [an English translation by K.A. Hirsch]
出版情報:
New York : Chelsea Pub. Co., c1960 2 v. ; 24 cm
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12.
図書
by Einar Hille
出版情報:
New York : Chelsea Pub. Co., 1977-1982 2 v. ; 24 cm
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目次情報:
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Number systems / 1：
The real number system / 1.1：
Further properties of real numbers / 1.2：
The complex number system 2. The complex plane / 1.3：
Geometry of complex numbers / 2.1：
Curves and regions in the complex plane / 2.2：
Regions and convexity / 2.3：
Paths / 2.4：
The extended plane; stereographic projection 3. Fractions, powers, and roots / 2.5：
Fractional linear transformations / 3.1：
Properties of Mobius transformations / 3.2：
Powers / 3.3：
Roots / 3.4：
The function $(z^2 +1)/(2z)$ 4. Holomorphic functions / 3.5：
Complex-valued functions and continuity / 4.1：
Differentiability; holomorphic functions / 4.2：
The Cauchy-Riemann equations / 4.3：
Laplace's equation / 4.4：
The inverse function / 4.5：
Conformal mapping / 4.6：
Function spaces 5. Power series / 4.7：
Infinite series / 5.1：
Operations on series / 5.2：
Double series / 5.3：
Convergence of power series / 5.4：
Power series as holomorphic functions / 5.5：
Taylor's series / 5.6：
Singularities; noncontinuable power series 6. Some elementary functions / 5.7：
The exponential function / 6.1：
The logarithm / 6.2：
Arbitrary powers; the binomial series / 6.3：
The trigonometric functions / 6.4：
Inverse trigonometric functions 7. Complex integration / 6.5：
Integration in the complex plane / 7.1：
Cauchy's theorem / 7.2：
Extensions / 7.3：
Cauchy's integral / 7.4：
Cauchy's formulas for the derivatives / 7.5：
Integrals of the Cauchy type / 7.6：
Analytic continuation: Schwarz's reflection principle / 7.7：
The theorem of Morera / 7.8：
The maximum principle / 7.9：
Uniformly convergent sequences of holomorphic functions 8. Representation theorems / 7.10：
The maximum modulus / 8.1：
The Laurent expansion / 8.3：
Isolated singularities / 8.4：
Meromorphic functions / 8.5：
Infinite products / 8.6：
Entire functions / 8.7：
The Gamma function 9. The calculus of residues / 8.8：
The residue theorem / 9.1：
The principle of the argument / 9.2：
Summation and expansion theorems / 9.3：
Inverse functions / 9.4：
Some properties of point sets / Appendix A：
Some properties of polygons / Appendix B：
On the theory of integration / Appendix C：
Bibliography
Index
Number systems / 1：
The real number system / 1.1：
Further properties of real numbers / 1.2：
13.
図書
edited by Torsten Husén ; associate editors, Benjamin S. Bloom ... [et al.]
出版情報:
Stockholm : Almqvist & Wiksell , New York : Wiley, c1967 2 v ; 24 cm
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14.
図書
I.P. Natanson ; translated from the Russian by Leo F. Boron
出版情報:
New York : F. Ungar, c1955-c1960 2 v. ; 26 cm
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15.
図書
by Oswald Veblen and John Wesley Young
出版情報:
Boston : Ginn, c1910-c1918 2 v. ; 24 cm
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16.
図書
Władysław Ślebodziński
17.
図書
herausgegeben von Philipp Frank und Richard v. Mises
出版情報:
New York : Dover , Braunschweig : Friedr. Vieweg & Sohn, 1961 2 v. ; 21 cm
子書誌情報:
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所蔵情報:
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目次情報:
t. 1. Mathematischer Teil
t. 2. Physikalischer Teil
t. 1. Mathematischer Teil
t. 2. Physikalischer Teil
18.
図書
N. Bourbaki
目次情報:
chapitre 1. Dérivées
chapitre 2. Primitives et intégrales
chapitre 3. Fonctions élémentaires
chapitre 1. Dérivées
chapitre 2. Primitives et intégrales
chapitre 3. Fonctions élémentaires
19.
図書
J.M. Ortega and W.C. Rheinboldt
目次情報:
続きを見る
Preface to Classics Edition
Preface
Acknowledgments
Glossary of Symbols
Introduction
Background Material / Part I：
Sample Problems / 1.：
Two-Point Boundary Value Problems / 1.1.：
Elliptic Boundary Value Problems / 1.2.：
Integral Equations / 1.3.：
Minimization Problems / 1.4.：
Two-Dimensional Variational Problems / 1.5.：
Linear Algebra / 2.：
A Review of Basic Matrix Theory / 2.1.：
Norms / 2.2.：
Inverses / 2.3.：
Partial Ordering and Nonnegative Matrices / 2.4.：
Analysis / 3.：
Derivatives and Other Basic Concepts / 3.1.：
Mean-Value Theorems / 3.2.：
Second Derivatives / 3.3.：
Convex Functionals / 3.4.：
Nonconstructive Existence Theorems / Part II：
Gradient Mappings and Minimization / 4.：
Minimizers, Critical Points, and Gradient Mappings / 4.1.：
Uniqueness Theorems / 4.2.：
Existence Theorems / 4.3.：
Applications / 4.4.：
Contractions and the Continuation Property / 5.：
Contractions / 5.1.：
The Inverse and Implicit Function Theorems / 5.2.：
The Continuation Property / 5.3.：
Monotone Operators and Other Applications / 5.4.：
The Degree of a Mapping / 6.：
Analytic Definition of the Degree / 6.1.：
Properties of the Degree / 6.2.：
Basic Existence Theorems / 6.3.：
Monotone and Coercive Mappings / 6.4.：
Additional Analytic Results / 6.5. Appendix.：
Iterative Methods / Part III：
General Iterative Methods / 7.：
Newton's Method and Some of Its Variations / 7.1.：
Secant Methods / 7.2.：
Modification Methods / 7.3.：
Generalized Linear Methods / 7.4.：
Continuation Methods / 7.5.：
General Discussion of Iterative Methods / 7.6.：
Minimization Methods / 8.：
Paraboloid Methods / 8.1.：
Descent Methods / 8.2.：
Steplength Algorithms / 8.3.：
Conjugate-Direction Methods / 8.4.：
The Gauss-Newton and Related Methods / 8.5.：
Convergence of the Conjugate Gradient and the Davidon--Fletcher--Powell Algorithms for Quadratic Functionals / 8.6. Appendix 1.：
Search Methods for One-Dimensional Minimization / 8.7. Appendix 2.：
Local Convergence / Part IV：
Rates of Convergence--General / 9.：
The Quotient Convergence Factors / 9.1.：
The Root Convergence Factors / 9.2.：
Relations between the R and Q Convergence Factors / 9.3.：
One-Step Stationary Methods / 10.：
Basic Results / 10.1.：
Newton's Method and Some of Its Modifications / 10.2.：
Generalized Linear Iterations / 10.3.：
Comparison Theorems and Optimal [omega] for SOR Methods / 10.4.：
Multistep Methods and Additional One-Step Methods / 11.：
Introduction and First Results / 11.1.：
Consistent Approximations / 11.2.：
The General Secant Method / 11.3.：
Semilocal and Global Convergence / Part V：
Contractions and Nonlinear Majorants / 12.：
Some Generalizations of the Contraction Theorem / 12.1.：
Approximate Contractions and Sequences of Contractions / 12.2.：
Iterated Contractions and Nonexpansions / 12.3.：
Nonlinear Majorants / 12.4.：
More General Majorants / 12.5.：
Newton's Method and Related Iterations / 12.6.：
Convergence under Partial Ordering / 13.：
Contractions under Partial Ordering / 13.1.：
Monotone Convergence / 13.2.：
Convexity and Newton's Method / 13.3.：
Newton-SOR Interactions / 13.4.：
M-Functions and Nonlinear SOR Processes / 13.5.：
Convergence of Minimization Methods / 14.：
Introduction and Convergence of Sequences / 14.1.：
Steplength Analysis / 14.2.：
Gradient and Gradient-Related Methods / 14.3.：
Newton-Type Methods / 14.4.：
Univariate Relaxation and Related Processes / 14.5.：
An Annotated List of Basic Reference Books
Bibliography
Author Index
Subject Index
Preface to Classics Edition
Preface
Acknowledgments
20.
