1.
図書
Avner Friedman
2.
図書
Vadim Komkov
3.
図書
edited by Eli Mishkin and Ludwig Braun, Jr. ; contributors, John G. Truxal ... [et al.]
4.
図書
Robert D. Carmichael
出版情報:
New York : Dover Publications, 1956 xiv, 447 p. ; 20 cm
シリーズ名:
Dover books on science
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5.
図書
Noam Chomsky
出版情報:
New York ; London : Harper & Row, c1966 xi, 119 p. ; 22 cm
シリーズ名:
Studies in languages
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6.
図書
Dimitris N. Chorafas
7.
図書
by Claude Chevalley
8.
図書
by Kai Lai Chung
9.
図書
J. C. Clegg
10.
図書
by Thomas S. Ferguson
11.
図書
H.F. Bohnenblust ... [et al.] ; edited by H.W. Kuhn and A.W. Tucker
12.
図書
edited by D.J.A. Welsh
出版情報:
London ; New York : Academic Press, 1971 x, 364 p. ; 24 cm
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13.
図書
edited by Bernard Harris
14.
図書
R.J. Aumann ... [et al.] ; edited by M. Dresher, L.S. Shapley, A.W. Tucker
15.
図書
Masanao Aoki
16.
図書
edited by J. M. Mendel and K. S. Fu
17.
図書
[edited by Herbert S. Wilf and Frank Harary]
出版情報:
Providence, R.I. : American Mathematical Society, 1971 206 p. ; 26 cm
シリーズ名:
SIAM-AMS proceedings ; v. 3
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18.
図書
N.I. Andreyev ; translated by Scripta Technica, Inc. ; edited by Wendell H. Flemin
19.
図書
Harry C. Andrews ; with contributions by William K. Pratt and Kenneth Caspari
出版情報:
New York : Academic Press, 1970 ix, 187 p. ; 24 cm
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20.
図書
Rutherford Aris
21.
図書
F.V. Atkinson
22.
図書
[by] A. A. Afifi [and] S. P. Azen
出版情報:
New York : Academic Press, [1972] xviii, 366 p. ; 24 cm
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23.
図書
William F. Ames
24.
図書
J. Aczél, Z. Daróczy
25.
図書
N.M. Amosov ; translated by Leo Finegold for Scripta Technica, Inc. ; translation editor, Lawrence J. Fogel
出版情報:
New York : Spartan Books , London : Macmillan, 1967 xiii, 192 p. ; 24 cm
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26.
図書
edited by H. Amann, N. Bazley, K. Kirchgässner
27.
図書
edited by V. Lakshmikantham
出版情報:
New York : Academic Press, 1979 xx, 726 p. ; 24 cm
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28.
図書
J. Dieudonné
29.
図書
edited by G. Pollák
30.
図書
by Ranan B. Banerji
31.
図書
editors, A.K. Aziz, J.W. Wingate, M.J. Balas
出版情報:
New York : Academic Press, 1977 ix, 278 p. ; 24 cm
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32.
図書
Melvin S. Berger
33.
図書
Richard Bellman and Charlene Paule Smith
34.
図書
[by] Edward J. Beltrami
35.
図書
edited by Arthur W. Burks
出版情報:
Urbana : University of Illinois Press, 1970 xxvi, 375 p. ; 24 cm
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36.
図書
by Armand Borel ; with contributions by G. Bredon ... [et al.]
37.
図書
Thomas L. Boullion, Patrick L. Odell
出版情報:
New York : Wiley-Interscience, c1971 x, 103 p. ; 23 cm
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38.
図書
James R. Brown
39.
図書
[by] Garrett Birkhoff and Thomas C. Bartee
出版情報:
New York : McGraw-Hill, c1970 xi, 431 p. ; 23 cm
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40.
図書
[by] M. Bongard ; edited by Joseph K. Hawkins ; translated by Theodore Cheron
出版情報:
New York : Spartan Books, [1970] xvii, 253 p. ; 25 cm
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41.
図書
Siegmund Brandt
出版情報:
Amsterdam : North-Holland Pub. Co. , New York : American Elsevier Pub. Co., 1970 xii, 322 p ; 23 cm
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42.
図書
editor, A. T. Bharucha-Reid
43.
図書
U. Narayan Bhat
目次情報:
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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:
44.
図書
by George E.P. Box and Gwilym M. Jenkins
45.
