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1.

図書
図書
1. Numerical solution of partial differential equations in science and engineering
Leon Lapidus, George F. Pinder
出版情報: New York : Wiley, c1982  677 p. ; 24 cm
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目次情報: 続きを見る
Fundamental Concepts / Chapter 1.：
Notation / 1.0.：
First-Order Partial Differential Equations / 1.1.：
First-Order Quasilinear Partial Differential Equations / 1.1.1.：
Initial Value or Cauchy Problem / 1.1.2.：
Application of Characteristic Curves / 1.1.3.：
Nonlinear First-Order Partial Differential Equations / 1.1.4.：
Second-Order Partial Differential Equations / 1.2.：
Linear Second-Order Partial Differential Equations / 1.2.1.：
Classification and Canonical Form of Selected Partial Differential Equations / 1.2.2.：
Quasilinear Partial Differential Equations and Other Ideas / 1.2.3.：
Systems of First-Order PDEs / 1.3.：
First-Order and Second-Order PDEs / 1.3.1.：
Characteristic Curves / 1.3.2.：
Applications of Characteristic Curves / 1.3.3.：
Initial and Boundary Conditions / 1.4.：
References
Basic Concepts in the Finite Difference and Finite Element Methods / Chapter 2.：
Introduction / 2.0.：
Finite Difference Approximations / 2.1.：
Taylor Series Expansions / 2.1.1.：
Operator Notation for u(x) / 2.1.3.：
Finite Difference Approximations in Two Dimensions / 2.1.4.：
Additional Concepts / 2.1.5.：
Introduction to Finite Element Approximations / 2.2.：
Method of Weighted Residuals / 2.2.1.：
Application of the Method of Weighted Residuals / 2.2.2.：
The Choice of Basis Functions / 2.2.3.：
Two-Dimensional Basis Functions / 2.2.4.：
Approximating Equations / 2.2.5.：
Relationship between Finite Element and Finite Difference Methods / 2.3.：
Finite Elements on Irregular Subspaces / Chapter 3.：
Triangular Elements / 3.0.：
The Linear Triangular Element / 3.1.1.：
Area Coordinates / 3.1.2.：
The Quadratic Triangular Element / 3.1.3.：
The Cubic Triangular Element / 3.1.4.：
Higher-Order Triangular Elements / 3.1.5.：
Isoparametric Finite Elements / 3.2.：
Transformation Functions / 3.2.1.：
Numerical Integration / 3.2.2.：
Isoparametric Serendipity Hermitian Elements / 3.2.3.：
Isoparametric Hermitian Elements in Normal and Tangential Coordinates / 3.2.4.：
Boundary Conditions / 3.3.：
Three-Dimensional Elements / 3.4.：
Parabolic Partial Differential Equations / Chapter 4.：
Partial Differential Equations / 4.0.：
Well-Posed Partial Differential Equations / 4.1.1.：
Model Difference Approximations / 4.2.：
Well-Posed Difference Forms / 4.2.1.：
Derivation of Finite Difference Approximations / 4.3.：
The Classic Explicit Approximation / 4.3.1.：
The Dufort-Frankel Explicit Approximation / 4.3.2.：
The Richardson Explicit Approximation / 4.3.3.：
The Backwards Implicit Approximation / 4.3.4.：
The Crank-Nicolson Implicit Approximation / 4.3.5.：
The Variable-Weighted Implicit Approximation / 4.3.6.：
Consistency and Convergence / 4.4.：
Stability / 4.5.：
Heuristic Stability / 4.5.1.：
Von Neumann Stability / 4.5.2.：
Matrix Stability / 4.5.3.：
Some Extensions / 4.6.：
Influence of Lower-Order Terms / 4.6.1.：
Higher-Order Forms / 4.6.2.：
Predictor-Corrector Methods / 4.6.3.：
Asymmetric Approximations / 4.6.4.：
Variable Coefficients / 4.6.5.：
Nonlinear Parabolic PDEs / 4.6.6.：
The Box Method / 4.6.7.：
Solution of Finite Difference Approximations / 4.7.：
Solution of Implicit Approximations / 4.7.1.：
Explicit versus Implicit Approximations / 4.7.2.：
Composite Solutions / 4.8.：
Global Extrapolation / 4.8.1.：
Some Numerical Results / 4.8.2.：
Local Combination / 4.8.3.：
Composites of Different Approximations / 4.8.4.：
Finite Difference Approximations in Two Space Dimensions / 4.9.：
Explicit Methods / 4.9.1.：
Irregular Boundaries / 4.9.2.：
Implicit Methods / 4.9.3.：
Alternating Direction Explicit (ADE) Methods / 4.9.4.：
Alternating Direction Implicit (ADI) Methods / 4.9.5.：
LOD and Fractional Splitting Methods / 4.9.6.：
Hopscotch Methods / 4.9.7.：
Mesh Refinement / 4.9.8.：
Three-Dimensional Problems / 4.10.：
ADI Methods / 4.10.1.：
Iterative Solutions / 4.10.2.：
Finite Element Solution of Parabolic Partial Differential Equations / 4.11.：
Galerkin Approximation to the Model Parabolic Partial Differential Equation / 4.11.1.：
Approximation of the Time Derivative / 4.11.2.：
Approximation of the Time Derivative for Weakly Nonlinear Equations / 4.11.3.：
Finite Element Approximations in One Space Dimension / 4.12.：
Formulation of the Galerkin Approximating Equations / 4.12.1.：
