close
1.

図書
図書
1. Banach algebras and compact operators
Corneliu Constantinescu
出版情報: Amsterdam : Elsevier, 2001  xxi, 597 p. ; 23 cm
シリーズ名: North-Holland mathematical library ; v. 59 . C*-algebras / Corneliu Constantinescu ; v. 2
所蔵情報: loading…
目次情報: 続きを見る
Introduction
Banach Algebras / 2：
Algebras / 2.1：
General Results / 2.1.1：
Invertible Elements / 2.1.2：
The Spectrum / 2.1.3：
Standard Examples / 2.1.4：
Complexification of Algebras / 2.1.5：
Exercises
Normed Algebras / 2.2：
The Standard Examples / 2.2.1：
The Exponential Function and the Neumann Series / 2.2.3：
Invertible Elements of Unital Banach Algebras / 2.2.4：
The Theorems of Riesz and Gelfand / 2.2.5：
Poles of Resolvents / 2.2.6：
Modules / 2.2.7：
Involutive Banach Algebras / 2.3：
Involutive Algebras / 2.3.1：
Sesquilinear Forms / 2.3.2：
Positive Linear Forms / 2.3.4：
The State Space / 2.3.5：
Involutive Modules / 2.3.6：
Gelfand Algebras / 2.4：
The Gelfand Transform / 2.4.1：
Involutive Gelfand Algebras / 2.4.2：
Examples / 2.4.3：
Locally Compact Additive Groups / 2.4.4：
The Fourier Transform / 2.4.5：
Compact Operators / 3：
The General Theory / 3.1：
Fredholm Operators / 3.1.1：
Point Spectrum / 3.1.4：
Spectrum of a Compact Operator / 3.1.5：
Integral Operators / 3.1.6：
Linear Differential Equations / 3.2：
Boundary Value Problems for Differential Equations / 3.2.1：
Supplementary Results / 3.2.2：
Linear Partial Differential Equations / 3.2.3：
Name
Index Subject
Index Symbol
Index
Introduction
Banach Algebras / 2：
Algebras / 2.1：
2.

図書
図書
2. Quantum dynamical systems
Robert Alicki and Mark Fannes
出版情報: Oxford : Oxford University Press, c2001  xiv, 278 p. ; 24 cm
所蔵情報: loading…
目次情報: 続きを見る
Introduction / 1：
Basic tools for quantum mechanics / 2：
Hilbert spaces and operators / 2.1：
Vector spaces / 2.1.1：
Banach and Hilbert spaces / 2.1.2：
Geometrical properties of Hilbert spaces / 2.1.3：
Orthonormal bases / 2.1.4：
Subspaces and projectors / 2.1.5：
Linear maps between Banach spaces / 2.1.6：
Linear functionals and Dirac notation / 2.1.7：
Adjoints of bounded operators / 2.1.8：
Hermitian, unitary and normal operators / 2.1.9：
Partial isometries and polar decomposition / 2.1.10：
Spectra of operators / 2.1.11：
Unbounded operators / 2.1.12：
Measures / 2.2：
Measures and integration / 2.2.1：
Distributions / 2.2.2：
Hilbert spaces of functions / 2.2.3：
Spectral measures / 2.2.4：
Probability in quantum mechanics / 2.3：
Pure states / 2.3.1：
Mixed states, density matrices / 2.3.2：
Observables in quantum mechanics / 2.4：
Compact operators / 2.4.1：
Weyl quantization / 2.4.2：
Composed systems / 2.5：
Direct sums / 2.5.1：
Tensor products / 2.5.2：
Observables and states of composite systems / 2.5.3：
Notes / 2.6：
Deterministic dynamics / 3：
Deterministic quantum dynamics / 3.1：
Time-independent Hamiltonians / 3.1.1：
Perturbations of Hamiltonians / 3.1.2：
Time-dependent Hamiltonians / 3.1.3：
Periodic perturbations and Floquet operators / 3.1.4：
Kicked dynamics / 3.1.5：
Classical limits / 3.2：
Classical differentiable dynamics / 3.3：
Self-adjoint Laplacians on compact manifolds / 3.4：
Spin chains / 3.5：
Local observables / 4.1：
States of a spin system / 4.2：
Symmetries and dynamics / 4.3：
Algebraic tools / 5：
C*-algebras / 5.1：
Examples / 5.2：
States and representations / 5.3：
Dynamical systems and von Neumann algebras / 5.4：
Fermionic dynamical systems / 5.5：
Fermions in Fock space / 6.1：
Fock space / 6.1.1：
Creation and annihilation / 6.1.2：
Second quantization / 6.1.3：
The CAR-algebra / 6.2：
Canonical anticommutation relations / 6.2.1：
Quasi-free automorphisms / 6.2.2：
Quasi-free states / 6.2.3：
Ergodic theory / 6.3：
Ergodicity in classical systems / 7.1：
Ergodicity in quantum systems / 7.2：
Asymptotic Abelianness / 7.2.1：
Multitime correlations / 7.2.2：
Fluctuations around ergodic means / 7.2.3：
Lyapunov exponents / 7.3：
Classical dynamics / 7.3.1：
Quantum dynamics / 7.3.2：
Quantum irreversibility / 7.4：
Measurement theory / 8.1：
Open quantum systems / 8.2：
Complete positivity / 8.3：
Quantum dynamical semigroups / 8.4：
Quasi-free completely positive maps / 8.5：
Entropy / 8.6：
von Neumann entropy / 9.1：
Technical preliminaries / 9.1.1：
Properties of von Neumann's entropy / 9.1.2：
Mean entropy / 9.1.3：
Entropy of quasi-free states / 9.1.4：
Relative entropy / 9.2：
Finite-dimensional case / 9.2.1：
Maximum entropy principle / 9.2.2：
Algebraic setting / 9.2.3：
Dynamical entropy / 9.3：
Operational partitions / 10.1：
Symbolic dynamics / 10.2：
The entropy / 10.2.2：
Some technical results / 10.3：
The quantum shift / 10.4：
The free shift / 10.4.2：
Infinite entropy / 10.4.3：
Powers-Price shifts / 10.4.4：
Classical dynamical entropy / 10.5：
The Kolmogorov-Sinai invariant / 11.1：
H-density / 11.2：
Finite quantum systems / 12：
Quantum chaos / 12.1：
Time scales / 12.1.1：
Spectral statistics / 12.1.2：
Semi-classical limits / 12.1.3：
The kicked top / 12.2：
The model / 12.2.1：
The classical limit / 12.2.2：
Kicked mean-field Heisenberg model / 12.2.3：
Chaotic properties / 12.2.4：
Gram matrices / 12.3：
Entropy production / 12.4：
Model systems / 12.5：
Entropy of the quantum cat map / 13.1：
Ruelle's inequality / 13.2：
Non-commutative Riemannian structures / 13.2.1：
Non-commutative Lyapunov exponents / 13.2.2：
Quasi-free Fermion dynamics / 13.2.3：
Description of the model / 13.3.1：
Main result / 13.3.2：
Sketch of the proof / 13.3.3：
Epilogue / 13.4：
References
Index
Introduction / 1：
Basic tools for quantum mechanics / 2：
Hilbert spaces and operators / 2.1：
3.