図書
William M. Boothby
目次情報:
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Preface to the Revised Second Edition
Preface to the Second Edition
Preface to the First Edition
Introduction to Manifolds / I.:
Preliminary Comments on R[superscript n] / 1.:
R[superscript n] and Euclidean Space / 2.:
Topological Manifolds / 3.:
Further Examples of Manifolds. Cutting and Pasting / 4.:
Abstract Manifolds. Some Examples / 5.:
Functions of Several Variables and Mappings / II.:
Differentiability for Functions of Several Variables
Differentiability of Mappings and Jacobians
The Space of Tangent Vectors at a Point of R[superscript n]
Another Definition of T[subscript a](R[superscript n])
Vector Fields on Open Subsets of R[superscript n]
The Inverse Function Theorem / 6.:
The Rank of a Mapping / 7.:
Differentiable Manifolds and Submanifolds / III.:
The Definition of a Differentiable Manifold
Further Examples
Differentiable Functions and Mappings
Rank of a Mapping, Immersions
Submanifolds
Lie Groups
The Action of a Lie Group on a Manifold. Transformation Groups
The Action of a Discrete Group on a Manifold / 8.:
Covering Manifolds / 9.:
Vector Fields on a Manifold / IV.:
The Tangent Space at a Point of a Manifold
Vector Fields
One-Parameter and Local One-Parameter Groups Acting on a Manifold
The Existence Theorem for Ordinary Differential Equations
Some Examples of One-Parameter Groups Acting on a Manifold
One-Parameter Subgroups of Lie Groups
The Lie Algebra of Vector Fields on a Manifold
Frobenius's Theorem
Homogeneous Spaces
Tensors and Tensor Fields on Manifolds / V.:
Tangent Covectors
Covectors on Manifolds
Covector Fields and Mappings
Bilinear Forms. The Riemannian Metric
Riemannian Manifolds as Metric Spaces
Partitions of Unity
Some Applications of the Partition of Unity
Tensor Fields
Tensors on a Vector Space
Mappings and Covariant Tensors
The Symmetrizing and Alternating Transformations
Multiplication of Tensors
Multiplication of Tensors on a Vector Space
Multiplication of Tensor Fields
Exterior Multiplication of Alternating Tensors
The Exterior Algebra on Manifolds
Orientation of Manifolds and the Volume Element
Exterior Differentiation
An Application to Frobenius's Theorem
Integration on Manifolds / VI.:
Integration in R[superscript n] Domains of Integration
Basic Properties of the Riemann Integral
A Generalization to Manifolds
Integration on Riemannian Manifolds
Integration on Lie Groups
Manifolds with Boundary
Stokes's Theorem for Manifolds
Homotopy of Mappings. The Fundamental Group
Homotopy of Paths and Loops. The Fundamental Group
Some Applications of Differential Forms. The de Rham Groups
The Homotopy Operator
Some Further Applications of de Rham Groups
The de Rham Groups of Lie Groups
Covering Spaces and Fundamental Group
Differentiation on Riemannian Manifolds / VII.:
Differentiation of Vector Fields along Curves in R[superscript n]
The Geometry of Space Curves
Curvature of Plane Curves
Differentiation of Vector Fields on Submanifolds of R[superscript n]
Formulas for Covariant Derivatives
[down triangle, open subscript x subscript p] Y and Differentiation of Vector Fields
Constant Vector Fields and Parallel Displacement
Addenda to the Theory of Differentiation on a Manifold
The Curvature Tensor
The Riemannian Connection and Exterior Differential Forms
Geodesic Curves on Riemannian Manifolds
The Tangent Bundle and Exponential Mapping. Normal Coordinates
Some Further Properties of Geodesics
Symmetric Riemannian Manifolds
Some Examples
Curvature / VIII.:
The Geometry of Surfaces in E[superscript 3]
The Principal Curvatures at a Point of a Surface
The Gaussian and Mean Curvatures of a Surface
The Theorema Egregium of Gauss
Basic Properties of the Riemann Curvature Tensor
Curvature Forms and the Equations of Structure
Differentiation of Covariant Tensor Fields
Manifolds of Constant Curvature
Spaces of Positive Curvature
Spaces of Zero Curvature
Spaces of Constant Negative Curvature
References
Index
Preface to the Revised Second Edition
Preface to the Second Edition
Preface to the First Edition
46.
図書
[by] R. Boudarel, J. Delmas [and] P. Guichet ; translated by R.N. McDonough
47.
図書
A. Hanyga ; translation editor, R.W. Ogden
48.