Linear Basis Function Approximation / 4.12.2.：
Higher-Degree Polynomial Basis Function Approximation / 4.12.3.：
Formulation Using the Dirac Delta Function / 4.12.4.：
Orthogonal Collocation Formulation / 4.12.5.：
Asymmetric Weighting Functions / 4.12.6.：
Finite Element Approximations in Two Space Dimensions / 4.13.：
Galerkin Approximation in Space and Time / 4.13.1.：
Galerkin Approximation in Space Finite Difference in Time / 4.13.2.：
Asymmetric Weighting Functions in Two Space Dimensions / 4.13.3.：
Lumped and Consistent Time Matrices / 4.13.4.：
Collocation Finite Element Formulation / 4.13.5.：
Treatment of Sources and Sinks / 4.13.6.：
Alternating Direction Formulation / 4.13.7.：
Finite Element Approximations in Three Space Dimensions / 4.14.：
Example Problem / 4.14.1.：
Summary / 4.15.：
Elliptic Partial Differential Equations / Chapter 5.：
Model Elliptic PDEs / 5.0.：
Specific Elliptic PDEs / 5.1.1.：
Further Items / 5.1.2.：
Finite Difference Solutions in Two Space Dimensions / 5.2.：
Five-Point Approximations and Truncation Error / 5.2.1.：
Nine-Point Approximations and Truncation Error / 5.2.2.：
Approximations to the Biharmonic Equation / 5.2.3.：
Boundary Condition Approximations / 5.2.4.：
Matrix Form of Finite Difference Equations / 5.2.5.：
Direct Methods of Solution / 5.2.6.：
Iterative Concepts / 5.2.7.：
Formulation of Point Iterative Methods / 5.2.8.：
Convergence of Point Iterative Methods / 5.2.9.：
Line and Block Iteration Methods / 5.2.10.：
Acceleration and Semi-Iterative Overlays / 5.2.11.：
Finite Difference Solutions in Three Space Dimensions / 5.3.：
Iteration Concepts / 5.3.1.：
Finite Element Methods for Two Space Dimensions / 5.3.3.：
Galerkin Approximation / 5.4.1.：
Collocation Approximation / 5.4.2.：
Mixed Finite Element Approximation / 5.4.4.：
Approximation of the Biharmonic Equation / 5.4.5.：
Boundary Integral Equation Methods / 5.5.：
Fundamental Theory / 5.5.1.：
Boundary Element Formulation / 5.5.2.：
Linear Interpolation Functions / 5.5.3.：
Poisson's Equation / 5.5.5.：
Nonhomogeneous Materials / 5.5.6.：
Combination of Finite Element and Boundary Integral Equation Methods / 5.5.7.：
Three-Dimensional Finite Element Simulation / 5.6.：
Hyperbolic Partial Differential Equations / 5.7.：
Equations of Hyperbolic Type / 6.0.：
Finite Difference Solution of First-Order Scalar Hyperbolic Partial Differential Equations / 6.2.：
Stability, Truncation Error, and Other Features / 6.2.1.：
Other Approximations / 6.2.2.：
Dissipation and Dispersion / 6.2.3.：
Hopscotch Methods and Mesh Refinement / 6.2.4.：
Finite Difference Solution of First-Order Vector Hyperbolic Partial Differential Equations / 6.3.：
Finite Difference Solution of First-Order Vector Conservative Hyperbolic Partial Differential Equations / 6.4.：
Finite Difference Solutions to Two- and Three-Dimensional Hyperbolic Partial Differential Equations / 6.5.：
Finite Difference Schemes / 6.5.1.：
Two-Step, ADI, and Strang-Type Algorithms / 6.5.2.：
Conservative Hyperbolic Partial Differential Equations / 6.5.3.：
Finite Difference Solution of Second-Order Model Hyperbolic Partial Differential Equations / 6.6.：
One-Space-Dimension Hyperbolic Partial Differential Equation / 6.6.1.：
Explicit Algorithms / 6.6.2.：
Implicit Algorithms / 6.6.3.：
Simultaneous First-Order Partial Differential Equations / 6.6.4.：
Mixed Systems / 6.6.5.：
Two- and Three-Space-Dimensional Hyperbolic Partial Differential Equations / 6.6.6.：
Implicit ADI and LOD Methods / 6.6.7.：
Finite Element Solution of First-Order Model Hyperbolic Partial Differential Equations / 6.7.：
Asymmetric Weighting Function Approximation / 6.7.1.：
An H[superscript -1] Galerkin Approximation / 6.7.3.：
Orthogonal Collocation with Asymmetric Bases / 6.7.4.：
Finite Element Solution of Two- and Three-Space-Dimensional First-Order Hyperbolic Partial Differential Equations / 6.7.6.：
Galerkin Finite Element Formulation / 6.8.1.：
Finite Element Solution of First-Order Vector Hyperbolic Partial Differential Equations / 6.8.2.：
Finite Element Solution of Two- and Three-Space-Dimensional First-Order Vector Hyperbolic Partial Differential Equations / 6.9.1.：
Finite Element Solution of One-Space-Dimensional Second-Order Hyperbolic Partial Differential Equations / 6.10.1.：
Time Approximations / 6.11.1.：
Finite Element Solution of Two- and Three-Space-Dimensional Second-Order Hyperbolic Partial Differential Equations / 6.11.3.：
Index / 6.12.1.：
Fundamental Concepts / Chapter 1.：
Notation / 1.0.：
First-Order Partial Differential Equations / 1.1.：
2.