図書
図書
3. The theory of 2-structures : a framework for decomposition and transformation of graphs
A. Ehrenfeucht, T. Harju, G. Rozenberg
出版情報: Singapore : World Scientific, c1999  xvi, 290 p. ; 23 cm
所蔵情報: loading…
目次情報: 続きを見る
Preface
Preliminaries / Chapter 1：
Notations / 1.1：
Sets and functions / 1.1.1：
Closure operators / 1.1.2：
Relations / 1.1.3：
Equivalence relations / 1.1.4：
Partial orders / 1.2：
Downsets / 1.2.1：
Order embeddings / 1.2.2：
Linear orders / 1.2.3：
Semigroups and groups / 1.3：
Notations for semigroups and monoids / 1.3.1：
Free monoids (with involution) / 1.3.2：
Preliminaries on groups / 1.3.3：
Group actions / 1.3.4：
Free groups, commutators and verbal identities / 1.3.5：
Graph Theoretical Preliminaries / Chapter 2：
Directed and Undirected Graphs / 2.1：
Basic notions / 2.1.1：
Connectivity of graphs / 2.1.2：
Some special graphs / 2.1.3：
Comparability graphs / 2.2：
Transitively oriented graphs / 2.2.1：
Permutation graphs and cographs / 2.2.2：
Construction trees of cographs / 2.2.3：
2-Structures and Their Clans / Chapter 3：
Introduction and representations / 3.1：
Definition of a 2-structure / 3.1.1：
Isomorphic 2-structures / 3.1.2：
Reversibility / 3.1.3：
Substructures and clans / 3.2：
Substructures, clans and factors / 3.2.1：
Refinements and similarity / 3.2.2：
Reversible version / 3.2.3：
Graphs and packed components / 3.2.4：
Some special 2-structures / 3.2.5：
Closure properties of clans / 3.3：
Basic closures / 3.3.1：
Sibas: set theoretic closure properties / 3.3.2：
Clans of factors / 3.3.3：
Prime clans / 3.4：
Prime members in sibas / 3.4.1：
Minimal overlapping clans / 3.4.2：
Quotients and Homomorphisms / Chapter 4：
Quotients / 4.1：
Factorizations and quotients / 4.1.1：
Homomorphisms / 4.1.2：
Natural epimorphisms and decompositions / 4.1.3：
Clans and epimorphisms / 4.2：
Homomorphism theorem / 4.2.1：
Prime clans in quotients / 4.2.2：
Primitive quotients / 4.2.3：
Other operations / 4.3：
Premorphisms / 4.3.1：
Extensions / 4.3.2：
Clan Decomposition / Chapter 5：
The clan decomposition theorem / 5.1：
Maximal prime clans / 5.1.1：
Special sibas and 2-structures / 5.1.2：
The relationship of sibas to 2-structures / 5.1.3：
The shape of a 2-structure / 5.2：
The shape and its representation as a tree / 5.2.1：
Same shapes / 5.2.2：
A construction of prime clans / 5.3：
A construction of clans / 5.3.1：
Primitive 2-Structures / 5.3.2：
Small primitive substructures / 6.1：
Uniformly imprimitive 2-structures / 6.1.1：
Primitive substructures of 3 or 4 nodes / 6.1.2：
Hereditary properties / 6.2：
Local and global nodes / 6.2.1：
Critically primitive 2-structures / 6.2.2：
The parity theorem / 6.3.1：
The list of critically primitive 2-structures / 6.3.2：
Angular 2-Structures / Chapter 7：
Angularity / 7.1：
All-connectivity / 7.1.1：
All-connected skew angular 2-structures / 7.1.2：
T-structures / 7.2：
T-structures and partial orders / 7.2.1：
T[subscript 2]-structures / 7.2.2：
Linear orders and Schroder numbers / 7.3：
Bi-orders and linear orders / 7.3.1：
Uniformly imprimitive linear orders / 7.3.2：
Parenthesis words and Schroder numbers / 7.3.3：
Labelled 2-Structures / Chapter 8：
Introduction to l2-structures / 8.1：
Definitions / 8.1.1：
Substructures, clans and quotients / 8.1.2：
Clan decomposition of l2-structures / 8.2：
Uniqueness of decompositions / 8.2.1：
The shape of an l2-structure / 8.2.2：
Graphs and their representations / 8.2.3：
Graphs as l2-structures / 8.3.1：
On comparability graphs / 8.3.2：
Unstable Labelled 2-Structures / Chapter 9：
Triangle free and unstable l2-structures / 9.1：
Removable edges / 9.1.1：
Internal and external nodes / 9.1.2：
Triangle-free l2-structures / 9.1.3：
Heredity in unstable l2-structures / 9.2：
The partition of nodes / 9.2.1：
Alternating structures / 9.2.2：
Degrees of nodes / 9.2.3：
A composition of unstable l2-structures / 9.3：
A constructive reduction of primitive l2-structures / 9.3.1：
Pendant components / 9.3.2：
Automorphisms of Labelled 2-Structures / Chapter 10：
Label preserving automorphisms / 10.1：
The l-automorphism groups / 10.1.1：
Transitivity / 10.1.2：
Automorphic actions on factors / 10.1.3：
Universality of l-automorphism groups / 10.1.4：
Nonpreserving automorphisms / 10.2：
Connections to l-automorphisms / 10.2.1：
Transitivity and associated permutations / 10.2.2：
Representing labels by automorphisms / 10.2.3：
Switching of Graphs / Chapter 11：
Introduction to switching / 11.1：
The group of graphs / 11.1.1：
Switching classes / 11.1.3：
Structural properties of switching classes / 11.2：
A local characterization / 11.2.1：
Automorphisms / 11.2.2：
Special problems on undirected graphs / 11.3：
Two-graphs / 11.3.1：
Eulerian graphs / 11.3.2：
Pancyclic graphs / 11.3.3：
Trees / 11.3.4：
Labelled Structures over Groups / Chapter 12：
Introduction / 12.1：
Groups and involutions / 12.1.1：
Selectors and switching classes / 12.1.2：
An interpretation in networks / 12.2：
Concurrent behaviour in networks / 12.2.1：
Reducing the actions to groups / 12.2.2：
Introducing reversibility / 12.2.3：
Examples for some special groups / 12.3：
The cyclic groups Z[subscript 3] and Z[subscript 4] / 12.3.1：
The symmetric group S[subscript 3] / 12.3.2：
Clans of Switching Classes / Chapter 13：
Associated groups / 13.1：
The group of selectors / 13.1.1：
The group of abelian switching classes / 13.1.2：
Clans and horizons / 13.2：
Spanning trees / 13.2.1：
Horizons and constant selectors / 13.2.2：
Clans / 13.2.3：
Cardinalities of switching classes / 13.3：
Some special cases / 13.3.1：
Centralizers / 13.3.2：
Some improvements / 13.3.3：
Quotients and Plane Trees / Chapter 14：
Quotients of switching classes / 14.1：
Planes and plane trees / 14.1.1：
Planes / 14.2.1：
Plane trees / 14.2.2：
Bijective correspondence of plane trees / 14.2.3：
Forms / 14.2.4：
Invariants / Chapter 15：
Free invariants / 15.1：
General invariants / 15.1.1：
Edge monoids / 15.1.2：
Variable functions and free invariants / 15.1.3：
Group properties of free invariants / 15.2：
Abelian property / 15.2.1：
Graphs of words / 15.2.2：
Verbal identities / 15.2.3：
Invariants on abelian groups / 15.3：
Independency of free invariants / 15.3.1：
Complete sets of invariants / 15.3.2：
Invariants on nonabelian groups / 15.4：
General observations / 15.4.1：
Central characters / 15.4.2：
A characterization theorem / 15.4.3：
Bibliography
Index
Preface
Preliminaries / Chapter 1：
Notations / 1.1：
4.