図書
Leonard Meirovitch
目次情報:
続きを見る
Preface
Fundamentals of Newtonian Mechanics / Chapter 1：
Historical Survey of Mechanics / 1.1：
Newton's Laws / 1.2：
Impulse and Momentum / 1.3：
Moment of a Force and Angular Momentum / 1.4：
Work and Energy / 1.5：
Energy Diagrams / 1.6：
Systems of Particles / 1.7：
The Two-Body Central Force Problem / 1.8：
The Inverse Square Law. Orbits of Planets and Satellites / 1.9：
Scattering by a Repulsive Central Force / 1.10：
Problems
Suggested References
Fundamentals of Analytical Mechanics / Chapter 2：
Degrees of Freedom. Generalized Coordinates / 2.1：
Systems with Constraints / 2.2：
The Stationary Value of a Function / 2.3：
The Stationary Value of a Definite Integral / 2.4：
The Principle of Virtual Work / 2.5：
D'Alembert's Principle / 2.6：
Hamilton's Principle / 2.7：
Lagrange's Equations of Motion / 2.8：
Lagrange's Equations for Impulsive Forces / 2.9：
Conservation Laws / 2.10：
Routh's Method for the Ignoration of Coordinates / 2.11：
Rayleigh's Dissipation Function / 2.12：
Hamilton's Equations / 2.13：
Motion Relative to Rotating Reference Frames / Chapter 3：
Transformation of Coordinates / 3.1：
Rotating Coordinate Systems / 3.2：
Expressions for the Motion in Terms of Moving Reference Frames / 3.3：
Motion Relative to the Rotating Earth / 3.4：
Motion of a Free Particle Relative to the Rotating Earth / 3.5：
Foucault's Pendulum / 3.6：
Rigid Body Dynamics / Chapter 4：
Kinematics of a Rigid Body / 4.1：
The Linear and Angular Momentum of a Rigid Body / 4.2：
Translation Theorem for the Angular Momentum / 4.3：
The Kinetic Energy of a Rigid Body / 4.4：
Principal Axes / 4.5：
The Equations of Motion for a Rigid Body / 4.6：
Euler's Equations of Motion / 4.7：
Euler's Angles / 4.8：
Moment-Free Inertially Symmetric Body / 4.9：
General Case of a Moment-Free Body / 4.10：
Motion of a Symmetric Top / 4.11：
The Lagrangian Equations for Quasi-Coordinates / 4.12：
The Equations of Motion Referred to an Arbitrary System of Axes / 4.13：
The Rolling of a Coin / 4.14：
Behavior of Dynamical Systems. Geometric Theory / Chapter 5：
Fundamental Concepts / 5.1：
Motion of Single-Degree-of-Freedom Autonomous Systems about Equilibrium Points / 5.2：
Conservative Systems. Motion in the Large / 5.3：
The Index of Poincare / 5.4：
Limit Cycles of Poincare / 5.5：
Stability of Multi-Degree-of-Freedom Autonomous Systems / Chapter 6：
General Linear Systems / 6.1：
Linear Autonomous Systems / 6.2：
Stability of Linear Autonomous Systems. Routh-Hurwitz Criterion / 6.3：
The Variational Equations / 6.4：
Theorem on the First-Approximation Stability / 6.5：
Variation from Canonical Systems. Constant Coefficients / 6.6：
The Liapunov Direct Method / 6.7：
Geometric Interpretation of the Liapunov Direct Method / 6.8：
Stability of Canonical Systems / 6.9：
Stability in the Presence of Gyroscopic and Dissipative Forces / 6.10：
Construction of Liapunov Functions for Linear Autonomous Systems / 6.11：
Nonautonomous Systems / Chapter 7：
Linear Systems with Periodic Coefficients. Floquet's Theory / 7.1：
Stability of Variational Equations with Periodic Coefficients / 7.2：
Orbital Stability / 7.3：
Variation from Canonical Systems. Periodic Coefficients / 7.4：
Second-Order Systems with Periodic Coefficients / 7.5：
Hill's Infinite Determinant / 7.6：
Mathieu's Equation / 7.7：
Analytical Solutions by Perturbation Techniques / 7.8：
The Fundamental Perturbation Technique / 8.1：
Secular Terms / 8.2：
Lindstedt's Method / 8.3：
The Krylov-Bogoliubov-Mitropolsky (KBM) Method / 8.4：
A Perturbation Technique Based on Hill's Determinants / 8.5：
Periodic Solutions of Nonautonomous Systems. Duffing's Equation / 8.6：
The Method of Averaging / 8.7：
Transformation Theory. The Hamilton-Jacobi Equation / Chapter 9：
The Principle of Least Action / 9.1：
Contact Transformations / 9.2：
Further Extensions of the Concept of Contact Transformations / 9.3：
Integral Invariants / 9.4：
The Lagrange and Poisson Brackets / 9.5：
Infinitesimal Contact Transformations / 9.6：
The Hamilton-Jacobi Equation / 9.7：
Separable Systems / 9.8：
Action and Angle Variables / 9.9：
Perturbation Theory / 9.10：
The Gyroscope: Theory and Applications / Chapter 10：
Oscillations of a Symmetric Gyroscope / 10.1：
Effect of Gimbal Inertia on the Motion of a Free Gyroscope / 10.2：
Effect of Rotor Shaft Flexibility on the Frequency of Oscillation of a Free Gyroscope / 10.3：
The Gyrocompass / 10.4：
The Gyropendulum. Schuler Tuning / 10.5：
Rate and Integrating Gyroscopes / 10.6：
Problems in Celestial Mechanics / Chapter 11：
Kepler's Equation. Orbit Determination / 11.1：
The Many-Body Problem / 11.2：
The Three-Body Problem / 11.3：
The Restricted Three-Body Problem / 11.4：
Stability of Motion Near the Lagrangian Points / 11.5：
The Equations of Relative Motion. Disturbing Function / 11.6：
Gravitational Potential and Torques for an Arbitrary Body / 11.7：
Precession and Nutation of the Earth's Polar Axis / 11.8：
Variation of the Orbital Elements / 11.9：
The Resolution of the Disturbing Function / 11.10：
Problems in Spacecraft Dynamics / Chapter 12：