図書
Henryk Minc ; with a foreword by Marvin Marcus
目次情報:
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Editor's statement
Section editor's foreword
Preface
The theory of permanents in the historical order of development / 1:
Properties of permanents / 2:
(0, 1)-Matrices / 3:
Lower bounds for permanents / 4:
The van der Waerden conjecture / 5:
Upper bounds for permanents / 6:
Evaluation of permanents / 7:
More about permanents / 8:
Bibliography
Index to bibliography
Index of notation
Index
Editor's statement
Section editor's foreword
Preface
49.
図書
edited by A.V. Balakrishnan, Lucien W. Neustadt
出版情報:
New York : Academic Press, 1967 xv, 459 p. ; 24 cm
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50.
図書
Nicos Christofides
51.
図書
Luis A. Santaló ; with a foreword by Mark Kac
目次情報:
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Integral Geometry in the Plane / Part I:
Convex sets in the plane / 1:
Sets of points and Poisson processes in the plane / 2:
Sets of lines in the plane / 3:
Pairs of points and pairs of lines / 4:
Sets of strips in the plane / 5:
The group of motions in the plane: kinematic density / 6:
Fundamental formulas of Poincare and Blaschke / 7:
Lattices of figures / 8:
General Integral Geometry / Part II:
Differential forms and Lie groups / 9:
Density and measure in homogenous spaces / 10:
The affine groups / 11:
The group of motions in En / 12:
Integral Geometry in En / Part III:
Convex sets in En / 13:
Linear subspaces, convex sets and compact manifolds / 14:
The kinematic density in En / 15:
Geometric and statistical applications: stereology / 16:
Integral Geometry in Spaces of Constant Curvature / Part IV:
Noneuclidean integral geometry / 17:
Crofton's formulas and the kinematic fundamental formula in noneuclidean spaces / 18:
Integral geometry and foliated spaces: trends in integral geometry / 19:
Integral Geometry in the Plane / Part I:
Convex sets in the plane / 1:
Sets of points and Poisson processes in the plane / 2:
52.
図書
Shelemyahu Zacks
53.
図書
Nathaniel F.G. Martin, James W. England ; foreword by James K. Brooks
54.
図書
Dimitri P. Bertsekas
55.
図書
James O. Berger
56.
図書
A.A. Borovkov ; translated by Kenneth Wickwire
57.
図書
William R. Derrick
58.
図書
George E. Andrews
59.
図書
Wilhelm Flügge
出版情報:
Berlin : Springer-Verlag, 1972 vii, 207 p. ; 24 cm
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60.
図書
Peter J. Huber
61.
図書
Robert Ellis
62.
図書
[by] Charles L. Lawson [and] Richard J. Hanson
目次情報:
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Preface to the Classics Edition
Preface
Introduction / 1:
Analysis of the Least Squares Problem / 2:
Orthogonal Decomposition by Certain Elementary Orthogonal Transformations / 3:
Orthogonal Decomposition by Singular Value Decomposition / 4:
Perturbation Theorems for Singular Values / 5:
Bounds for the Condition Number of a Triangular Matrix / 6:
The Pseudoinverse / 7:
Perturbation Bounds for the Pseudoinverse / 8:
Perturbation Bounds for the Solution of Problem LS / 9:
Numerical Computations Using Elementary Orthogonal Transformations / 10:
Computing the Solution for the Overdetermined or Exactly Determined Full Rank Problem / 11:
Computation of the Covariance Matrix of the Solution Parameters / 12:
Computing the Solution for the Underdetermined Full Rank Problem / 13:
Computing the Solution for Problem LS with Possibly Deficient Pseudorank / 14:
Analysis of Computing Errors for Householder Transformations / 15:
Analysis of Computing Errors for the Problem LS / 16:
Analysis of Computing Errors for the Problem LS Using Mixed Precision Arithmetic / 17:
Computation of the Singular Value Decomposition and the Solution of Problem LS / 18:
Other Methods for Least Squares Problems / 19:
Linear Least Squares with Linear Equality Constraints Using a Basis of the Null Space / 20:
Linear Least Squares with Linear Equality Constraints by Direct Elimination / 21:
Linear Least Squares with Linear Equality Constraints by Weighting / 22:
Linear Least Squares with Linear Inequality Constraints / 23:
Modifying a QR Decomposition to Add or Remove Column Vectors / 24:
Practical Analysis of Least Squares Problems / 25:
Examples of Some Methods of Analyzing a Least Squares Problem / 26:
Modifying a QR Decomposition to Add or Remove Row Vectors with Application to Sequential Processing of Problems Having a Large or Banded Coefficient Matrix / 27:
Basic Linear Algebra Including Projections / Appendix A:
Proof of Global Quadratic Convergence of the QR Algorithm / Appendix B:
Description and Use of FORTRAN Codes for Solving Problem LS / Appendix C:
Developments from 1974 to 1995 / Appendix D:
Bibliography
Index
Preface to the Classics Edition
Preface
Introduction / 1:
63.