図書
図書
2. The mathematics of Paul Erdös (1 : hardcover : acid-free paper ; 2 : hardcover : acid-free paper)
Ronald L. Graham, Jaroslav Nešetřil (eds.)
出版情報: Berlin : Springer, c1997  2 v. ; 25 cm
シリーズ名: Algorithms and combinatorics ; 13-14
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3.

図書
図書
3. Probability theory. 4th ed (v. 1 : us - v. 2 : gw)
M. Loève
出版情報: New York ; Berlin : Springer-Verlag, c1977-1978  2 v. ; 24 cm
シリーズ名: Graduate texts in mathematics ; 45-46
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4.

図書
図書
4. Differential thermal analysis (v. 1 ; v. 2)
edited by R.C. Mackenzie
出版情報: London ; New York : Academic Press, 1970-1972  2 v. ; 24 cm
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5.

図書
図書
5. The theory of groups. 2nd English ed (v. 1 ; v. 2)
by A.G. Kurosh ; translated from the Russian and edited by K.A. Hirsch
出版情報: New York : Chelsea Pub. Co., c1960  v. ; 23 cm
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6.

図書
図書
6. Spectral analysis and time series (v. 1 ; v. 2)
M.B. Priestley
出版情報: London : New York : Academic Press, c1981  2 v. (xvii, [45], 890 p.) ; 24 cm
シリーズ名: Probability and mathematical statistics : a series of monographs and textbooks
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目次情報:
v. 1. Univariate series
v. 2. Multivariate series, prediction and control
v. 1. Univariate series
v. 2. Multivariate series, prediction and control
7.

図書
図書
7. Dynamical systems : an international symposium (v. 1 ; v. 2)
edited by Lamberto Cesari, Jack K. Hale, Joseph P. LaSalle
出版情報: New York : Academic Press, 1976  2 v. ; 24 cm
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8.

図書
図書
8. Quantum mechanics (v. 1 : hard - v. 2 : pbk)
Albert Messiah ; [translated from the French by G.M. Temmer]
出版情報: Amsterdam : North-Holland , New York : Sole dostributors for U.S.A., Intersicence Publishers, 1961-1962  2 v. (xv, 1136 p.) ; 22 cm
シリーズ名: Series in physics
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9.

図書
図書
9. Eigenfunction expansions associated with second-order differential equations ([pt. 1] ; pt. 2)
by E.C. Titchmarsh
出版情報: Oxford : Clarendon Press, 1946-1958  2 v. ; 25 cm
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10.

図書
図書
10. Contributions to probability theory (pt. 1 ; pt. 2)
edited by Lucien M. Le Cam and Jerzy Neyman
出版情報: Berkeley : University of California Press, 1967  2 v. ; 26 cm
シリーズ名: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability / edited by Lucien M. Le Cam and Jerzy Neyman ; v. 2
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11.

図書
図書
11. Geometry of quantum theory (v. 1 ; v. 2)
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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12.

図書
図書
12. The theory of matrices (v. 1 ; v. 2)
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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13.

図書
図書
13. Stochastic methods in quantum mechanics
Stanley P. Gudder
出版情報: New York : North Holland, c1979  x, 219 p. ; 23 cm
シリーズ名: North Holland series in probability and applied mathematics
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目次情報: 続きを見る
Preface
The History of Quantum Mechanics / 1：
Early History / 1.1：
Enter Probability / 1.2：
Some Comparisons / 1.3：
Notes and References / 1.4：
Exercises / 1.5：
A Different Kind of Probability / 2：
Interference Effects / 2.1：
Classical and Quantum Probability / 2.2：
Conditional Expectation / 2.3：
The Quantum Logic Approach / 2.4：
States and Observables / 3.1：
Event Structures / 3.2：
Compatibility / 3.3：
A Variance Theorem / 3.4：
Uniqueness and Existence / 3.5：
Hidden Variables / 3.6：
Generalized Probability Spaces / 3.7：
The Operational Approach / 3.8：
Convex Structures / 4.1：
Operations and Instruments / 4.2：
Examples / 4.3：
Conditional Expectations / 4.4：
Total Convex Structures / 4.5：
Hilbert Space Quantum Mechanics / 4.6：
Mathematical Interlude / 4.7：
Tempered Distributions / 5.1：
Orthogonal Additivity / 5.2：
C*-Algebras / 5.3：
Random Fields / 5.4：
The Wiener Process / 6.1：
Definitions and Examples / 6.2：
Gaussian Random Fields / 6.3：
Random Fields on [characters not reproducible] (R[superscript n]) / 6.4：
Quantum Field Theory / 6.5：
Canonical Commutation Relations / 7.1：
Infinite Degrees of Freedom / 7.2：
The Wightman Axioms / 7.3：
Fock Space / 7.4：
Euclidean Random Fields / 7.5：
Bibliography / 7.6：
Index
Preface
The History of Quantum Mechanics / 1：
Early History / 1.1：
14.

図書
図書
14. Advances in probability and related topics (v. 1 ; v. 2 ; v. 3)
edited by Peter Ney
出版情報: New York : M. Dekker, 1970-  v. ; 24 cm
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15.

図書
図書
15. The logarithmic integral (1 ; 2)
Paul Koosis
出版情報: Cambridge [Eng.] : Cambridge University Press, 1988-1992  2 v. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 12, 21
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目次情報:
JensenG++s formula again / 9：
Why we want to have multiplier theorems / 10：
Multiplier theorems / 11：
JensenG++s formula again / 9：
Why we want to have multiplier theorems / 10：
Multiplier theorems / 11：
16.

図書
図書
16. Analytic function theory (v. 1 ; v. 2)
Einar Hille
出版情報: Boston : Ginn and Company, 1959  2 v. ; 24 cm
シリーズ名: Introductions to higher mathematics
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17.