Transfer Orbits. Changes in the Orbital Elements Due to a Small Impulse / 12.1：
Perturbations of a Satellite Orbit in the Gravitational Field of an Oblate Planet / 12.2：
The Effect of Atmospheric Drag on Satellite Orbits / 12.3：
The Attitude Motion of Orbiting Satellites. General Considerations / 12.4：
The Attitude Stability of Earth-Pointing Satellites / 12.5：
The Attitude Stability of Spinning Symmetrical Satellites / 12.6：
Variable-Mass Systems / 12.7：
Rocket Dynamics / 12.8：
Dyadics / Appendix A：
Elements of Topology and Modern Analysis / Appendix B：
Sets and Functions / B.1：
Metric Spaces / B.2：
Topological Spaces / B.3：
Name Index
Subject Index
Preface
Fundamentals of Newtonian Mechanics / Chapter 1：
Historical Survey of Mechanics / 1.1：
21.
図書
par Arnaud Denjoy
出版情報:
Paris : Gauthier-Villars, 1946-1954 4 v. in 5 (xxxvii, 969 p.) ; 26 cm
子書誌情報:
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22.
図書
Einar, Hille
23.
図書
von Gustav Doetsch
24.
図書
László Fuchs
25.
図書
by Einar Hille
26.
図書
von P. Alexandroff ; [Autorisierte Übersetzung aus dem Russischen, Hans Günter Bothe]
目次情報:
1. Abgeschlossene Mengen
2. Nichtabgeschlossene Mengen
1. Abgeschlossene Mengen
2. Nichtabgeschlossene Mengen
27.
図書
Martin Schechter
出版情報:
New York : North Holland, c1981 xx, 324 p. ; 24 cm
子書誌情報:
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目次情報:
続きを見る
Preface
Acknowledgments
A Message to the Reader
List of Symbols
One-Dimensional Motion / Chapter 1.：
Position / 1.1.：
Mathematical Expectation / 1.2.：
Momentum / 1.3.：
Energy / 1.4.：
Observables / 1.5.：
Operators / 1.6.：
Functions of Observables / 1.7.：
Self-Adjoint Operators / 1.8.：
Hilbert Space / 1.9.：
The Spectral Theorem / 1.10.：
Exercises
The Spectrum / Chapter 2.：
The Resolvent / 2.1.：
Finding the Spectrum / 2.2.：
The Position Operator / 2.3.：
The Momentum Operator / 2.4.：
The Energy Operator / 2.5.：
The Potential / 2.6.：
A Class of Functions / 2.7.：
The Spectrum of H / 2.8.：
The Essential Spectrum / Chapter 3.：
An Example / 3.1.：
A Calculation / 3.2.：
Finding the Eigenvalues / 3.3.：
The Domain of H / 3.4.：
Back to Hilbert Space / 3.5.：
Compact Operators / 3.6.：
Relative Compactness / 3.7.：
Proof of Theorem 3.7.5 / 3.8.：
The Negative Eigenvalues / Chapter 4.：
The Possibilities / 4.1.：
Forms Extensions / 4.2.：
The Remaining Proofs / 4.3.：
Negative Eigenvalues / 4.4.：
Existence of Bound States / 4.5.：
Existence of Infinitely Many Bound States / 4.6.：
Existence of Only a Finite Number of Bound States / 4.7.：
Another Criterion / 4.8.：
Estimating the Spectrum / Chapter 5.：
Introduction / 5.1.：
Some Crucial Lemmas / 5.2.：
A Lower Bound for the Spectrum / 5.3.：
Lower Bounds for the Essential Spectrum / 5.4.：
An Inequality / 5.5.：
Bilinear Forms / 5.6.：
Intervals Containing the Essential Spectrum / 5.7.：
Coincidence of the Essential Spectrum with an Interval / 5.8.：
The Harmonic Oscillator / 5.9.：
The Morse Potential / 5.10.：
Scattering Theory / Chapter 6.：
Time Dependence / 6.1.：
Scattering States / 6.2.：
Properties of the Wave Operators / 6.3.：
The Domains of the Wave Operators / 6.4.：
Local Singularities / 6.5.：
Long-Range Potentials / Chapter 7.：
The Coulomb Potential / 7.1.：
Some Examples / 7.2.：
The Estimates / 7.3.：
The Derivatives of V(x) / 7.4.：
The Relationship Between X[subscript t] and V(x) / 7.5.：
An Identity / 7.6.：
The Reduction / 7.7.：
Mollifiers / 7.8.：
Time-Independent Theory / Chapter 8.：
The Resolvent Method / 8.1.：
The Theory / 8.2.：
A Simple Criterion / 8.3.：
The Application / 8.4.：
Completeness / Chapter 9.：
Definition / 9.1.：
The Abstract Theory / 9.2.：
Some Identities / 9.3.：
Another Form / 9.4.：
The Unperturbed Resolvent Operator / 9.5.：
The Perturbed Operator / 9.6.：
Analytic Dependence / 9.7.：
Projections / 9.9.：
An Analytic Function Theorem / 9.10.：
The Combined Results / 9.11.：
Absolute Continuity / 9.12.：
The Intertwining Relations / 9.13.：
Strong Completeness / 9.14.：
The More Difficult Problem / 10.1.：
The Technique / 10.2.：
Verification for the Hamiltonian / 10.4.：
An Extension / 10.5.：
The Principle of Limiting Absorption / 10.6.：
Oscillating Potentials / Chapter 11.：
A Surprise / 11.1.：
The Hamiltonian / 11.2.：
A Variation / 11.3.：
Examples / 11.5.：
Eigenfunction Expansions / Chapter 12.：
The Usefulness / 12.1.：
The Problem / 12.2.：
Operators on L[superscript p] / 12.3.：
Weighted L[superscript p]-Spaces / 12.4.：
Extended Resolvents / 12.5.：
The Formulas / 12.6.：
Some Consequences / 12.7.：
Summary / 12.8.：
Restricted Particles / Chapter 13.：
A Particle Between Walls / 13.1.：
The Energy Levels / 13.2.：
Compact Resolvents / 13.3.：
One Opaque Wall / 13.4.：
Scattering on a Half-Line / 13.5.：
The Spectral Resolution for the Free Particle on a Half-Line / 13.6.：
Hard-Core Potentials / Chapter 14.：
Local Absorption / 14.1.：
The Modified Hamiltonian / 14.2.：
The Resolvent Operator for H[subscript 1] / 14.3.：
The Wave Operators W[subscript plus or minus] (H[subscript 1] H[subscript 0]) / 14.4.：
Propagation / 14.5.：
Proof of Theorem 14.5.1 / 14.6.：