図書
図書
4. Mathematical anaysis during the 20th century (: hbk)
Jean-Paul Pier
出版情報: Oxford : Oxford University Press, 2001  x, 428 p. ; 25 cm
所蔵情報: loading…
目次情報: 続きを見る
Introduction / 1：
The scope of analysis / 1.1：
The great classics on analysis / 1.1.1：
The changing object of analysis / 1.1.2：
Main streams in a turbulent activity / 1.2：
The question of subdividing mathematical analysis / 1.2.1：
How to organize the subject / 1.2.2：
General Topology / 2：
Evolution 1900-1950 / 2.1：
Topological axiomatizations / 2.1.1：
Topological algebra / 2.1.2：
Filtrations / 2.1.3：
Dimension theory / 2.1.4：
Complementary inputs / 2.1.5：
Flashes 1950-2000 / 2.2：
An accomplished subject / 2.2.1：
Generalized topological concepts / 2.2.2：
Integration and Measure / 3：
Lebesgue integration / 3.1：
The general concept of measure / 3.1.2：
Paradoxical decomposition / 3.1.3：
Period of consolidation / 3.1.4：
Standing problems / 3.2：
Abstract formulations / 3.2.2：
Generalized Riemann integrals / 3.2.3：
Outlook / 3.2.4：
Functional analysis / 4：
New objectives / 4.1：
Theory of integral equations / 4.1.2：
Banach spaces / 4.1.3：
Hilbert spaces / 4.1.4：
von Neumann algebras / 4.1.5：
Banach algebras / 4.1.6：
Distributions / 4.1.7：
Topological vector spaces / 4.2：
Extension of Weierstra[beta]'s theorem / 4.2.2：
Frechet spaces, Schwartz spaces, Sobolev spaces / 4.2.3：
Banach space properties / 4.2.4：
Hilbert space properties / 4.2.5：
Banach algebra and C*-algebra properties / 4.2.6：
Approximation properties / 4.2.7：
Nuclearity / 4.2.8：
von Neumann algebra properties / 4.2.9：
Specific topics / 4.2.10：
Harmonic analysis / 5：
Fourier series / 5.1：
Invariant measures / 5.1.2：
Almost periodic functions / 5.1.3：
Uniqueness of invariant measures / 5.1.4：
Convolutions / 5.1.5：
An evolution linked to the history of physics / 5.1.6：
Representation theory / 5.1.7：
Structural properties of topological groups / 5.1.8：
Positive-definite functions / 5.1.9：
Harmonic synthesis / 5.1.10：
Metric locally compact Abelian groups / 5.1.11：
Fourier transforms / 5.2：
Convolution properties / 5.2.2：
Group representations / 5.2.3：
Remarkable Banach algebras of functions on a locally compact group / 5.2.4：
Specific sets / 5.2.5：
Specific groups / 5.2.6：
Harmonic analysis on semigroups / 5.2.7：
Wavelets / 5.2.8：
Generalized actions / 5.2.9：
Lie groups / 6：
Lie groups and Lie algebras / 6.1：
Symmetric Riemannian spaces / 6.1.2：
Hilbert's problem for Lie groups / 6.1.3：
Representations of Lie groups / 6.1.4：
The wide range of Lie group theory / 6.2：
Solution of Hilbert's problem on Lie groups / 6.2.2：
Ergodicity problems / 6.2.3：
Specific classes of Lie groups / 6.2.4：
Extensions of Lie group theory / 6.2.5：
Theory of functions and analytic geometry / 7：
The nineteenth century continued / 7.1：
Potential theory / 7.1.2：
Conformal mappings / 7.1.3：
Towards a theory of several complex variables / 7.1.4：
Accomplishments on previous topics / 7.2：
Hardy spaces / 7.2.2：
The dominance of the theory of several complex variables / 7.2.3：
Iteration problems / 7.2.4：
Ordinary and Partial Differential Equations / 8：
New trends for classical problems / 8.1：
Fixed point properties / 8.1.2：
From the ordinary differential case to the partial differential case / 8.1.3：
Differential equations / 8.2：
Partial differential equations / 8.2.2：
Tentacular subjects / 8.2.3：
Algebraic topology / 9：
The origins of algebraic topology / 9.1：
Simplicial theories / 9.1.2：
Homotopy theory / 9.1.3：
Fibres and fibrations / 9.1.4：
The breakthroughs due to Eilenberg, MacLane, and Leray / 9.1.5：
The power of the machinery / 9.2：
Generalizations / 9.2.2：
Differential topology / 10：
The beginning of the century / 10.1：
E. Cartan's work / 10.1.2：
Tensor products and exterior differentials / 10.1.3：
Morse theory / 10.1.4：
Whitney's work / 10.1.5：
De Rham's work / 10.1.6：
Hodge theory / 10.1.7：
The framing of the subject / 10.1.8：
The status of differentiable manifolds / 10.2：
Foliations / 10.2.2：
From Poincare's heritage / 10.2.3：
Global analysis / 10.2.5：
Probability / 11：
First results / 11.1：
Brownian motion / 11.1.2：
Ergodicity / 11.1.3：
Probabilities as measures / 11.1.4：
Stochastic integrals / 11.1.5：
Probability theory, a part of analysis / 11.2：
Dynamical systems and ergodicity / 11.2.2：
Entropy / 11.2.3：
Stochastic processes / 11.2.4：
Algebraic geometry / 12：
Algebraic geometry and number theory / 12.1：
The Mordell conjecture / 12.1.2：
Transcendence and prime numbers / 12.1.3：
The Riemann conjecture / 12.1.4：
Arithmetical properties / 12.2：
Investigations on transcendental numbers / 12.2.2：
A central object of study / 12.2.3：
Etale cohomology / 12.2.4：
The general Riemann-Roch theorems / 12.2.5：
K-theory / 12.2.6：
Further studies / 12.2.7：
References
Index of Names
Index of Terms
List of Symbols / Appendix：
Introduction / 1：
The scope of analysis / 1.1：
The great classics on analysis / 1.1.1：
5.