図書
[editor, Ralph D. James]
出版情報:
[Vancouver] : [Canadian Mathematical Congress], c1975 2 v. ; 24 cm
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64.
図書
edited by Jon Barwise ; with the cooperation of H.J. Keisler ... [et al.]
目次情報:
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Model Theory / J. Barwise ; P.C. Eklof ; H.J. Keisler ; A. Kock ; A. Macintyre ; M. Makkai ; M. Morley ; G.E. Reyes ; K.D. Stroyan
Set Theory / J.P. Burgess ; K.J. Devlin ; T.J. Jech ; I. Juhasz ; K. Kunen ; M.E. Rudin ; J.R. Schoenfield
Recursion Theory / P. Aczel ; M. Davis ; H.B. Enderton ; A. Kechris ; D.A. Martin ; Y.N. Moschovakis ; M.O. Rabin ; R.A. Shore ; S.G. Simpson
Proof Theory and Constructive Mathematics / H. Barendregt ; S. Feferman ; M.P. Fourman ; L. Harrington ; J. Paris ; H. Schwichtenberg ; C. Smorynski ; R. Statman ; A.S. Troelstra
Indices
Model Theory / J. Barwise ; P.C. Eklof ; H.J. Keisler ; A. Kock ; A. Macintyre ; M. Makkai ; M. Morley ; G.E. Reyes ; K.D. Stroyan
Set Theory / J.P. Burgess ; K.J. Devlin ; T.J. Jech ; I. Juhasz ; K. Kunen ; M.E. Rudin ; J.R. Schoenfield
Recursion Theory / P. Aczel ; M. Davis ; H.B. Enderton ; A. Kechris ; D.A. Martin ; Y.N. Moschovakis ; M.O. Rabin ; R.A. Shore ; S.G. Simpson
65.
図書
Adhemar Bultheel
66.
図書
Jared L. Cohon
67.
図書
Solomon Lefschetz
68.
図書
R. Courant, K.O. Friedrichs
目次情報:
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Compressible Fluids / I:
Mathematical Theory of Hyperbolic Flow Equations for Functions of Two Variables / II:
One-Dimensional Flow / III:
Isentropic Irrotational Steady Plane Flow / IV:
Flow in Nozzles and Jets / V:
Flow in Three Dimensions / VI:
Compressible Fluids / I:
Mathematical Theory of Hyperbolic Flow Equations for Functions of Two Variables / II:
One-Dimensional Flow / III:
69.
図書
edited by David F. Findley
出版情報:
New York : Academic Press, 1978 x, 345 p. ; 24 cm
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70.
図書
Walter Rudin
目次情報:
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Preface
General Theory / Part 1:
Topological Vector Space Introduction Separation properties Linear Mappings Finite-dimensional spaces Metrization Boundedness and continuity Seminorms and local convexity Quotient spaces Examples Exercises / 1:
Completeness Baire category The Banach-Steinhaus theorem The open mapping theorem The closed graph theorem Bilinear mappings Exercises / 2:
Convexity The Hahn-Banach theorems Weak topologies Compact convex sets Vector-valued integration Holomorphic functions Exercises / 3:
Duality in Banach Spaces The normed dual of a normed space Adjoints Compact operators Exercises / 4:
Some Applications A continuity theorem Closed subspaces ofL p -spaces The range of a vector-valued measure A generalized Stone-Weierstrass theorem Two interpolation theorems Kakutani's fixed point theorem Haar measure on compact groups Uncomplemented subspaces Sums of Poisson kernels Two more fixed point theorems Exercises / 5:
Distributions and Fourier Transforms / Part 2:
Test Functions and Distributions Introduction Test function spaces Calculus with distributions Localization Supports of distributions Distributions as derivatives Convolutions Exercises / 6:
Fourier Transforms Basic properties Tempered distributions Paley-Wiener theorems Sobolev's lemma Exercises / 7:
Applications to Differential Equations Fundamental solutions Elliptic equations Exercises / 8:
Tauberian Theory Wiener's theorem The prime number theorem The renewal equation Exercises / 9:
Banach Algebras and Spectral Theory / Part 3:
Banach Algebras Introduction Complex homomorphisms Basic properties of spectra Symbolic calculus The group of invertible elements Lomonosov's invariant subspace theorem Exercises / 10:
Commutative Banach Algebras Ideals and homomorphisms Gelfand transforms Involutions Applications to noncommutative algebras Positive functionals Exercises / 11:
Bounded Operators on a Hillbert Space Basic facts Bounded operators A commutativity theorem Resolutions of the identity The spectral theorem Eigenvalues of normal operators Positive operators and square roots The group of invertible operators A characterization of B*-algebras An ergodic theorem Exercises / 12:
Unbounded Operators Introduction Graphs and symmetric operators The Cayley transform Resolutions of the identity The spectral theorem Semigroups of operators Exercises / 13:
Compactness and Continuity / Appendix A:
Notes and Comments / Appendix B:
Bibliography List of Special Symbols
Index
Preface
General Theory / Part 1:
Topological Vector Space Introduction Separation properties Linear Mappings Finite-dimensional spaces Metrization Boundedness and continuity Seminorms and local convexity Quotient spaces Examples Exercises / 1:
71.