Completeness of the Wave Operators W[subscript plus or minus], (H[subscript 1] H[subscript 0]) / 14.7.：
The Wave Operators W[subscript plus or minus] (H, H[subscript 1]) / 14.8.：
A Regularity Theorem / 14.9.：
A Family of Spaces / 14.10.：
The Invariance Principle / Chapter 15.：
A Simple Result / 15.1.：
Trace Class Operators / 15.3.：
The Abstract Theorem / 16.1.：
Hilbert--Schmidt Operators / 16.2.：
The Fourier Transform / 16.4.：
Exercises A
Exercises B / Appendix B.：
Holder's Inequality and Banach Space / Appendix C.：
Bibliography
Index
Preface
Acknowledgments
A Message to the Reader
28.
図書
Nikolaus von Kues ; hrsg. von paul Wilpert
29.
図書
David Gilbarg, Neil S. Trudinger
目次情報:
続きを見る
Introduction / Chapter 1：
Linear Equations / Part I：
Laplace''s Equation / Chapter 2：
The Mean Value Inequalities / 2.1：
Maximum and Minimum Principle / 2.2：
The Harnack Inequality / 2.3：
Green''s Representation / 2.4：
The Poisson Integral / 2.5：
Convergence Theorems / 2.6：
Interior Estimates of Derivatives / 2.7：
The Dirichlet Problem; the Method of Subharmonic Functions / 2.8：
CapacityProblems / 2.9：
The Classical Maximum Principle / Chapter 3：
The Weak Maximum Principle / 3.1：
The Strong Maximum Principle / 3.2：
Apriori Bounds / 3.3：
Gradient Estimates for Poisson''s Equation / 3.4：
A Harnack Inequality / 3.5：
Operators in Divergence FormNotesProblems / 3.6：
Poisson''s Equation and Newtonian Potential / Chapter 4：
H+ lder Continuity / 4.1：
The Dirichlet Problem for Poisson''s Equation / 4.2：
H+ lder Estimates for the Second Derivatives / 4.3：
Estimates at the Boundary / 4.4：
H+ lder Estimates for the First DerivativesNotes Problems / 4.5：
Banach and Hilbert Spaces / Chapter 5：
The Contraction Mapping / 5.1：
The Method of Cintinuity / 5.2：
The Fredholm Alternative / 5.3：
Dual Spaces and Adjoints / 5.4：
Hilbert Spaces / 5.5：
The Projection Theorem / 5.6：
The Riesz Representation Theorem / 5.7：
The Lax-Milgram Theorem / 5.8：
The Fredholm Alternative in Hilbert Spaces / 5.9：
Weak CompactnessNotesProblems / 5.10：
Classical Solutions; the Schauder Approach / Chapter 6：
The Schauder Interior Estimates / 6.1：
Boundary and Global Estimates / 6.2：
The Dirichlet Problem / 6.3：
Interior and Boundary Regularity / 6.4：
An Alternative Approach / 6.5：
Non-Uniformly Elliptic Equations / 6.6：
Other Boundary Conditions; the Obliue Derivative Problem / 6.7：
Appendix 1: Interpolation Inequalities / 6.8：
Appendix 2: Extension LemmasNotesProblems / 6.9：
Sobolev Spaces / Chapter 7：
L^p spaces / 7.1：
Regularization and Approximation by Smooth Functions / 7.2：
Weak Derivatives / 7.3：
The Chain Rule / 7.4：
The W^(k,p) Spaces / 7.5：
Density Theorems / 7.6：
Imbedding Theorems / 7.7：
Potential Estimates and Imbedding Theorems / 7.8：
The Morrey and John-Nirenberg Estimes / 7.9：
Compactness Results / 7.10：
Difference Quotients / 7.11：
Extension and InterpolationNotesProblems / 7.12：
Generalized Solutions and Regularity / Chapter 8：
Solvability of the Dirichlet Problem / 8.1：
Diferentiability of Weak Solutions / 8.3：
Global Regularity / 8.4：
Global Boundedness of Weak Solutions / 8.5：
Local Properties of Weak Solutions / 8.6：
Local Estimates at the Boundary / 8.7：
H+ lder Estimates for the First Derivatives / 8.11：
The Eigenvalue ProblemNotesProblems / 8.12：
Strong Solutions / Chapter 9：
Maximum Princiles for Strong Solutions / 9.1：
L^p Estimates: Preliminary Analysis / 9.2：
The Marcinkiewicz Interpolation Theorem / 9.3：
The Calderon-Zygmund Inequality / 9.4：
L^p Estimates / 9.5：
A Local Maximum Principle / 9.6：
H+ lder and Harnack Estimates / 9.8：
Local Estimates at the BoundaryNotesProblems / 9.9：
Quasilinear Equations / Part II：
Maximum and Comparison Principles / Chapter 10：
The Comparison Principle / 10.1：
Maximum Principles / 10.2：
A Counterexample / 10.3：
Comparison Principles for Divergence Form Operators / 10.4：
Maximum Principles for Divergence Form Operators Notes Problems / 10.5：
Topological Fixed Point Theorems and Their Application / Chapter 11：
The Schauder Fixes Point Theorem / 11.1：
The Leray-Schauder Theorem: a Special Case / 11.2：
An Application / 11.3：
The Leray-Schauder Fixed Point Theorem / 11.4：
Variational ProblemsNotes / 11.5：
Equations in Two Variables / Chapter 12：
Quasiconformal Mappings / 12.1：
h+ lder Gradient Estimates for Linear Equations / 12.2：
The Dirichlet Problem for Uniformly Elliptic Equations / 12.3：
Non-Uniformly Elliptic EquationsNotesProblems / 12.4：
H+ lder Estimates for the Gradient / Chapter 13：
Equations of Divergence Form / 13.1：
Equations of General Form; the Interior Estimate / 13.2：
Equations of General Form; the Boundary Estimate / 13.4：
Application to the Dirichlet ProblemNotes / 13.5：
Boundary Gradient Estimates / Chapter 14：
General Domains / 14.1：
Convex Domains / 14.2：
Boundary Curvature Conditions / 14.3：
Non-Existence Results / 14.4：
Continuity Estimates / 14.5：
Appendix: Boundary Curvature and the Distance FunctionNotesProblems / 14.6：
Introduction / Chapter 1：
Linear Equations / Part I：
Laplace''s Equation / Chapter 2：
30.