図書
図書
5. Qualitative methods in nonlinear dynamics : novel approaches to Liapunov's matrix functions
A.A. Martynyuk
出版情報: New York : Marcel Dekker, c2002  x, 301 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 246
所蔵情報: loading…
目次情報: 続きを見る
Preface
Preliminaries / 1：
Introduction / 1.1：
Nonlinear Continuous Systems / 1.2：
General equations of nonlinear dynamics / 1.2.1：
Perturbed motion equations / 1.2.2：
Definitions of Stability / 1.3：
Scalar, Vector and Matrix-Valued Liapunov Functions / 1.4：
Auxiliary scalar functions / 1.4.1：
Comparison functions / 1.4.2：
Vector Liapunov functions / 1.4.3：
Matrix-valued metafunction / 1.4.4：
Comparison Principle / 1.5：
Liapunov-Like Theorems / 1.6：
Matrix-valued function and its properties / 1.6.1：
A version of the original theorems of Liapunov / 1.6.2：
Advantages of Cone-Valued Liapunov Functions / 1.7：
Stability with respect to two measures / 1.7.1：
Stability analysis of large scale systems / 1.7.2：
Liapunov's Theorems for Large Scale Systems in General / 1.8：
Why are matrix-valued Liapunov functions needed? / 1.8.1：
Stability and instability of large scale systems / 1.8.2：
Notes / 1.9：
Qualitative Analysis of Continuous Systems / 2：
Nonlinear Systems with Mixed Hierarchy of Subsystems / 2.1：
Mixed hierarchical structures / 2.2.1：
Hierarchical matrix function structure / 2.2.2：
Structure of hierarchical matrix function derivative / 2.2.3：
Stability and instability conditions / 2.2.4：
Linear autonomous system / 2.2.5：
Examples of third order systems / 2.2.6：
Dynamics of the Systems with Regular Hierarchy Subsystems / 2.3：
Ikeda-Siljak hierarchical decomposition / 2.3.1：
Hierarchical Liapunov's matrix-valued functions / 2.3.2：
Linear nonautonomous systems / 2.3.3：
Stability Analysis of Large Scale Systems / 2.4：
A class of large scale systems / 2.4.1：
Construction of nondiagonal elements of matrix-valued function / 2.4.2：
Test for stability analysis / 2.4.3：
Linear large scale system / 2.4.4：
Discussion and numerical example / 2.4.5：
Overlapping Decomposition and Matrix-Valued Function Construction / 2.5：
Dynamical system extension / 2.5.1：
Liapunov matrix-valued function construction / 2.5.2：
Test for stability of system (2.5.1) / 2.5.3：
Numerical example / 2.5.4：
Exponential Polystability Analysis of Separable Motions / 2.6：
Statement of the Problem / 2.6.1：
A method for the solution of the problem / 2.6.2：
Autonomous system / 2.6.3：
Polystability by the first order approximations / 2.6.4：
Integral and Lipschitz Stability / 2.7：
Definitions / 2.7.1：
Sufficient conditions for integral and asymptotic integral stability / 2.7.2：
Uniform Lipschitz stability / 2.7.3：
Qualitative Analysis of Discrete-Time Systems / 2.8：
Systems Described by Difference Equations / 3.1：
Matrix-Valued Liapunov Functions Method / 3.3：
Auxiliary results / 3.3.1：
Comparison principle application / 3.3.2：
General theorems on stability / 3.3.3：
Large Scale System Decomposition / 3.4：
Stability and Instability of Large Scale Systems / 3.5：
Auxiliary estimates / 3.5.1：
Autonomous Large Scale Systems / 3.5.2：
Hierarchical Analysis of Stability / 3.7：
Hierarchical decomposition and stability conditions / 3.7.1：
Novel tests for connective stability / 3.7.2：
Controlled Systems / 3.8：
Nonlinear Dynamics of Impulsive Systems / 3.9：
Large Scale Impulsive Systems in General / 4.1：
Notations and definitions / 4.2.1：
Sufficient stability conditions / 4.2.2：
Instability conditions / 4.2.4：
Hierarchical Impulsive Systems / 4.3：
Analytical Construction of Liapunov Function / 4.4：
Structure of hierarchical matrix-valued Liapunov function / 4.4.1：
Structure of the total derivative of hierarchical matrix-valued function / 4.4.2：
Uniqueness and Continuability of Solutions / 4.5：
On Boundedness of the Solutions / 4.6：
Novel Methodology for Stability / 4.7：
Stability conditions / 4.7.1：
Applications / 4.8：
Estimations of Asymptotic Stability Domains in General / 5.1：
A fundamental Zubov's result / 5.2.1：
Some estimates for quadratic matrix-valued functions / 5.2.2：
Algorithm of constructing a point network covering boundary of domain E / 5.2.3：
Numerical realization and discussion of the algorithm / 5.2.4：
Illustrative examples / 5.2.5：
Construction of Estimate for the Domain E of Power System / 5.3：
Oscillations and Stability of Some Mechanical Systems / 5.4：
Three-mass systems / 5.4.1：
Nonautonomous oscillator / 5.4.2：
Absolute Stability of Discrete Systems / 5.5：
References / 5.6：
Subject Index
Preface
Preliminaries / 1：
Introduction / 1.1：
6.