図書
図書
17. Wavelets : an analysis tool (: hbk ; : pbk)
M. Holschneider
出版情報: Oxford : Clarendon Press , New York : Oxford University Press, 1995  xiii, 423 p. ; 24 cm
シリーズ名: Oxford mathematical monographs
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目次情報: 続きを見る
Introduction to wavelet analysis over R / Chapter 1：
A short motivation / 1：
Time-frequency analysis / 1.1：
Wavelets and approximation theory / 1.2：
Some easy properties of the wavelet transform / 2：
Wavelet transform in Fourier space / 3：
Co-variance of wavelet transforms / 4：
Voices, zooms, and convolutions / 5：
Laplace convolution / 5.1：
Scale convolution / 5.2：
Mellin transforms / 5.3：
The basic functions: the wavelets / 6：
The real wavelets / 7：
The progressive wavelets / 8：
Progressive wavelets with real-valued frequency representation / 8.1：
Chirp wavelets / 8.2：
On the modulus of progressive functions / 8.3：
Some explicit analysed functions and easy examples / 9：
The wavelet transform of pure frequencies / 9.1：
The real oscillations / 9.2：
The onsets / 9.4：
The wavelet analysis of a hyperbolic chirp / 9.5：
Interactions / 9.6：
Two deltas / 9.7：
Delta and pure frequency / 9.8：
The influence cone and easy localization properties / 10：
Polynomial localization / 11：
More precise results / 11.1：
The influence regions for pure frequencies / 12：
The space of highly time-frequency localized functions / 13：
The inversion formula / 14：
Fourier transform in wavelet space / 14.1：
Reconstruction with singular reconstruction wavelets / 15：
The wavelet synthesis operator / 16：
Reconstruction without reconstruction wavelet / 17：
Localization properties of the wavelet synthesis / 18：
Frequency localization / 18.1：
Time localization / 18.2：
Wavelet analysis over S[subscript +](R) / 19：
Schwartz space / 19.1：
The regularity of the image space / 19.2：
The reproducing kernel / 20：
The cross-kernel / 20.1：
The wavelet transform of a white noise / 21：
The wavelet transform in L[superscript 2](R) / 22：
The inverse wavelet transform / 23：
The wavelet transform over S[prime subscript +](R) / 24：
Definition of the wavelet transform / 24.1：
The wavelet transform on S[prime](R) / 25：
A class of operators / 26：
The derivation operator and Riesz potentials / 26.1：
Differentiation and integration over S[prime subscript 0](R) / 26.2：
Singular support of distributions / 27：
Bounded sets in S[subscript 0](R) and S[prime subscript 0](R) / 28：
Some explicit wavelet transforms of distributions / 29：
The distributions..., [Characters not reproducible] / 29.1：
The distributions [Characters not reproducible] / 29.2：
Extension to higher dimensions / 30：
Proof of Theorem 11.1.1 / 31：
Discretizing and periodizing the half-plane / Chapter 2：
Interpolation
Reconstruction over voices
One single voice / 2.1：
Infinitely many voices / 2.2：
An iteration procedure
Calderon-Zygmund operators: a first contact
Reconstruction over strips
The pointwise and uniform convergence of the inversion formula
Uniform convergence in L[superscript p](R), 1< p< [infinity] / 6.1：
Pointwise convergence in L[superscript p](R), 1 [greater than or equal] p< [infinity] / 6.2：
Pointwise convergence in L[superscript infinity](R) / 6.3：
The 'Gibbs' phenomenon for s[subscript epsilon, rho]
Gibbs phenomenon / 7.1：
No Gibbs phenomenon / 7.2：
Reconstruction over cones
The Poisson summation formula
Periodic functions
The periodizing operator
Sequences and sampling
The Fourier transform over the circle
Some sampling theorems
The continuous wavelet transform over T
Wavelet analysis of S(T) and S[prime](T) / 10.1：
The wavelet transform of L[superscript 2](T) / 10.2：
Sampling of voices
Frames and moments
Some wavelet frames
Irregular sampling / 13.1：
Calderon-Zygmund operators again / 13.2：
A functional calculus
The case of self-adjoint operators
The function e[superscript itA] / 14.2：
Multi-resolution analysis / Chapter 3：
Riesz bases
The Fourier space picture
Translation invariant orthonormal basis / 1.3：
Skew projections / 1.4：
Perfect sampling spaces / 1.5：
Splines / 1.6：
Exponential localization / 1.7：
Perfect sampling spaces of spline functions / 1.8：
Sampling spaces over Z, T, and Z/NZ
Sampling space over Z
Oversampling of sampling spaces / 2.3：
Sampling spaces over T / 2.4：
Periodizing a sampling space over R / 2.5：
Periodizing a sampling space over T / 2.6：
Sampling spaces over Z/NZ / 2.7：
Quadrature mirror filters in L[superscript 2](Z)
Completing a QMF-system / 3.1：
Complements over R / 3.2：
QMF over Z/NZ and complements over T / 3.3：
Multi-resolution analysis over R
Localization and regularity of [psi] / 4.1：
Examples of multi-resolution analysis and wavelets
The Haar system
Splines wavelets
Band-limited functions
Littlewood-Paley analysis / 5.4：
The partial reconstruction operator
Multi-resolution analysis of L[superscript 2](Z)
Isometrics and the shift operator
QMF and multi-resolution analysis over Z
Wavelets over Z / 7.3：
QMF and multi-resolution analysis
Compact support
An easy regularity estimate
The dyadic interpolation spaces
The Lagrange interpolation spaces
Compactly supported wavelets
Wavelet frames
Bi-orthogonal expansions
Bi-orthogonal expansions of L[superscript 2](Z) / 12.1：
Bi-orthogonal expansions in L[superscript 2](R) / 12.2：
QMF and loop groups
The group of unitary operators with [U, T[subscript 2]] = 0
Some subclasses of QMF / 13.3：
The factorization problem / 13.5：
Multi-resolution analysis over T
Multi-resolution analysis over Z/2[superscript M]Z
Computing the discrete wavelet transform
Filterbanks over Z / 16.1：
Computing the orthonormal wavelet transform over a dyadic grid / 16.2：
More general wavelet / 16.3：
Denser grids / 16.4：
Interpolation of the voices / 16.5：
The 'a trous' algorithm / 16.6：
Computation over Z/2[superscript N]Z / 16.7：
Computing over R by using data over Z/NZ
Fractal analysis and wavelet transforms / Chapter 4：
Self-similarity and the re-normalization group
Re-normalization in wavelet-space
The order of magnitude of wavelet coefficients
Inverse theorems for global regularity
The class of Zygmund
Inverse theorems for local regularity
Pointwise differentiability and wavelet analysis
The class W[superscript alpha]
Asymptotic behaviour at small scales
The Brownian motion
The Weierstrass non-differentiable function
The Riemann-Weierstrass function
The orbit of 0
The orbit of 1
The non-degenerated fixed points
The irrational points / 6.4：
The baker's map
A family of dynamical systems and fractal measures
Self-similar fractal measure
The evolution in wavelet space
Some fractal measures
Fractal dimensions
Capacity
The generalized fractal dimensions
Fractal dimensions and wavelet transforms
Time evolution and the dimension [kappa](2)
Local self-similarity and singularities
The f([alpha]) spectrum
On the fractality of orthonormal wavelets
Group theory as unifying language / Chapter 5：
Some notions of group theory
Direct sum of groups
Quotient groups
Homomorphisms
Representations
Schur's lemma
Group action
Invariant measures
Regular representations
Group convolutions / 1.9：
Square integrable representations / 1.10：
The 'wavelet' analysis associated to square integrable representations
A priori estimates
Transformation properties
Energy conservation
The left- and right-synthesis
Co-variance
The inversion formulae
On the constant c[subscript g,h]
More general reconstruction
The reproducing kernel equation
Fourier transform over Abelian groups
The Fourier transform
Group-translations
The convolution theorem
Periodizing, sampling, and M. Poisson
Sampling
Periodization
Sampling spaces over Abelian groups
The discrete wavelet transform over Abelian groups
A group of operators
Polynomial loops: the factorization problem / 10.3：
The wavelet transform in two dimensions
Reconstruction formulae / 11.2：
A class of inverse problems / 11.3：
The Radon transform as wavelet transform
The Radon-inversion formula
Functional analysis and wavelets / Chapter 6：
Some function spaces
Wavelet multipliers
The class of highly regular Calderon-Zygmund operators (CZOs)
The dilation co-variance
Fourier multipliers as highly regular CZO
Singular integrals as highly regular CZO
Pointwise properties of highly regular CZO
Littlewood-Paley theory
The Sobolev spaces
Bibliography
Index
Introduction to wavelet analysis over R / Chapter 1：
A short motivation / 1：
Time-frequency analysis / 1.1：
18.