図書
Richard Dedekind ; herausgegeben von Robert Fricke, Emmy Noether, Oystein Ore
出版情報:
Bronx, N.Y. : Chelsea, 1969 3 v. in 2 ; 21 cm
子書誌情報:
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31.
図書
Constantine M. Dafermos
目次情報:
続きを見る
Balance Laws / Chapter I：
Formulation of the Balance Law / 1.1：
Reduction to Field Equations / 1.2：
Change of Coordinates / 1.3：
Systems of Balance Laws / 1.4：
Companion Systems of Balance Laws / 1.5：
Weak and Shock Fronts / 1.6：
Survey of the Theory of BV Functions / 1.7：
BV Solutions of Systems of Balance Laws / 1.8：
Rapid Oscillations and the Stabilizing Effect of Companion Balance Laws / 1.9：
Notes / 1.10：
Introduction to Continuum Physics / Chapter II：
Bodies and Motions / 2.1：
Balance Laws in Continuum Physics / 2.2：
The Balance Laws of Continuum Thermomechanics / 2.3：
Material Frame Indifference / 2.4：
Thermoelasticity / 2.5：
Thermoviscoelasticity / 2.6：
Hyperbolic Systems of Balance Laws / 2.7：
Hyperbolicity / 3.1：
Entropy-Entropy Flux Pairs / 3.2：
Examples of Hyperbolic Systems of Balance Laws / 3.3：
The Initial-Value Problem: Admissibility of Solutions / 3.4：
The Initial-Value Problem / 4.1：
The Burgers Equation and Nonuniqueness of Weak Solutions / 4.2：
Entropies and Admissible Solutions / 4.3：
The Vanishing Viscosity Approach / 4.4：
Initial-Boundary-Value Problems / 4.5：
Entropy and the Stability of Classical Solutions / 4.6：
Convex Entropy and the Existence of Classical Solutions / 5.1：
Convex Entropy and the Stability of Classical Solutions / 5.2：
Partially Convex Entropies and Involutions / 5.3：
The Initial-Value Problem: Perseverance and Demise of Classical Solutions / 5.4：
Admissible Weak Solutions and Their Stability Properties / 6.2：
The Method of Vanishing Viscosity / 6.3：
Solutions as Trajectories of a Contraction Semigroup / 6.4：
The Layering Method / 6.5：
A Kinetic Formulation / 6.6：
Relaxation / 6.7：
Hyperbolic Systems of Balance Laws in One-Space Dimension / 6.8：
Balance Laws in One-Space Dimension / 7.1：
Hyperbolicity and Strict Hyperbolicity / 7.2：
Riemann Invariants / 7.3：
Genuine Nonlinearity and Linear Degeneracy / 7.4：
Simple Waves / 7.6：
Breakdown of Classical Solutions / 7.7：
Weak Solutions / 7.8：
Admissible Shocks / 7.9：
Strong Shocks, Weak Shocks, and Shocks of Moderate Strength / 8.1：
The Hugoniot Locus / 8.2：
The Lax Shock Admissibility Criterion / 8.3：
The Liu Shock Admissibility Criterion / 8.4：
The Entropy Shock Admissibility Criterion / 8.5：
Viscous Shock Profiles / 8.6：
Admissible Wave Fans and the Riemann Problem / 8.7：
Self-similar Solutions and the Riemann Problem / 9.1：
Wave Fan Admissibility Criteria / 9.2：
Solution of the Riemann Problem with Admissible Shocks / 9.3：
The Entropy Rate Admissibility Criterion / 9.4：
Viscous Wave Fans / 9.5：
Interaction of Wave Fans / 9.6：
Generalized Characteristics / 9.7：
BV Solutions / 10.1：
Extremal Backward Characteristics / 10.2：
Genuinely Nonlinear Scalar Conservation Laws / 10.4：
Admissible BV Solutions and Generalized Characteristics / 11.1：
The Spreading of Rarefaction Waves / 11.2：
Regularity of Solutions / 11.3：
Divides, Invariants and the Lax Formula / 11.4：
Decay of Solutions Induced by Entropy Dissipation / 11.5：
Spreading of Characteristics and Development of A-Waves / 11.6：
Confinement of Characteristics and Formation of Sawtoothed Profiles / 11.7：
Genuinely Nonlinear Systems of Two Conservation Laws / 11.8：
Notation and Assumptions / 12.1：
Local Structure of Solutions / 12.2：
Propagation of Riemann Invariants Along Extremal Backward Characteristics / 12.4：
Bounds on Solutions / 12.5：
Spreading of Rarefaction Waves / 12.6：
Initial Data with Compact Support / 12.7：
Periodic Solutions / 12.10：
The Random Choice Method / 12.11：
The Construction Scheme / 13.1：
Compactness and Consistency / 13.2：
Wave Interactions, Approximate Conservation Laws / 13.3：
The Glimm Functional / 13.4：
Bounds on the Total Variation / 13.5：
Bounds on the Supremum / 13.6：
Wave Partitioning / 13.7：
Inhomogeneous Systems of Balance Laws / 13.8：
Breakdown of Weak Solutions / 13.9：
The Front Tracking Method and Standard Riemann Semigroups / 13.10：
The Scalar Conservation Law / 14.1：
Front Tracking for Systems of Conservation Laws / 14.2：
The Global Wave Pattern / 14.3：
Approximate Solutions / 14.4：
Bounds on the Combined Strength of Pseudoshocks / 14.5：
Continuous Dependence on Initial Data / 14.7：
The Standard Riemann Semigroup / 14.9：
Uniqueness of Solutions / 14.10：
Structure of Solutions / 14.11：
Compensated Compactness / 14.12：
The Young Measure / 15.1：
Compensated Compactness and the div-curl Lemma / 15.2：
Measure-Valued Solutions for Systems of Conservation Laws and Compensated Compactness / 15.3：
Scalar Conservation Laws / 15.4：
A Relaxation Scheme for Scalar Conservation Laws / 15.5：
The System of Isentropic Elasticity / 15.6：
The System of Isentropic Gas Dynamics / 15.8：
Bibliography / 15.9：
Author Index
Subject Index
Balance Laws / Chapter I：
Formulation of the Balance Law / 1.1：
Reduction to Field Equations / 1.2：
32.