図書
図書
6. Dynamics : numerical explorations. 2nd, rev. and enl. ed
Helena E. Nusse, James A. Yorke
出版情報: New York : Springer, c1998  xvi, 608 p., [8] p. of plates ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 101
所蔵情報: loading…
目次情報: 続きを見る
Preface
Getting the program running / 1：
The Dynamics program and hardware Smalldyn: a small version of Dynamics / 1.1：
Getting started with Dynamics Using the mouse Appendix: description of the interrupts / 1.2：
Questions / 1.3：
Samples of Dynamics: pictures you can make simply / 2：
Introduction Example / 2.1：
Plot a trajectory Example / 2-1a：
Draw a box Example / 2-1b：
Viewing the Parameter Menu Example / 2-1c：
Refresh the screen and continue plotting Example / 2-1d：
Clear the screen and continue plotting Example / 2-1e：
Single stepping through a trajectory Example / 2-1f：
Plot a cross at current position Example / 2-1g：
Draw axes and print picture Example / 2-1h：
Initializing Example / 2-1i：
Viewing the Y Vectors Example / 2-1j：
Find a fixed point Example / 2-1k：
Find a period 2 orbit Example / 2-1l：
Search for all periodic points of period 5 Example / 2-1m：
Change RHO Example / 2-1n：
Plotting permanent crosses Example / 2-1o：
Set storage vector y1 and initialize Example / 2-1p：
Change X Scale or Y Scale / 2-1q：
Complex pictures that are simple to make Example / 2.2：
Chaotic attractor Example / 2-2a：
Computing Lyapunov exponents Example / 2-2b：
Plotting trajectory versus time Example / 2-2c：
Graph of iterate of one dimensional map Example / 2-3a：
Cobweb plot of a trajectory Example / 2-3b：
The Henon attractor Example / 2-3c：
The first iterate of a quadrilateral Example / 2-5：
Plotting direction field and trajectories Example / 2-6：
Bifurcation diagram for the quadratic map Example / 2-7：
Bifurcation diagram with bubbles Example / 2-8：
All the Basins and Attractors Example / 2-9：
Metamorphoses in the basin of infinity Example / 2-10：
Search for all periodic points with period 10 Example / 2-11：
Search for all period 1 and period 2 points Example / 2-12：
Following orbits as a parameter is varied Example / 2-13：
The Mandelbrot set Example / 2-14：
3-Dimensional views on the Lorenz attractor Example / 2-15：
Unstable manifold of a fixed point Example / 2-17：
Stable and unstable manifolds Example / 2-18：
Plotting a Saddle Straddle Trajectory Example / 2-19a：
The unstable manifold of a fixed point Example / 2-19b：
The stable manifold of a fixed point Example / 2-19c：
Saddle Straddle Trajectory, and manifolds Example / 2-19d：
The basin of attraction of infinity Example / 2-20：
A trajectory on a basin boundary Example / 2-21：
A BST trajectory for the Tinkerbell map Example / 2-22：
Lyapunov exponent bifurcation diagram Example / 2-23：
Chaotic parameters Example / 2-24：
Box-counting dimension of an attractor Example / 2-25：
Zooming in on the Tinkerbell attractor Example / 2-26：
Period plot in the Mandelbrot set Appendix Commands for plotting a graph Commands from the Numerical / 2-27：
Explorations Menu Plotting multiple trajectories simultaneously
Screen utilities / 3：
Basic screen features (Screen Menu SM) / 3.1：
Commands for clearing the screen Commands for controlling the screen Level of Text output
Writing on pictures
The arrow keys and boxes (BoX Menu, BXM) / 3.2：
Initializing trajectories, plotting crosses, drawing circles and their iterates (Kruis Menu KM) / 3.3：
Drawing axes (AXes Menu AXM) / 3.4：
Windows and rescaling (Window Menu WM) Detailed view on the structure of an attractor / 3.5：
Zooming in or zooming out (ZOOm Menu ZOOM) / 3.6：
Setting colors (Color Menu CM and Color Table Menu CTM) Color screens Core copy of the picture / 3.7：
Color planes Commands for erasing colors
Utilities / 4：
Setting parameters (Parameter Menu PM) / 4.1：
Setting and replacing a vector (Vector Menu VM) Y Vectors "Own" and the coordinates of yÃââÇ ÃâÅô / 4.2：
Setting step size (Differential Equation Menu DEM) / 4.3：
Saving pictures and data (Disk Menu DM) Creating a batch file of commands Commands for reading disk files / 4.4：
Setting the size of the core (Size of Core Menu SCM) / 4.5：
Printing pictures (PriNter Menu PNM) Commands for specifying printer / 4.6：
Encapsulated PostScript Commands for printer options
Text to printer Printing color pictures
Printing pictures with any p
Preface
Getting the program running / 1：
The Dynamics program and hardware Smalldyn: a small version of Dynamics / 1.1：
7.

図書
図書
7. Moduli of families of curves for conformal and quasiconformal mappings
Alexander Vasilʹev
出版情報: Berlin ; Tokyo : Springer-Verlag, c2002  ix, 211 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1788
所蔵情報: loading…
目次情報: 続きを見る
Introduction / 1：
Moduli of Families of Curves and Extremal Partitions / 2：
Simple definition and properties of the modulus / 2.1：
Definition / 2.1.1：
Properties / 2.1.2：
Examples / 2.1.3：
Grötzsch lemmas / 2.1.4：
Exercises / 2.1.5：
Reduced moduli and capacity / 2.2：
Reduced modulus / 2.2.1：
Capacity and transfinite diameter / 2.2.2：
Digons, triangles and their reduced moduli / 2.2.3：
Elliptic functions and integrals / 2.3：
Elliptic functions / 2.3.1：
Elliptic integrals and JacobiÆs functions / 2.3.2：
Some frequently used moduli / 2.4：
Moduli of doubly connected domains / 2.4.1：
Moduli of quadrilaterals / 2.4.2：
Reduced moduli / 2.4.3：
Reduced moduli of digons / 2.4.4：
Symmetrization and polarization / 2.5：
Circular symmetrization / 2.5.1：
Polarization / 2.5.2：
Quadratic differentials on Riemann surfaces / 2.6：
Riemann surfaces / 2.6.1：
Quadratic differentials / 2.6.2：
Local trajectory structure / 2.6.3：
Trajectory structure in the large / 2.6.4：
Free families of homotopy classes of curves and extremal par- titions / 2.7：
The case of ring domains and quadrangles / 2.7.1：
The case of circular, strip domains, and triangles / 2.7.2：
Continuous and differentiable moduli / 2.7.3：
Moduli in Extremal Problems for Conformal Mapping / 3：
Classical extremal problems for univalent functions / 3.1：
Koebe set, growth, distortion / 3.1.1：
Lower boundary curve for the range of ( / 3.1.2：
Special moduli / 3.1.3：
Upper boundary curve for the range of ( / 3.1.4：
Two-point distortion for univalent functions / 3.2：
Bounded univalent functions / 3.2.1：
Elementary estimates / 3.3.1：
Boundary curve for the range of ( / 3.3.2：
Montel functions / 3.4：
Covering theorems / 3.4.1：
Distortion at the points of normalization / 3.4.2：
The range of ( / 3.4.3：
Univalent functions with the angular derivatives / 3.5：
Estimates of the angular derivatives / 3.5.1：
Moduli in Extremal Problems for Quasiconformal Mapping / 3.5.2：
General information and simple extremal problems / 4.1：
Quasiconformal mappings of Riemann surfaces / 4.1.1：
Growth and Hölder continuity / 4.1.2：
Quasiconformal motion of a quadruple of points / 4.1.3：
Two-point distortion for quasiconformal maps of the plane / 4.2：
Special differentials and extremal partitions / 4.2.1：
Quasisymmetric functions and the extremal maps / 4.2.2：
Boundary parameterization / 4.2.3：
The class QK. Estimations of functionals / 4.2.4：
Conclusions and unsolved problems / 4.2.5：
Two-point distortion for quasiconformal maps of the unit disk / 4.3：
Extremal problems / 4.3.1：
Moduli on Teichmüller Spaces / 5：
Some information on Teichmüller spaces / 5.1：
Moduli on Teichmüller spaces / 5.2：
Variational formulae / 5.2.1：
Three lemmas / 5.2.2：
Harmonic properties of the moduli / 5.3：
Descriptions of the Teichmüller metric / 5.4：
Invariant metrics / 5.5：
References
List of symbols
Index
Introduction / 1：
Moduli of Families of Curves and Extremal Partitions / 2：
Simple definition and properties of the modulus / 2.1：
8.