図書
図書
18. Iterative solution of nonlinear equations in several variables
J.M. Ortega and W.C. Rheinboldt
出版情報: New York : Academic Press, 1970  xx, 572 p. ; 24 cm
シリーズ名: Computer science and applied mathematics
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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
19.

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図書
19. Identification and system parameter estimation : proceedings of the 3rd IFAC Symposium, The Hague/Delft, The Netherlands, 12-15 June 1973 (ne : set - Pt. 2)
edited by P. Eykhoff
出版情報: Amsterdam : North-Holland Pub. Co , New York : American Elsevier, 1973  2 v. ; 27 cm
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20.

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図書
20. Progress in operations research (v. 1 ; v. 2)
edited by A. Prékopa
出版情報: Amsterdam ; London : North-Holland Publishing Co., 1976  2 v. (969 p.) ; 25 cm
シリーズ名: Colloquia Mathematica Societatis János Bolyai ; 12
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21.

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図書
21. Mathematical topics in fluid mechanics (v. 1 ; v. 2)
Pierre-Louis Lions
出版情報: Oxford : Clarendon Press, 1996-1998  2 v. ; 24 cm
シリーズ名: Oxford lecture series in mathematics and its applications ; 3, 10
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目次情報: 続きを見る
Compressible models / Part 2：
Compactness results for compressible isentropic Navier-Stokes equations / 5：
Stationary problems / 6：
Existence results for Cauchy problems / 7：
Related problems / 8：
A few facts about some function spaces / Appendix A：
On a weakly continuous product / Appendix B：
A remark on the limiting case for Sobolev inequalities / Appendix C：
Continua and limits Appendix E. On sums of Lp spaces / Appendix D：
A remark on parabolic equations / Appendix F：
Bibliography of Volumes 1 and 2 Erratum (Volume 1)
Index
Preface
Presentation of the models / 1：
Incompressible Models / Part 1：
Density-dependent Navier-Stokes equations / 2：
Navier-Stokes equations / 3：
Euler equations and other incompressible models / 4：
Truncation of divergence-free vectorfields
Two facts on D1,2(R2)
Compactness in time with values in weak topologies
Weak L1 estimates for solutions of the heat equation
A short proof of the existence of renormalized solutions for parabolic equations / Appendix E：
Intended Table of Contents of Volume 2
Compressible Models
Compactness results for compressible isentropic Navier-Stokes
Existence results
Related questions
Asymptotic limites / Part 3：
Asymptotic limits / 9：
Compressible models / Part 2：
Compactness results for compressible isentropic Navier-Stokes equations / 5：
Stationary problems / 6：
22.

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図書
22. Stochastic differential equations and applications (v. 1 ; v. 2)
Avner Friedman
出版情報: New York : Academic Press, 1975-1976  2 v. (xiii, 528 p.) ; 24 cm.
シリーズ名: Probability and mathematical statistics : a series of monographs and textbooks ; v. 28
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23.

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図書
23. Harmonic analysis on semi-simple Lie groups (v. 1 : gw - v. 2 : pbk)
Garth Warner
出版情報: Berlin ; New York : Springer-Verlag, 1972  2 v. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 188-189
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24.