図書
Laurent Schwartz
33.
図書
by Percy A. MacMahon
出版情報:
Cambridge : Cambridge University Press, 1915-1916 2 v. ; 27 cm
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34.
図書
by Thomas Muir
出版情報:
London : Macmillan, 1906-1923 v. ; 23 cm
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35.
図書
edited by L. M. Le Cam, Jerzy Neyman, and Elizabeth L. Scott
36.
図書
P. M. Cohn
出版情報:
Chichester : Wiley, 1974- v. ; 24 cm
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目次情報:
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Sets
Lattices
Field Theory
Modules
Rings and Algebras
Quadratic Forms and Ordered Fields
Representation Theory of Finite Groups
Valuation Theory
Commutative Rings
Coding Theory
Languages and Automata
Bibliography
List of Notations
Index
Sets
Lattices
Field Theory
37.
図書
L. Arnold, H. Crauel, J.-P. Eckmann (eds.)
38.
図書
edited by Bert Hubbard
出版情報:
New York ; London : Academic Press, 1971 ix, 649 p. ; 24cm
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39.
図書
by Charles S. Peirce ; edited by Carolyn Eisele
出版情報:
Hague : Mouton Publishers , Atlantic Highlands, N.J. : Humanities Press, 1976 2 v. (xxxix, 1153 p.) ; 24 cm
シリーズ名:
The new elements of mathematics ; v. 3
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40.
図書
by Barry Simon
出版情報:
Princeton, N.J. : Princeton University Press, 1974 xx, 392 p. ; 25 cm
シリーズ名:
Princeton series in physics
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41.
図書
Serge Lang
42.
図書
V.V. Kalashnikov, V.M. Zolotarev (eds.)
43.
図書
International Congress of Mathematicians
出版情報:
Helsinki : ICM, 1980 2 v. (1022 p.) ; 25 cm
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44.
図書
[by] William L. Hays [and] Robert L. Winkler
45.
図書
by James Pierpont
出版情報:
Boston : Ginn, c1905-c1912 2 v. ; 24 cm
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46.
図書
by R. Courant ; translated by E.J. McShane
出版情報:
London ; Glasgow : Blackie , New York : Interscience Pub. Inc., 1937 v. ; 23 cm
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47.
図書
Karl Petersen
目次情報:
続きを見る
Preface
Introduction and preliminaries / 1：
The basic questions of ergodic theory / 1.1：
The basic examples / 1.2：
Hamiltonian dynamics / A.：
Stationary stochastic processes / B.：
Bernoulli shifts / C.：
Markov shifts / D.：
Rotations of the circle / E.：
Rotations of compact abelian groups / F.：
Automorphisms of compact groups / G.：
Gaussian systems / H.：
Geodesic flows / I.：
Horocycle flows / J.：
Flows and automorphisms on homogeneous spaces / K.：
The basic constructions / 1.3：
Factors
Products
Skew products
Flow under a function
Induced transformations
Inverse limits
Natural extensions
Some useful facts from measure theory and functional analysis / 1.4：
Change of variables
Proofs by approximation
Measure algebras and Lebesgue spaces
Conditional expectation
The Spectral Theorem
Topological groups, Haar measure, and character groups
The fundamentals of ergodic theory / 2：
The Mean Ergodic Theorem / 2.1：
The Pointwise Ergodic Theorem / 2.2：
Recurrence / 2.3：
Ergodicity / 2.4：
Strong mixing / 2.5：
Weak mixing / 2.6：
More about almost everywhere convergence / 3：
More about the Maximal Ergodic Theorem / 3.1：
Positive contractions
The maximal equality
Sign changes of the partial sums
The Dominated Ergodic Theorem and its converse
More about the Pointwise Ergodic Theorem / 3.2：
Maximal inequalities and convergence theorems
The speed of convergence in the Ergodic Theorem
Differentiation of integrals and the Local Ergodic Theorem / 3.3：
The Martingale convergence theorems / 3.4：
The maximal inequality for the Hilbert transform / 3.5：
The ergodic Hilbert transform / 3.6：
The filling scheme / 3.7：
The Chacon-Ornstein Theorem / 3.8：
More about recurrence / 4：
Construction of eigenfunctions / 4.1：
Existence of rigid factors
Almost periodicity
Construction of the eigenfunction
Some topological dynamics / 4.2：
Topological ergodicity and mixing
Equicontinuous and distal cascades
Uniform distribution mod 1
Structure of distal cascades
The Szemeredi Theorem / 4.3：
Furstenberg's approach to the Szemeredi and van der Waerden Theorems
Topological multiple recurrence, van der Waerden's Theorem, and Hindman's Theorem
Weak mixing implies weak mixing of all orders along multiples
Outline of the proof of the Furstenberg-Katznelson Theorem
The topological representation of ergodic transformations / 4.4：
Preliminaries
Recurrence along IP-sets
Perturbation to uniformity
Uniform polynomials
Conclusion of the argument
Two examples / 4.5：
Metric weak mixing without topological strong mixing
A prime transformation
Entropy / 5：
Entropy in physics, information theory, and ergodic theory / 5.1：
Physics
Information theory
Ergodic theory
Information and conditioning / 5.2：
Generators and the Kolmogorov-Sinai Theorem / 5.3：
More about entropy / 6：
More examples of the computation of entropy / 6.1：
Entropy of an automorphism of the torus
Entropy of a skew product
Entropy of an induced transformation
The Shannon-McMillan-Breiman Theorem / 6.2：
Topological entropy / 6.3：
Introduction to Ornstein Theory / 6.4：
Finitary coding between Bernoulli shifts / 6.5：
Sketch of the proof
Reduction to the case of a common weight
Framing the code
What to put in the s
Sociology
Construction of the isomorphism
References
Index
Preface
Introduction and preliminaries / 1：
The basic questions of ergodic theory / 1.1：
48.