図書
図書
8. Statistics of extremes
by E.J. Gumbel
出版情報: New York : Columbia University Press, 1958  xx, 375 p. ; 24 cm
所蔵情報: loading…
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.：
9.

図書
図書
9. C[*]-algebras and numerical analysis
Roland Hagen, Steffen Roch, Bernd Silbermann
出版情報: New York : Marcel Dekker, c2001  376 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 236
所蔵情報: loading…
目次情報: 続きを見る
Preface
Introduction / 0：
Numerical analysis / 0.1：
Operator chemistry / 0.2：
The algebraic language of numerical analysis / 0.3：
Microscoping / 0.4：
A few remarks on economy / 0.5：
Brief description of the contents / 0.6：
Approximation methods / 1：
Basic definitions / 1.1.1：
Projection methods / 1.1.2：
Finite section method / 1.1.3：
Banach algebras and stability / 1.2：
Algebras, ideals and homomorphisms / 1.2.1：
Algebraization of stability / 1.2.2：
Small perturbations / 1.2.3：
Compact perturbations / 1.2.4：
Finite sections of Toeplitz operators with continuous generating function / 1.3：
Laurent, Toeplitz and Hankel operators / 1.3.1：
Invertibility and Fredholmness of Toeplitz operators / 1.3.2：
The finite section method / 1.3.3：
C*-algebras of approximation sequences / 1.4：
C*-algebras, their ideals and homomorphisms / 1.4.1：
The Toeplitz C*-algebra and the C*-algebra of the finite section method for Toeplitz operators / 1.4.2：
Stability of sequences in the C*-algebra of the finite section method for Toeplitz operators / 1.4.3：
Symbol of the finite section method for Toeplitz operators / 1.4.4：
Asymptotic behaviour of condition numbers / 1.5：
The condition of an operator / 1.5.1：
Convergence of norms / 1.5.2：
Condition numbers of finite sections of Toeplitz operators / 1.5.3：
Fractality of approximation methods / 1.6：
Fractal homomorphisms, fractal algebras, fractal sequences / 1.6.1：
Fractal algebras, and convergence of norms / 1.6.2：
Notes and references
Regularization of approximation methods / 2：
Stably regularizable sequences / 2.1：
Moore-Penrose inverses and regularizations of matrices / 2.1.1：
Moore-Penrose inverses and regularization of operators / 2.1.2：
Stably regularizable approximation sequences / 2.1.3：
Algebraic characterization of stably regularizable sequences / 2.2：
Moore-Penrose invertibility in C*-algebras / 2.2.1：
Stable regularizability, and Moore-Penrose invertibility in F/G / 2.2.2：
Finite sections of Toeplitz operators and their stable regularizability / 2.2.3：
Convergence of generalized condition numbers / 2.2.4：
Difficulties with Moore-Penrose stability / 2.2.5：
Approximation of spectra / 3：
Set sequences / 3.1：
Limiting sets of set functions / 3.1.1：
Coincidence of the partial and uniform limiting set / 3.1.2：
Spectra and their limiting sets / 3.2：
Limiting sets of spectra of norm convergent sequences / 3.2.1：
Limiting sets of spectra: the general case / 3.2.2：
The case of fractal sequences / 3.2.3：
Limiting sets of singular values / 3.2.4：
Pseudospectra and their limiting sets / 3.3：
[varepsilon]-invertibility / 3.3.1：
Limiting sets of pseudospectra / 3.3.2：
Pseudospectra of operator polynomials / 3.3.3：
Numerical ranges and their limiting sets / 3.4：
Spatial and algebraic numerical ranges / 3.4.1：
Limiting sets of numerical ranges / 3.4.2：
Stability analysis for concrete approximation methods / 3.4.3：
Local principles / 4.1：
Commutative C*-algebras / 4.1.1：
The local principle by Allan and Douglas / 4.1.2：
Fredholmness of Toeplitz operators with piecewise continuous generating function / 4.1.3：
Finite sections of Toeplitz operators generated by a piecewise continuous function / 4.2：
The lifting theorem / 4.2.1：
Application of the local principle / 4.2.2：
Galerkin methods with spline ansatz for singular integral equations / 4.2.3：
Finite sections of Toeplitz operators generated by a quasi-continuous function / 4.3：
Quasicontinuous functions / 4.3.1：
Stability of the finite section method / 4.3.2：
Some other classes of oscillating functions / 4.3.3：
Polynomial collocation methods for singular integral operators with piecewise continuous coefficients / 4.4：
Singular integral operators / 4.4.1：
Stability of the polynomial collocation method / 4.4.2：
Collocation versus Galerkin methods / 4.4.3：
Paired circulants and spline approximation methods / 4.5：
Circulants and paired circulants / 4.5.1：
The stability theorem / 4.5.2：
Finite sections of band-dominated operators / 4.6：
Multidimensional band dominated operators / 4.6.1：
Fredholmness of band dominated operators / 4.6.2：
Finite sections of band dominated operators / 4.6.3：
Representation theory / 5：
Representations / 5.1：
The spectrum of a C*-algebra / 5.1.1：
Primitive ideals / 5.1.2：
The spectrum of an ideal and of a quotient / 5.1.3：
Representations of some concrete algebras / 5.1.4：
Postliminal algebras / 5.2：
Liminal and postliminal algebras / 5.2.1：
Dual algebras / 5.2.2：
Finite sections of Wiener-Hopf operators with almost periodic generating function / 5.2.3：
Lifting theorems and representation theory / 5.3：
Lifting one ideal / 5.3.1：
Sufficient families of homomorphisms / 5.3.2：
Structure of fractal lifting homomorphisms / 5.3.4：
Fredholm sequences / 6：
Fredholm sequences in standard algebras / 6.1：
The standard model / 6.1.1：
Fredholm sequences and stable regularizability / 6.1.2：
Fredholm sequences and Moore-Penrose stability / 6.1.4：
Fredholm sequences and the asymptotic behavior of singular values / 6.2：
The main result / 6.2.1：
A distinguished element and its range dimension / 6.2.2：
Upper estimate of dim Im [Pi subscript n] / 6.2.3：
Lower estimate of dim Im [Pi subscript n] / 6.2.4：
Some examples / 6.2.5：
A general Fredholm theory / 6.3：
Centrally compact and Fredholm sequences / 6.3.1：
Fredholmness modulo compact elements / 6.3.2：
Weakly Fredholm sequences / 6.3.3：
Sequences with finite splitting property / 6.4.1：
Properties of weakly Fredholm sequences / 6.4.2：
Strong limits of weakly Fredholm sequences / 6.4.3：
Weakly Fredholm sequences of matrices / 6.4.4：
Some applications / 6.5：
Numerical determination of the kernel dimension / 6.5.1：
Around the finite section method for Toeplitz operators / 6.5.2：
Discretization of shift operators / 6.5.3：
Self-adjoint approximation sequences / 7：
The spectrum of a self-adjoint approximation sequence / 7.1：
Essential and transient points / 7.1.1：
Fractality of self-adjoint sequences / 7.1.2：
Arveson dichotomy: band operators / 7.1.3：
Arveson dichotomy: standard algebras / 7.1.4：
Szego-type theorems / 7.2：
Folner and Szego algebras / 7.2.1：
Szego's theorem revisited / 7.2.2：
A further generalization of Szego's theorem / 7.2.3：
Algebras with unique tracial state / 7.2.4：
Bibliography
Index
Preface
Introduction / 0：
Numerical analysis / 0.1：
10.