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図書
24. Nonlinear processes
[by] Richard Bellman
出版情報: New York : Academic Press, 1971  xix, 306 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v.40 . Introduction to the mathematical theory of control processes ; v. 2
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25.

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図書
25. SL[2](R)
Serge Lang
出版情報: Reading, Mass. : Addison-Wesley Pub. Co., c1975  xvi, 428 p. ; 25 cm
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26.

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図書
26. Selected topics in graph theory ([1] ; 2 ; 3)
edited by Lowell W. Beineke and Robin J. Wilson
出版情報: London ; Tokyo : Academic Press, 1978-1988  3 v. ; 24 cm
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27.

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図書
27. Proceedings of the International Congress of Mathematicians (v. 1 ; v. 2)
[editor, Ralph D. James]
出版情報: [Vancouver] : [Canadian Mathematical Congress], c1975  2 v. ; 24 cm
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28.

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図書
28. Differential equations in celestial mechanics (pt. 1 ; pt. 2)
萩原, 雄祐(1897-1979)
出版情報: Tokyo : Japan Society for the Promotion of Science, 1974  2 v. ; 24 cm
シリーズ名: Celestial mechanics / Yusuke Hagihara ; v. 3
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29.

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図書
29. Computing methods in optimization problems-2
edited by Lotfi A. Zadeh, Lucien W. Neustadt, A.V. Balakrishnan
出版情報: New York : Academic Press, 1969  ix, 393 p. ; 24 cm
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30.

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図書
30. Markov processes (v. 1 ; v. 2)
by E.B. Dynkin ; translated with the authorization and assistance of the author by J. Fabius ... [et al.]
出版情報: Berlin : Springer, 1965  2 v. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 121-122
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31.

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図書
31. Lectures on modern mathematics (v. 1 ; v. 2 ; v. 3)
edited by T.L. Saaty
出版情報: New York : Wiley, c1963-c1965  3 v. ; 22 cm
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32.

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図書
32. Elements of applied stochastic processes
U. Narayan Bhat
出版情報: New York : J. Wiley, c1972  xvi, 414 p. ; 23 cm
シリーズ名: Wiley series in probability and mathematical statistics
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目次情報: 続きを見る
Preface
Stochastic Processes: Description and Definition / 1：
Introduction / 1.1：
Description and Definition / 1.2：
Probability Distributions / 1.3：
The Markov Process / 1.4：
The Renewal Process / 1.5：
The Stationary Process / 1.6：
A Plan for the Remaining Chapters / 1.7：
References
Exercises
Elementary Review Exercises
Advanced Review Exercises
Markov Chains / 2：
The n-Step Transition Probability Matrix / 2.1：
Classification of States / 2.3：
A Canonical Representation of the Transition Probability Matrix / 2.4：
Classification of States in Practice / 2.5：
Finite Markov Chains with Transient States / 2.6：
Irreducible Markov Chains with Ergodic States / 3：
Transient Behavior / 3.1：
Limiting Behavior / 3.2：
First Passage and Related Results / 3.3：
Branching Processes and other Special Topics / 4：
Branching Processes / 4.1：
Markov Chains of Order Higher than 1 / 4.2：
Lumpable Markov Chains / 4.3：
Reversed Markov Chains / 4.4：
Statistical Inference for Markov Chains / 5：
Estimation of the Elements in a Transition Probability Matrix / 5.1：
Hypothesis Testing Issues for Markov Chains / 5.2：
Inference From Partially Observable Markov Chains / 5.3：
Statistical Inference for Branching Processes / 5.4：
Additional Comments / 5.5：
Applied Markov Chains / 6：
Queueing Models / 6.1：
Inventory Systems / 6.2：
Storage Models / 6.3：
Industrial Mobility of Labor / 6.4：
Educational Advancement / 6.5：
Human Resource Management / 6.6：
Term Structure / 6.7：
Income Determination under Uncertainty / 6.8：
A Markov Decision Process / 6.9：
Simple Markov Processes / 7：
Examples / 7.1：
Markov Processes: General Properties / 7.2：
The Poisson Process / 7.3：
The Pure Birth Process / 7.4：
The Pure Death Process / 7.5：
Birth and Death Processes / 7.6：
Limiting Distributions / 7.7：
Markovian Networks / 7.8：
Additional Examples / 7.9：
Statistical Inference for Simple Markov Processes / 8：
Estimation of Parameters / 8.1：
Hypothesis Testing for Simple Markov Processes / 8.2：
Statistical Inference for Queues / 8.3：
Applied Markov Processes / 8.4：
The Machine Interference Problem / 9.1：
Queueing Networks / 9.3：
Flexible Manufacturing Systems / 9.4：
Reliability Models / 9.5：
Markovian Combat Models / 9.7：
Stochastic Models for Social Networks / 9.8：
Recovery, Relapse, and Death Due to Disease / 9.9：
Renewal Processes / 10：
Renewal Processes when Time is Discrete / 10.1：
Renewal Processes when Time is Continuous / 10.3：
Alternating Renewal Processes / 10.4：
Markov Renewal Processes (Semi-Markov Processes) / 10.5：
Renewal Reward Processes / 10.6：
Statistical Inference for Renewal Processes / 10.7：
Stationary Processes and Time Series Analysis / 10.8：
Definition / 11.1：
Some Examples / 11.2：
Ergodic Theorems / 11.3：
Covariance Stationary Processes in the Frequency Domain / 11.4：
Time Series Analysis: Introduction / 11.5：
Stochastic Models for Time Series / 11.6：
The Autoregressive Process / 11.7：
The Moving Average Process / 11.8：
A Mixed Autoregressive Moving Average Process / 11.9：
Autoregressive Integrated Moving Average Processes / 11.10：
Time Series Analysis in the Time Domain / 11.11：
Spectral Analysis of Time Series Data / 11.12：
Simulation and Markov Chain Monte Carlo / 12：
Simulation / 12.1：
Markov Chain Monte Carlo / 12.3：
Answers to Selected Exercises
Appendix
Author Index
Subject Index
Preface
Stochastic Processes: Description and Definition / 1：
Introduction / 1.1：
33.