図書
Michael Spivak
出版情報:
Houston, Texas : Publish or Perish, Inc., c1979 5 v. ; 24 cm
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49.
図書
K. Kuratowski ; translated from French by J. Jaworowski
出版情報:
New York : Academic Press, 1966-1968 2 v. ; 24 cm
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50.
図書
X. Li, J. Yong (eds.)
51.
図書
by A.B. Basset
52.
図書
edited by V.G. Bar´yakhtar ... [et al.]
出版情報:
Singapore ; Teaneck, N.J. : World Scientific, c1990 2 v. ; 23 cm
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53.
図書
by P. S. Aleksandrov ; [translated from the first (1947) Russian edition by Horace Komm]
出版情報:
Rochester, N. Y. : Graylock Press, 1956-1960 3 v. ; 24 cm
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目次情報:
Vol. 2. The Betti groups.
Vol. 2. The Betti groups.
54.
図書
edited by A. Rényi
出版情報:
Budapest : János Bolyai Mathematical Society, c1968 2 v. (520 p.) ; 25 cm
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55.
図書
Jack P.C. Kleijnen
56.
図書
Marvin Marcus
57.
図書
C.シュヴァレー著 ; 銀林浩訳
出版情報:
東京 : 東京図書, 1975.9 2冊 ; 22cm
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58.
図書
59.
図書
N. Bourbaki
目次情報:
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chapitre 1. Algèbre de Lie
chapitre 2. Algèbres de Lie libres
chapitre 3. Groupes de Lie
chapitre 4. Groupes de Coxeter et systèmes de Tits
chapitre 5. Groupes engendrés par des réflexions
chapitre 6. Systèmes de racines
chapitre 7. Sous-algèbres de Cartan, éléments réguliers
chapitre 8. Algèbres de Lie semi-simples déployées
chapitre 1. Algèbre de Lie
chapitre 2. Algèbres de Lie libres
chapitre 3. Groupes de Lie
60.
図書
edited by J. Rose
出版情報:
London ; New York : Gordon and Breach, c1974 3 v. ; 24 cm
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61.
図書
Roger W. Brockett, Richard S. Millman, Hector J. Sussmann, editors
62.
図書
Leonid P. Shilnikov ... [et al.]
63.
図書
by G. Polya
64.
図書
edited by R.P. Gupta
出版情報:
Amsterdam : North-Holland , New York : American Elsevier, 1975 x, 416 p. ; 23 cm
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65.
図書
von Ludwig Holzer
66.
図書
Carlo Miranda ; translated by Zane C. Motteler
67.
図書
Carathéodory, Constantin, 1873-1950 ; Dean, Robert B. ; Brandstatter, Julius J.
68.
図書
by C.E. Weatherburn
出版情報:
Cambridge : Cambridge University Press, 1927-1930 2 v. ; 22 cm
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69.
図書
by Charles S. Peirce ; edited by Carolyn Eisele
70.
図書
カントロヴィチ, アキーロフ著 ; 山崎三郎, 柴岡泰光訳
出版情報:
東京 : 東京図書, 1964.12-1967.9 2冊 ; 22cm
シリーズ名:
数学選書
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71.
図書
Oscar Zariski, Pierre Samuel ; with the cooperation of I.S. Cohen
72.
図書
by W.V.D. Hodge and D. Pedoe
出版情報:
Cambridge : Cambridge University Press, 1947-1954 3 v. ; 23 cm
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73.
図書
[edited by Guido Weiss, Stephen Wainger ; prepared by the American Mathematical Society ...]
74.
図書
publiés sous la direction du Comité d'organisation du congrés
出版情報:
Paris : Gauthier-Villars Editeur, 1971 3 v. ; 25 cm
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目次情報:
v. 1. Documents- médailles fields, conférences générales (G), logique (A)- algébre (B)
V. 2. Géométrie et topologie (C), analyse (D)
v. 3. Mathématiques appliquées (E), histoire et enseignement (F)
v. 1. Documents- médailles fields, conférences générales (G), logique (A)- algébre (B)
V. 2. Géométrie et topologie (C), analyse (D)
v. 3. Mathématiques appliquées (E), histoire et enseignement (F)
75.
図書
G. P. Patil, editor
出版情報:
[University Park] : Pennsylvania State University Press, 1970 3 v ; 24 cm
シリーズ名:
Penn State statistics series
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目次情報:
v. 1. Random counts in models and structures
v. 2. Random counts in biomedical and social sciences
v. 3. Random counts in physical sciences, geoscience, and business
v. 1. Random counts in models and structures
v. 2. Random counts in biomedical and social sciences
v. 3. Random counts in physical sciences, geoscience, and business
76.
図書
by Nathan Jacobson
目次情報:
v. 1. Basic concepts
v. 2. Linear algebra
v. 3. Theory of fields and Galois theory
v. 1. Basic concepts
v. 2. Linear algebra
v. 3. Theory of fields and Galois theory
77.
図書
河野伊三郎著
出版情報:
東京 : 共立出版, 1954.6 2, 2, 194, 5p ; 19cm
シリーズ名:
共立全書 ; 82
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78.
図書
Hermann Weyl ; herausgegeben von K. Chandrasekharan
出版情報:
Berlin ; New York : Springer-Verlag, 1968 4 v. ; 26 cm
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79.
図書
by B.A. Fuchs and B.V. Shabat ; original translation by J. Berry ; revised and expanded by J.W. Reed
80.