図書
H. Dym, H.P. McKean
目次情報:
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Historical Introduction
Fourier Series
Fourier Integrals
Fourier Integrals and Complex Function Theory
Fourier Series and Integrals on Groups
Additional Reading
Bibliography
Historical Introduction
Fourier Series
Fourier Integrals
72.
図書
Kerson Huang
出版情報:
Singapore : World Scientific, c1982 x, 281 p. ; 24 cm
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73.
図書
editors, Jerzy Łoś and Maria W. Łoś ; contributors, A. Anastasopoulos ... [et al.]
出版情報:
Amsterdam : North-Holland , New York : American Elsevier, 1974 xvii, 483 p. ; 24 cm
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74.
図書
editor, J. Abadie ; contributors, S. Vajda ... [et al.]
出版情報:
Amsterdam : North-Holland, 1967 xxii, 316 p. ; 23 cm
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75.
図書
W.F. Ames
目次情報:
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Preface
Overview / 1:
Methods of Operator Approximation in System Modelling / I:
Nonlinear Operator Approximation with Preassigned Accuracy / 2:
Introduction / 2.1:
Generic formulation of the problem / 2.2:
Operator approximation in space C([0; 1]) / 2.3:
Operator approximation in Banach spaces by polynomial operators / 2.4:
Approximation on compact sets in topological vector spaces / 2.5:
Approximation on noncompact sets in Hilbert spaces / 2.6:
Special results for maps into Banach spaces / 2.7:
Concluding remarks / 2.8:
Interpolation of Nonlinear Operators 65 / 3:
Lagrange interpolation in Banach spaces / 3.1:
Weak interpolation of nonlinear operators / 3.3:
Some related results / 3.4:
Realistic Operators and their Approximation / 3.5:
Formalization of concepts related to description of real-world objects / 4.1:
Approximation of RÂícontinuous operators / 4.3:
Methods of Best Approximation for Nonlinear Operators / 4.4:
Best Approximation of nonlinear operators in Banach spaces: Deterministic case / 5.1:
Estimation of mean and covariance matrix for random vectors / 5.3:
Best Hadamard-quadratic approximation / 5.4:
Best polynomial approximation / 5.5:
Best causal approximation / 5.6:
Best hybrid approximations / 5.7:
Optimal Estimation of Random Vectors / 5.8:
Computational Methods for Optimal Filtering of Stochastic Signals / 6:
Optimal linear Filtering in Finite dimensional vector spaces / 6.1:
Optimal linear Filtering in Hilbert spaces / 6.3:
Optimal causal linear Filtering with piecewise constant memory / 6.4:
Optimal causal polynomial Filtering with arbitrarily variable memory / 6.5:
Optimal nonlinear Filtering with no memory constraint / 6.6:
Computational Methods for Optimal Compression and Reconstruction of Random Data / 6.7:
Standard Principal Component Analysis and Karhunen-Loeeve transform (PCA{KLT) / 7.1:
Rank-constrained matrix approximations / 7.3:
Generic PCA{KLT / 7.4:
Optimal hybrid transform based on Hadamard-quadratic approximation / 7.5:
Optimal transform formed by a combination of nonlinear operators / 7.6:
Optimal generalized hybrid transform / 7.7:
Bibliography / 7.8:
Index
Preface
Overview / 1:
Methods of Operator Approximation in System Modelling / I:
76.