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33. A course of mathematics for engineers and scientists (v. 1 - v. 6)
Brian H. Chirgwin and Charles Plumpton
出版情報: New York ; Oxford : Pergamon Press, 1961-1964  v. ; 22 cm
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34.

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34. Infinite series
I.I. Hirschman, Jr
出版情報: New York : Holt, Rinehart and Winston, c1962  x, 173 p. ; 24 cm
シリーズ名: Athena series : selected topics in mathematics
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35.

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35. Introduction to logic (: hard ; : International student ed)
by Patrick Suppes
出版情報: Princeton, N.J. : D. Van Nostrand, c1957  xviii, 312 p. ; 24 cm
シリーズ名: The university series in undergraduate mathematics
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目次情報: 続きを見る
Preface
Introduction
Principles of Inference and Definition / Part I：
The Sentential Connectives / Chapter 1.：
Negation and Conjunction / 1.1：
Disjunction / 1.2：
Implication: Conditional Sentences / 1.3：
Equivalence: Biconditional Sentences / 1.4：
Grouping and Parentheses / 1.5：
Truth Tables and Tautologies / 1.6：
Tautological Implication and Equivalence / 1.7：
Sentential Theory of Inference / Chapter 2.：
Two Major Criteria of Inference and Sentential Interpretations / 2.1：
The Three Sentential Rules of Derivation / 2.2：
Some Useful Tautological Implications / 2.3：
Consistency of Premises and Indirect Proofs / 2.4：
Symbolizing Everyday Language / Chapter 3.：
Grammar and Logic / 3.1：
Terms / 3.2：
Predicates / 3.3：
Quantifiers / 3.4：
Bound and Free Variables / 3.5：
A Final Example / 3.6：
General Theory of Inference / Chapter 4.：
Inference Involving Only Universal Quantifiers / 4.1：
Interpretations and Validity / 4.2：
Restricted Inferences with Existential Quantifiers / 4.3：
Interchange of Quantifiers / 4.4：
General Inferences / 4.5：
Summary of Rules of Inference / 4.6：
Further Rules of Inference / Chapter 5.：
Logic of Identity / 5.1：
Theorems of Logic / 5.2：
Derived Rules of Inference / 5.3：
Postscript on Use and Mention / Chapter 6.：
Names and Things Named / 6.1：
Problems of Sentential Variables / 6.2：
Juxtaposition of Names / 6.3：
Transition From Formal to Informal Proofs / Chapter 7.：
General Considerations / 7.1：
Basic Number Axioms / 7.2：
Comparative Examples of Formal Derivations and Informal Proofs / 7.3：
Examples of Fallacious Informal Proofs / 7.4：
Further Examples of Informal Proofs / 7.5：
Theory of Definition / Chapter 8.：
Traditional Ideas / 8.1：
Criteria for Proper Definitions / 8.2：
Rules for Proper Definitions / 8.3：
Definitions Which are Identities / 8.4：
The Problem of Division by Zero / 8.5：
Conditional Definitions / 8.6：
Five Approaches to Division by Zero / 8.7：
Padoa's Principle and Independence of Primitive Symbols / 8.8：
Elementary Intuitive Set Theory / Part II：
Sets / Chapter 9.：
Membership / 9.1：
Inclusion / 9.3：
The Empty Set / 9.4：
Operations on Sets / 9.5：
Domains of Individuals / 9.6：
Translating Everyday Language / 9.7：
Venn Diagrams / 9.8：
Elementary Principles About Operations on Sets / 9.9：
Relations / Chapter 10.：
Ordered Couples / 10.1：
Definition of Relations / 10.2：
Properties of Binary Relations / 10.3：
Equivalence Relations / 10.4：
Ordering Relations / 10.5：
Operations on Relations / 10.6：
Functions / Chapter 11.：
Definition / 11.1：
Operations on Functions / 11.2：
Church's Lambda Notation / 11.3：
Set-Theoretical Foundations of the Axiomatic Method / Chapter 12.：
Set-Theoretical Predicates and Axiomatizations of Theories / 12.1：
Isomorphism of Models for a Theory / 12.3：
Example: Probability / 12.4：
Example: Mechanics / 12.5：
Index
Preface
Introduction
Principles of Inference and Definition / Part I：
36.

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36. Topological vector spaces (v. 1 ; v. 2)
Gottfried Köthe ; translated by D.J.H. Garling
出版情報: Berlin ; New York : Springer-Verlag, 1969-1979  2 v. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 159, 237
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37.

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37. Probability theory ([v. 1] ; [v. 2])
edited by L. M. Le Cam, Jerzy Neyman, and Elizabeth L. Scott
出版情報: Berkeley : Univ. of California Press, 1972  2 v. ; 26 cm
シリーズ名: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability ; v. 2-3
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38.

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38. Operators, ergodic theory and almost periodic functions in a group
John von Neumann
出版情報: New York ; Oxford : Pergamon Press, 1961  x, 568 p., [1] leaf of plates ; 26 cm
シリーズ名: Collected works / John von Neumann ; general editor, A.H. Taub ; v. 2
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39.

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39. Computers and data processing
edited by Eugene M. Grabbe, Simon Ramo, Dean E. Wooldridge
出版情報: New York : Wiley , London : Chapman & Hall, c1959  1 v. (various pagings) ; 24 cm
シリーズ名: Handbook of automation, computation, and control / edited by Eugene M. Grabbe, Simon Ramo, Dean E. Wooldridge ; v. 2
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40.

