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1.

図書

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: 続きを見る
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

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

図書
Hans Föllmer, Alexander Schied
出版情報: Berlin : W. de Gruyter, 2002  ix, 422 p. ; 25 cm
シリーズ名: De Gruyter studies in mathematics ; 27
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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

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

図書
A. Galindo, P. Pascual ; translated by J.D. García and L. Alvarez-Gaumé
出版情報: Berlin ; Tokyo : Springer-Verlag, c1990-c1991  2 v. ; 25 cm
シリーズ名: Texts and monographs in physics
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6.

図書

図書
Luis Ribes, Pavel Zalesskii
出版情報: Berlin ; Tokyo : Springer, c2000  xiv, 435 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, v. 40
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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

図書
von Helmut Hasse
出版情報: Würzburg ; Wien : Physica-Verlag, 1965  2 v ; 25 cm
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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

図書
N. Bourbaki
出版情報: Paris : Hermann, c1962  315 p. ; 25 cm
シリーズ名: Actualités scientifiques et industrielles ; 1236
Éléments de mathématique / par N. Bourbaki ; livre 2
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目次情報:
ch. 2. Algébre linéaire
ch. 2. Algébre linéaire
9.

図書

図書
David Gilbarg, Neil S. Trudinger
出版情報: Berlin ; New York : Springer-Verlag, 1977 c1957  x, 401 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 224
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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

図書
by V.S. Varadarajan
出版情報: Princeton, N.J. : Van Nostrand, c1968-  v. ; 24 cm
シリーズ名: The University series in higher mathematics
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