図書
by Alfred North Whitehead and Bertrand Russell
出版情報:
Cambridge : Cambridge University Press, 1925-1927 3 v. ; 25 cm
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Volume 1
Preface
Alphabetical list of propositions referred to by names
Introduction to the second edition
Introduction
Mathematical Logic / Part I：
The theory of deduction / 1：
Theory of apparent variables / 2：
Classes and relations / 3：
Logic of relations / 4：
Products and sums of classes / 5：
Prolegomena to Cardinal Arithmetic / Part II：
Unit classes and couples / 6：
Sub-classes, sub-relations, and relative types / 7：
One-many, many-one, and one-one relations / 8：
Selections / 9：
Inductive relations / 10：
Appendixes
List of definitions
Prefactory statement of symbolic conventions / Volume II：
Cardinal Arithmetic / Part III：
Definition and logical properties of cardinal numbers / 11：
Addition, multiplication and exponentiation / 12：
Finite and infinite / 13：
Relation-Arithmetic / Part IV：
Ordinal similarity and relation-numbers / 14：
Addition of relations, and the product of two relations / 15：
The principle of first differences, and the multiplication and exponentiation of relations / 16：
Arithmetic of relation-numbers / 17：
Series / Part V：
General theory of series / 18：
On sections, segments, streches, and derivatives / 19：
On convergence, and the limits of functions / 20：
Series (continued) / Volume III：
Well-ordered series / 21：
Finite and infinite series and ordinals / 22：
Compact studies, rational series, and continuous series / 23：
Quantity / Part VI：
Generalization of number / 24：
Vector-families / 25：
Measurement / 26：
Cyclic families / 27：
Volume 1
Preface
Alphabetical list of propositions referred to by names
81.
図書
edited by I.M. James
出版情報:
Oxford : Pergamon Press, 1962 4 v. ; 26 cm
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v. 1. Differential geometry / with a biographical note by M.H.A. Newman and Barbara Whitehead ; and a mathematical appreciation by John W. Milnor
v. 2. Complexes and manifolds
v. 3. Homotopy theory
v. 4. Algebraic and classical topology
v. 1. Differential geometry / with a biographical note by M.H.A. Newman and Barbara Whitehead ; and a mathematical appreciation by John W. Milnor
v. 2. Complexes and manifolds
v. 3. Homotopy theory
82.
図書
N. Bourbaki
出版情報:
Paris : Hermann, c1958-1964 v. ; 24 cm
シリーズ名:
Actualités scientifiques et industrielles ; 1142, 1143, 1235, 1045, 1084, 1196 Éléments de mathématique / par N. Bourbaki ; livre 3, Fasc. 2, 3, 5, 8, 10, 16
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chapitre 1. Structures topologiques
chapitre 2. Structures uniformes
chapitre 3. Groupes topologiques (théorie élémentaire)
chapitre 4. Nombres réels
chapitre 5. Groupes a un paramètre
chapitre 6. Espaces numèriques et espaces projectifs
chapitre 7. Les groupes additifs R[n]
chapitre 8. Nombres complexes
chapitre 9. Utilisation des nombres réels en topologie générale
chapitre 10. Espaces fonctionnels
Fascicule de résultats
chapitre 1. Structures topologiques
chapitre 2. Structures uniformes
chapitre 3. Groupes topologiques (théorie élémentaire)
83.
図書
國井修二郎, 千田香苗共著
出版情報:
東京 : 丸善, 1952-1958.1 2冊 ; 18cm
シリーズ名:
エンジニアスライブラリ
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84.
図書
Herbert Busemann
85.
図書
David Hilbert
86.
図書
I. P. Natanson ; translated from the Russian by Leo F. Boron ; with the editorial collaboration of, and with annotations by Edwin Hewitt
出版情報:
New York : F. Ungar, 1961 2 v. ; 27 cm
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87.
図書
Oscar Zariski ; edited by M. Artin and D. Mumford
88.
図書
Frank Spitzer
89.
図書
Jean-Pierre Serre ; translated from the French by John Stillwell
出版情報:
Berlin ; New York : Springer-Verlag, 1980 ix, 142 p. ; 25 cm
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90.
図書
edited by Paruchuri R. Krishnaiah
出版情報:
New York : Academic Press, 1978-1983 4 v. ; 24 cm
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91.
図書
herausgegeben von Heinrich Wolgang Leopoldt und Peter Roquette
出版情報:
Berlin : Walter de Gruyter, 1975 3 v. ; 25 cm
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92.
図書
edited by Dietrich Stauffer
出版情報:
Singapore : World Scientific, 1994- v. ; 23 cm
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93.
図書
C. Foias ... [et al.] ; editors, E. Mosca, L. Pandolfi
94.
図書
R. Abraham, J.E. Marsden, T. Ratiu
目次情報:
続きを見る
Preface
Background Notation
Topology / Chapter 1：
Banach Spaces and Differential Calculus / Chapter 2：
Manifolds and Vector Bundles / Chapter 3：
Vector Fields and Dynamical Systems / Chapter 4：
Tensors / Chapter 5：
Differential Forms / Chapter 6：
Integration on Manifolds / Chapter 7：
Applications / Chapter 8：
References
Index
Supplementary Chapters
S-1 Lie Groups
S-2 Introduction to Differential Topology
S-3 Topics in Riemannian Geometry
Preface
Background Notation
Topology / Chapter 1：
95.
図書
[edited by A. Borel and W. Casselman ; prepared by the American Mathematical Society with partial support from National Science Foundation]
96.
図書
Emil Artin
97.
図書
Conference of the International Society for the Study of Time ; Fraser, J. T. ; Haber, F. C. ; Müller, G. H. (Gert Heinz), 1923- ; Lawrence, Nathaniel ; Park, David Allen, 1919-
出版情報:
Berlin ; New York : Springer-Verlag, 1972- v. ; 25 cm
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[v. 1]. Proceedings of the first conference of the International Society for the Study of Time, Oberwolfach (Black Forest), West Germany / edited by J.T. Fraser, F.C. Haber, G.H. Müller
2. Proceedings of the Second conference of the International Society for the Study of Time, Lake Yamanaka, Japan / edited by J.T. Fraser and N. Lawrence
3. Proceedings of the Third held in 1976 at Alpbach, Austria
4. Papers from Fourth conference of the International Society for the Study of Time, Alpbach-Austria / edited by J.T. Fraser, N. Lawrence, D. Park
[v. 1]. Proceedings of the first conference of the International Society for the Study of Time, Oberwolfach (Black Forest), West Germany / edited by J.T. Fraser, F.C. Haber, G.H. Müller
2. Proceedings of the Second conference of the International Society for the Study of Time, Lake Yamanaka, Japan / edited by J.T. Fraser and N. Lawrence
3. Proceedings of the Third held in 1976 at Alpbach, Austria
98.
図書
Carl Ludwig Siegel ; herausgegeben von K. Chandrasekharan und H. Maass
出版情報:
Berlin ; New York : Springer-Verlag, 1966-1979 4 v. ; 26 cm
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99.
図書
edited by N.L. Collins & Donald Michie
出版情報:
Edinburgh ; London : Oliver & Boyd, c1967- v. ; 26 cm
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100.
図書
N. Bourbaki
目次情報:
ch. 1. Structures algébriques
ch. 1. Structures algébriques
図書