図書
図書
10. Quantum gravity
Claus Kiefer
出版情報: Oxford : Clarendon, 2004  ix, 308 p. ; 25 cm
シリーズ名: The international series of monographs on physics ; 124
Oxford science publications
所蔵情報: loading…
目次情報: 続きを見る
Why quantum gravity? / 1：
Quantum theory and the gravitational field / 1.1：
Introduction / 1.1.1：
Main motivations for quantizing gravity / 1.1.2：
Relevant scales / 1.1.3：
Quantum mechanics and Newtonian gravity / 1.1.4：
Quantum field theory in curved space-time / 1.1.5：
Problems of a fundamental semiclassical theory / 1.2：
Approaches to quantum gravity / 1.3：
Covariant approaches to quantum gravity / 2：
The concept of a graviton / 2.1：
Weak gravitational waves / 2.1.1：
Gravitons from representations of the Poincare group / 2.1.2：
Quantization of the linear field theory / 2.1.3：
Path integrals and the background-field method / 2.2：
General properties of path integrals / 2.2.1：
Background-field method / 2.2.2：
Effective action and Feynman rules / 2.2.3：
Some general remarks on path integrals in perturbation theory / 2.2.4：
Quantum supergravity / 2.3：
Parametrized and relational systems / 3：
Particle systems / 3.1：
Parametrized non-relativistic particle / 3.1.1：
Some remarks on constrained systems / 3.1.2：
The relativistic particle / 3.1.3：
The free bosonic string / 3.2：
Parametrized field theories / 3.3：
Relational dynamical systems / 3.4：
Hamiltonian formulation of general relativity / 4：
The seventh route to geometrodynamics / 4.1：
Principle of path independence / 4.1.1：
Explicit form of generators / 4.1.2：
Geometrodynamics and gauge theories / 4.1.3：
The 3+1 decomposition of general relativity / 4.2：
The canonical variables / 4.2.1：
Hamiltonian form of the Einstein-Hilbert action / 4.2.2：
Discussion of the constraints / 4.2.3：
The case of open spaces / 4.2.4：
Structure of configuration space / 4.2.5：
Canonical gravity with connections and loops / 4.3：
Loop variables / 4.3.1：
Quantum geometrodynamics / 5：
The programme of canonical quantization / 5.1：
The problem of time / 5.2：
Time before quantization / 5.2.1：
Time after quantization / 5.2.2：
The geometrodynamical wave function / 5.3：
The diffeomorphism constraints / 5.3.1：
WKB approximation / 5.3.2：
Remarks on the functional Schrodinger picture / 5.3.3：
Connection with path integrals / 5.3.4：
Anomalies and factor ordering / 5.3.5：
Canonical quantum supergravity / 5.3.6：
The semiclassical approximation / 5.4：
Analogies from quantum mechanics / 5.4.1：
Derivation of the Schrodinger equation / 5.4.2：
Quantum-gravitational correction terms / 5.4.3：
Quantum gravity with connections and loops / 6：
The Gauss and diffeomorphism constraints / 6.1：
Connection representation / 6.1.1：
Loop representation / 6.1.2：
Quantization of area / 6.2：
Quantum Hamiltonian constraint / 6.3：
Quantization of black holes / 7：
Black-hole thermodynamics and Hawking radiation / 7.1：
The laws of black-hole mechanics / 7.1.1：
Hawking and Unruh radiation / 7.1.2：
Bekenstein-Hawking entropy / 7.1.3：
Canonical quantization of the Schwarzschild black hole / 7.2：
Classical formalism / 7.2.1：
Quantization / 7.2.2：
Black-hole spectroscopy and entropy / 7.3：
Quantum theory of collapsing dust shells / 7.4：
Covariant gauge fixing / 7.4.1：
Embedding variables for the classical theory / 7.4.2：
Quantum cosmology / 7.4.3：
Minisuperspace models / 8.1：
General introduction / 8.1.1：
Quantization of a Friedmann universe / 8.1.2：
(2+1)-dimensional quantum gravity / 8.1.3：
Introduction of inhomogeneities / 8.2：
Boundary conditions / 8.3：
DeWitt's boundary condition / 8.3.1：
No-boundary condition / 8.3.2：
Tunnelling condition / 8.3.3：
Comparison of no-boundary and tunnelling wave function / 8.3.4：
Symmetric initial condition / 8.3.5：
String theory / 9：
Quantum gravitational aspects / 9.1：
The Polyakov path integral / 9.2.1：
Effective actions / 9.2.2：
T-duality and branes / 9.2.3：
Superstrings / 9.2.4：
Black-hole entropy / 9.2.5：
Brane worlds / 9.2.6：
Quantum gravity and the interpretation of quantum theory / 10：
Decoherence and the quantum universe / 10.1：
Decoherence in quantum mechanics / 10.1.1：
Decoherence in quantum cosmology / 10.1.2：
Decoherence of primordial fluctuations / 10.1.3：
Arrow of time / 10.2：
Outlook / 10.3：
References
Index
Why quantum gravity? / 1：
Quantum theory and the gravitational field / 1.1：
Introduction / 1.1.1：
11.