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40. Modern mathematics for the engineer. 2nd ser
Arthur Erdélyi ... [et al.] ; edited by Edwin F. Beckenbach ; with an introduction by Magnus R. Hestenes
出版情報: New York : McGraw-Hill, 1961  xviii, 456 p. ; 24 cm
シリーズ名: University of California engineering extension series
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41.

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41. Eigenfunction expansions associated with second-order differential equations. 2nd ed (pt. 1 ; pt. 2)
by E.C. Titchmarsh
出版情報: Oxford : Clarendon Press, 1958-1962  2 v. ; 24 cm
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42.

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42. 双曲線函数表 (1 ; 2)
新数表シリーズ編集委員会
出版情報: 東京 : コロナ社, 1961.5-1962.10  2冊 ; 22cm
シリーズ名: 新数表シリーズ / 新数表シリーズ編集委員会編 ; 1-2
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43.

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図書
43. Methods of nonlinear analysis (v. 1 ; v. 2)
Richard Bellman
出版情報: New York : Academic Press, 1970-1973  2 v. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 61, 1-2
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44.

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図書
44. Contributions to the theory of games (v. 1 - v. 4)
H.F. Bohnenblust ... [et al.] ; edited by H.W. Kuhn and A.W. Tucker
出版情報: Princeton : Princeton University Press, 1950-1959  4 v. ; 26 cm
シリーズ名: Annals of mathematics studies ; no. 24, 28, 39, 40
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45.

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45. Combinatorial theory and its applications (v. 1 ; v. 2 ; v. 3)
edited by P. Erdős, A. Rényi, and Vera T. Sós
出版情報: [Budapest : János Bolyai Mathematical Society] , Amsterdam : Distributed by North-Holland Pub. Co, 1970  3 v ; 25 cm
シリーズ名: Colloquia Mathematica Societatis János Bolyai ; 4
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46.

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46. Group theory and its applications ([v. 1] ; v. 2 ; v. 3)
edited by Ernest M. Loebl ; [contributors, R.E. Behrends ... et al.]
出版情報: New York : Academic Press, 1968-1975  3 v. ; 24 cm
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47.

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図書
47. Stochastic processes (: pbk ; : [hardcover])
Emanuel Parzen
出版情報: San Francisco : Holden-Day, 1962  xi, 324 p. ; 23 cm
シリーズ名: Holden-Day series in probability and statistics
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目次情報: 続きを見る
Preface to the Classics Edition
Preface
Role of the Theory of Stochastic Processes
Statistical physics
Stochastic models for population growth
Communication and control
Management science
Time series analysis
Random Variables and Stochastic Processes / 1：
Random variables and probability laws / 1-1：
Describing the probability law of a stochastic process / 1-2：
The Wiener process and the Poisson process / 1-3：
Two-valued processes / 1-4：
Conditional Probability and Conditional Expectation / 2：
Conditioning by a discrete random variable / 2-1：
Conditioning by a continuous random variable / 2-2：
Properties of conditional expectation / 2-3：
Normal Processes and Covariance Stationary Processes / 3：
The mean value function and covariance kernel of a stochastic process / 3-1：
Stationary and evolutionary processes / 3-2：
Integration and differentiation of stochastic processes / 3-3：
Normal processes / 3-4：
Normal processes as limits of stochastic processes / 3-5：
Harmonic analysis of stochastic processes / 3-6：
Counting Processes and Poisson Processes / 4：
Axiomatic derivations of the Poisson process / 4-1：
Non-homogeneous, generalized, and compound Poisson processes / 4-2：
Inter-arrival times and waiting times / 4-3：
The uniform distribution of waiting times of a Poisson process / 4-4：
Filtered Poisson processes / 4-5：
Renewal Counting Processes / 5：
Examples of renewal counting processes / 5-1：
The renewal equation / 5-2：
Limit theorems for renewal counting processes / 5-3：
Markov Chains: Discrete Parameter / 6：
Formal definition of a Markov process / 6-1：
Transition probabilities and the Chapman-Kolmogorov equation / 6-2：
Decomposition of Markov chains into communicating classes / 6-3：
Occupation times and first passage times / 6-4：
Recurrent and non-recurrent states and classes / 6-5：
First passage and absorption probabilities / 6-6：
Mean absorption, first passage, and recurrence times / 6-7：
Long-run and stationary distributions / 6-8：
Limit theorems for occupation times / 6-9：
Limit theorems for transition probabilities of a finite Markov chain / 6-10：
The interchange of limiting processes / Appendix：
Markov Chains: Continuous Parameter / 7：
Limit theorems for transition probabilities of a continuous parameter Markov chain / 7-1：
Birth and death processes and their application to queueing theory / 7-2：
Kolmogorov differential equations for the transition probability functions / 7-3：
Two-state Markov chains and pure birth processes / 7-4：
Non-homogeneous birth and death processes / 7-5：
References
Author Index
Subject Index
Preface to the Classics Edition
Preface
Role of the Theory of Stochastic Processes
48.

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図書
48. 初等数値表 (1 ; 2)
出版情報: 東京 : コロナ社, 1962.6-1963.7  2冊 ; 22cm
シリーズ名: 新数表シリーズ / 新数表シリーズ編集委員会編 ; 4,5
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49.

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図書
49. Advances in cybernetics and systems (v. 1 ; v. 2 ; v. 3)
edited by J. Rose
出版情報: London ; New York : Gordon and Breach, c1974  3 v. ; 24 cm
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50.

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図書
50. Measure and category : a survey of the analogies between topological and measure spaces. 2nd ed (: us ; : gw)
John C. Oxtoby
出版情報: New York : Springer-Verlag, c1980  ix, 106 p. ; 24 cm
シリーズ名: Graduate texts in mathematics ; 2
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