図書
by J. Aczél ; translated by Scripta Technica, Inc. ; supplemented by the author ; edited by Hansjorg Oser
77.
図書
Emil Artin
78.
図書
edited by Kenneth J. Arrow, Samuel Karlin, Herbert Scarf ; contributions by Kenneth J. Arrow ... [et al.]
79.
図書
par V. I. Arnold et A. Avez
80.
図書
V. de Alfaro and T. Regge
出版情報:
Amsterdam : North-Holland Publishing Company, 1965. ix, 205p. ; 24 cm.
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81.
図書
by Claude Berge ; translated by Alison Doig
出版情報:
London : Methuen , New York : Wiley, 1962 x, 247 p. ; 24 cm.
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82.
図書
Gordon S. G. Beveridge and Robert S. Schechter
83.
図書
V.E. Beneš
84.
図書
edited by Lucien M. Le Cam and Jerzy Neyman
85.
図書
edited by Lucien M. Le Cam and Jerzy Neyman
86.
図書
Robert Betchov [and] William O. Criminale, Jr
87.
図書
Richard Bellman
88.
図書
E.J. Beltrami, M.R. Wohlers
出版情報:
New York : Academic Press, 1966 xiv, 116 p. ; 24 cm
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89.
図書
Julius S. Bendat
出版情報:
New York : John Wiley & Sons , London : Chapman & Hall, c1958 xxi, 431 p. ; 24 cm
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90.
図書
Bromwich, Thomas John I'Anson, 1875-1929
91.
図書
A.G. Butkovskiy ; Translated from the Russian by Scripta Technica ; Translation editor: George M. Krane
92.
図書
by A. Bruce Clarke [and] Ralph L. Disney
出版情報:
New York : Wiley, c1970 xv, 346 p. ; 24 cm
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93.
図書
edited by A.V. Balakrishnan
出版情報:
New York : Academic Press, 1972 ix, 509 p. ; 23 cm
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94.
図書
Rupert G. Miller, Jr
95.
図書
John C. Oxtoby
96.
図書
[by] Kenneth J. Arrow [and] F.H. Hahn
出版情報:
San Francisco : Holden-Day , Edinburgh : Oliver and Boyd, c1971 xii, 452 p. ; 24 cm
シリーズ名:
Mathematical economics texts ; 6
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97.
図書
[by] Frederick S. Hillier [and] Gerald J. Lieberman
98.
図書
Morris H. DeGroot
出版情報:
New York : McGraw-Hill, c1970 xvi, 489 p ; 24 cm
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Foreword
Preface
Survey of probability theory / Part 1:
Introduction / Chapter 1.:
Experiments, Sample Spaces, and Probability / Chapter 2.:
Experiments and Sample Spaces / 2.1:
Set Theory / 2.2:
Events and Probability / 2.3:
Conditional Probability / 2.4:
Binomial Coefficients / 2.5:
Exercises
Random Variables, Random Vectors, and Distribution Functions / Chapter 3.:
Random Variables and Their Distributions / 3.1:
Multivariate Distributions / 3.2:
Sums and Integrals / 3.3:
Marginal Distributions and Independence / 3.4:
Vectors and Matrices / 3.5:
Expectations, Moments, and Characteristic Functions / 3.6:
Transformations of Random Variables / 3.7:
Conditional Distributions / 3.8:
Some Special Univariate Distributions / Chapter 4.:
The Bernoulli Distribution / 4.1:
The Binomial Distribution / 4.3:
The Poisson Distribution / 4.4:
The Negative Binomial Distribution / 4.5:
The Hypergeometric Distribution / 4.6:
The Normal Distribution / 4.7:
The Gamma Distribution / 4.8:
The Beta Distribution / 4.9:
The Uniform Distribution / 4.10:
The Pareto Distribution / 4.11:
The t Distribution / 4.12:
The F Distribution / 4.13:
Some Special Multivariate Distributions / Chapter 5.:
The Multinomial Distribution / 5.1:
The Dirichlet Distribution / 5.3:
The Multivariate Normal Distribution / 5.4:
The Wishart Distribution / 5.5:
The Multivariate t Distribution / 5.6:
The Bilateral Bivariate Pareto Distribution / 5.7:
Subjective probability and utility / Part 2:
Subjective Probability / Chapter 6.:
Relative Likelihood / 6.1:
The Auxiliary Experiment / 6.3:
Construction of the Probability Distribution / 6.4:
Verification of the Properties of a Probability Distribution / 6.5:
Conditional Likelihoods / 6.6:
Utility / Chapter 7.:
Preferences among Rewards / 7.1:
Preferences among Probability Distributions / 7.2:
The Definition of a Utility Function / 7.3:
Some Properties of Utility Functions / 7.4:
The Utility of Monetary Rewards / 7.5:
Convex and Concave Utility Functions / 7.6:
The Axiomatic Development of Utility / 7.7:
Construction of the Utility Function / 7.8:
Verification of the Properties of a Utility Function / 7.9:
Extension of the Properties of a Utility Function to the Class P[subscript E] / 7.10:
Statistical decision problems / Part 3:
Decision Problems / Chapter 8.:
Elements of a Decision Problem / 8.1:
Bayes Risk and Bayes Decisions / 8.2:
Nonnegative Loss Functions / 8.3:
Concavity of the Bayes Risk / 8.4:
Randomization and Mixed Decisions / 8.5:
Convex Sets / 8.6:
Decision Problems in Which [similar]2 and D Are Finite / 8.7:
Decision Problems with Observations / 8.8:
Construction of Bayes Decision Functions / 8.9:
The Cost of Observation / 8.10:
Statistical Decision Problems in Which Both [Omega] and D Contain Two Points / 8.11:
Computation of the Posterior Distribution When the Observations Are Made in More Than One Stage / 8.12:
Conjugate Prior Distributions / Chapter 9.:
Sufficient Statistics / 9.1:
Conjugate Families of Distributions / 9.2:
Construction of the Conjugate Family / 9.3:
Conjugate Families for Samples from Various Standard Distributions / 9.4:
Conjugate Families for Samples from a Normal Distribution / 9.5:
Sampling from a Normal Distribution with Unknown Mean and Unknown Precision / 9.6:
Sampling from a Uniform Distribution / 9.7:
A Conjugate Family for Multinomial Observations / 9.8:
Conjugate Families for Samples from a Multivariate Normal Distribution / 9.9:
Multivariate Normal Distributions with Unknown Mean Vector and Unknown Precision Matrix / 9.10:
The Marginal Distribution of the Mean Vector / 9.11:
The Distribution of a Correlation / 9.12:
Precision Matrices Having an Unknown Factor / 9.13:
Limiting Posterior Distributions / Chapter 10.:
Improper Prior Distributions / 10.1:
Improper Prior Distributions for Samples from a Normal Distribution / 10.2:
Improper Prior Distributions for Samples from a Multivariate Normal Distribution / 10.3:
Precise Measurement / 10.4:
Convergence of Posterior Distributions / 10.5:
Supercontinuity / 10.6:
Solutions of the Likelihood Equation / 10.7:
Convergence of Supercontinuous Functions / 10.8:
Limiting Properties of the Likelihood Function / 10.9:
Normal Approximation to the Posterior Distribution / 10.10:
Approximations for Vector Parameters / 10.11:
Posterior Ratios / 10.12:
Estimation, Testing Hypotheses, and Linear Statistical Models / Chapter 11.:
Estimation / 11.1:
Quadratic Loss / 11.2:
Loss Proportional to the Absolute Value of the Error / 11.3:
Estimation of a Vector / 11.4:
Problems of Testing Hypotheses / 11.5:
Testing a Simple Hypothesis about the Mean of a Normal Distribution / 11.6:
Testing Hypotheses about the Mean of a Normal Distribution When the Precision Is Unknown / 11.7:
Deciding Whether a Parameter Is Smaller or Larger Than a Specified Value / 11.8:
Deciding Whether the Mean of a Normal Distribution Is Smaller or Larger Than a Specified Value / 11.9:
Linear Models / 11.10:
Testing Hypotheses in Linear Models / 11.11:
Investigating the Hypothesis That Certain Regression Coefficients Vanish / 11.12:
One-way Analysis of Variance / 11.13:
Sequential decisions / Part 4:
Sequential Sampling / Chapter 12.:
Gains from Sequential Sampling / 12.1:
Sequential Decision Procedures / 12.2:
The Risk of a Sequential Decision Procedure / 12.3:
Backward Induction / 12.4:
Optimal Bounded Sequential Decision Procedures / 12.5:
Illustrative Examples / 12.6:
Unbounded Sequential Decision Procedures / 12.7:
Regular Sequential Decision Procedures / 12.8:
Existence of an Optimal Procedure / 12.9:
Approximating an Optimal Procedure by Bounded Procedures / 12.10:
Regions for Continuing or Terminating Sampling / 12.11:
The Functional Equation / 12.12:
Approximations and Bounds for the Bayes Risk / 12.13:
The Sequential Probability-ratio Test / 12.14:
Characteristics of Sequential Probability-ratio Tests / 12.15:
Approximating the Expected Number of Observations / 12.16:
Optimal Stopping / Chapter 13.:
The Statistician's Reward / 13.1:
Choice of the Utility Function / 13.3:
Sampling without Recall / 13.4:
Further Problems of Sampling with Recall and Sampling without Recall / 13.5:
Sampling without Recall from a Normal Distribution with Unknown Mean / 13.6:
Sampling with Recall from a Normal Distribution with Unknown Mean / 13.7:
Existence of Optimal Stopping Rules / 13.8:
Existence of Optimal Stopping Rules for Problems of Sampling with Recall and Sampling without Recall / 13.9:
Martingales / 13.10:
Stopping Rules for Martingales / 13.11:
Uniformly Integrable Sequences of Random Variables / 13.12:
Martingales Formed from Sums and Products of Random Variables / 13.13:
Regular Supermartingales / 13.14:
Supermartingales and General Problems of Optimal Stopping / 13.15:
Markov Processes / 13.16:
Stationary Stopping Rules for Markov Processes / 13.17:
Entrance-fee Problems / 13.18:
The Functional Equation for a Markov Process / 13.19:
Sequential Choice of Experiments / Chapter 14.:
Markovian Decision Processes with a Finite Number of Stages / 14.1:
Markovian Decision Processes with an Infinite Number of Stages / 14.3:
Some Betting Problems / 14.4:
Two-armed-bandit Problems / 14.5:
Two-armed-bandit Problems When the Value of One Parameter Is Known / 14.6:
Two-armed-bandit Problems When the Parameters Are Dependent / 14.7:
Inventory Problems / 14.8:
Inventory Problems with an Infinite Number of Stages / 14.9:
Control Problems / 14.10:
Optimal Control When the Process Cannot Be Observed without Error / 14.11:
Multidimensional Control Problems / 14.12:
Control Problems with Actuation Errors / 14.13:
Search Problems / 14.14:
Search Problems with Equal Costs / 14.15:
Uncertainty Functions and Statistical Decision Problems / 14.16:
Sufficient Experiments / 14.17:
Examples of Sufficient Experiments / 14.18:
References
Supplementary Bibliography
Name Index
Subject Index
Foreword
Preface
Survey of probability theory / Part 1:
99.
図書
Béla Bollobás
出版情報:
London ; New York : Academic Press, 1978 xx, 488 p. ; 24 cm
シリーズ名:
L.M.S. monographs ; 11
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Preface
Basic Definitions
Connectivity / Chapter 1:
Elementary Properties / 1.:
Menger's Theorem and its Consequences / 2.:
The Structure of 2- and 3-Connected Graphs / 3.:
Minimally k-Connected Graphs / 4.:
Graphs with Given Maximal Local Connectivity / 5.:
Exercises, Problems and Conjectures / 6.:
Matching / Chapter 2:
Fundamental Matching Theorems
The Number of 1-Factors
f-Factors
Matching in Graphs with Restrictions on the Degrees
Coverings
Cycles / Chapter 3:
Graphs with Large Minimal Degree and Large Girth
Vertex Disjoint Cycles
Edge Disjoint Cycles
The Circumference
Graphs with Cycles of Given Lengths
The Diameter / Chapter 4:
Diameter, Maximal Degree and Size
Diameter and Connectivity
Graphs with Large Subgraphs of Small Diameter
Factors of Small Diameter
Colourings / Chapter 5:
General Colouring Theorems
Critical k-Chromatic Graphs
Colouring Graphs on Surfaces
Sparse Graphs of Large Chromatic Number
Perfect Graphs
Ramsey Type Theorems
Complete Subgraphs / 7.:
The Number of Complete Subgraphs
Complete Subgraphs of r-Partite Graphs
The Structure of Graphs
The Structure of Extremal Graphs without Forbidden Subgraphs
Independent Complete Subgraphs
Topological Subgraphs / Chapter 7:
Contractions
Topological Complete Subgraphs
Semi-Topological Subgraphs
Complexity and Packing / Chapter 8:
The Complexity of Graph Properties
Monotone Properties
The Main Packing Theorem
Packing Graphs of Small Size
Applications of Packing Results to Complexity
References
Index of Symbols
Index of Definitions
Preface
Basic Definitions
Connectivity / Chapter 1:
100.
図書
Samuel Eilenberg