図書
図書
11. Newton methods for nonlinear problems : affine invariance and adaptive algorithms
Peter Deuflhard
出版情報: Berlin ; Tokyo : Springer, c2004  xii, 424 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; 35
所蔵情報: loading…
目次情報: 続きを見る
Outline of Contents
Introduction / 1：
Newton-Raphson Method for Scalar Equations / 1.1：
Newton's Method for General Nonlinear Problems / 1.2：
Classical convergence theorems revisited / 1.2.1：
Affine invariance and Lipschitz conditions / 1.2.2：
The algorithmic paradigm / 1.2.3：
A Roadmap of Newton-type Methods / 1.3：
Adaptive Inner Solvers for Inexact Newton Methods / 1.4：
Residual norm minimization: GMRES / 1.4.1：
Energy norm minimization: PCG / 1.4.2：
Error norm minimization: CGNE / 1.4.3：
Error norm reduction: GBIT / 1.4.4：
Linear multigrid methods / 1.4.5：
Exercises
Algebraic Equations / Part I：
Systems of Equations: Local Newton Methods / 2：
Error Oriented Algorithms / 2.1：
Ordinary Newton method / 2.1.1：
Simplified Newton method / 2.1.2：
Newton-like methods / 2.1.3：
Broyden's 'good' rank-1 updates / 2.1.4：
Inexact Newton-ERR methods / 2.1.5：
Residual Based Algorithms / 2.2：
Broyden's 'bad' rank-1 updates / 2.2.1：
Inexact Newton-RES method / 2.2.4：
Convex Optimization / 2.3：
Inexact Newton-PCG method / 2.3.1：
Systems of Equations: Global Newton Methods / 3：
Globalization Concepts / 3.1：
Componentwise convex mappings / 3.1.1：
Steepest descent methods / 3.1.2：
Trust region concepts / 3.1.3：
Newton path / 3.1.4：
Residual Based Descent / 3.2：
Affine contravariant convergence analysis / 3.2.1：
Adaptive trust region strategies / 3.2.2：
Error Oriented Descent / 3.2.3：
General level functions / 3.3.1：
Natural level function / 3.3.2：
Convex Functional Descent / 3.3.3：
Affine conjugate convergence analysis / 3.4.1：
Least Squares Problems: Gauss-Newton Methods / 3.4.2：
Linear Least Squares Problems / 4.1：
Unconstrained problems / 4.1.1：
Equality constrained problems / 4.1.2：
Local Gauss-Newton methods / 4.2：
Global Gauss-Newton methods / 4.2.2：
Adaptive trust region strategy / 4.2.3：
Local convergence results / 4.3：
Local Gauss-Newton algorithms / 4.3.2：
Global convergence results / 4.3.3：
Adaptive rank strategies / 4.3.4：
Underdetermined Systems of Equations / 4.4：
Local quasi-Gauss-Newton method / 4.4.1：
Global Gauss-Newton method / 4.4.2：
Parameter Dependent Systems: Continuation Methods / 5：
Newton Continuation Methods / 5.1：
Classification of continuation methods / 5.1.1：
Affine covariant feasible stepsizes / 5.1.2：
Adaptive pathfollowing algorithms / 5.1.3：
Gauss-Newton Continuation Method / 5.2：
Discrete tangent continuation beyond turning points / 5.2.1：
Adaptive stepsize control / 5.2.2：
Computation of Simple Bifurcations / 5.3：
Augmented systems for critical points / 5.3.1：
Newton-like algorithm for simple bifurcations / 5.3.2：
Branching-off algorithm / 5.3.3：
Differential Equations / Part II：
Stiff ODE Initial Value Problems / 6：
Affine Similar Linear Contractivity / 6.1：
Nonstiff versus Stiff Initial Value Problems / 6.2：
Picard iteration versus Newton iteration / 6.2.1：
Newton-type uniqueness theorems / 6.2.2：
Uniqueness Theorems for Implicit One-step Methods / 6.3：
Pseudo-transient Continuation for Steady State Problems / 6.4：
Exact pseudo-transient continuation / 6.4.1：
Inexact pseudo-transient continuation / 6.4.2：
ODE Boundary Value Problems / 7：
Multiple Shooting for Timelike BVPs / 7.1：
Cyclic linear systems / 7.1.1：
Realization of Newton methods / 7.1.2：
Realization of continuation methods / 7.1.3：
Parameter Identification in ODEs / 7.2：
Periodic Orbit Computation / 7.3：
Single orbit computation / 7.3.1：
Orbit continuation methods / 7.3.2：
Fourier collocation method / 7.3.3：
Polynomial Collocation for Spacelike BVPs / 7.4：
Discrete versus continuous solutions / 7.4.1：
Quasilinearization as inexact Newton method / 7.4.2：
PDE Boundary Value Problems / 8：
Asymptotic Mesh Independence / 8.1：
Global Discrete Newton Methods / 8.2：
General PDEs / 8.2.1：
Elliptic PDEs / 8.2.2：
Inexact Newton Multilevel FEM for Elliptic PDEs / 8.3：
Local Newton-Galerkin methods / 8.3.1：
Global Newton-Galerkin methods / 8.3.2：
References
Software
Index
Outline of Contents
Introduction / 1：
Newton-Raphson Method for Scalar Equations / 1.1：
12.

図書
図書
12. Sieves in number theory
George Greaves
出版情報: Berlin ; Tokyo : Springer, c2001  xii, 304 p. ; 24 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, v. 43
所蔵情報: loading…
目次情報: 続きを見る
Introduction
The Structure of Sifting Arguments / 1：
The Sieves of Eratosthenes and Legendre / 1.1：
The Contribution of Eratosthenes / 1.1.1：
Legendre's Sieve / 1.1.2：
An Estimate for n(X) / 1.1.3：
The Distribution of Primes / 1.1.4：
Examples of Sifting Situations / 1.2：
Notations / 1.2.1：
The Integers in an Interval (Y - X, Y ) / 1.2.2：
Numbers Given by Polynomial Expressions / 1.2.3：
Arithmetic Progressions / 1.2.4：
Sums of Two Squares / 1.2.5：
Polynomials with Prime Arguments / 1.2.6：
A General Formulation of a Sifting Situation / 1.3：
The Basic Formulation / 1.3.1：
Legendre's Sieve in a General Setting / 1.3.2：
A Generalised Formulation / 1.3.3：
A Further Generalisation / 1.3.4：
Sifting Density / 1.3.5：
The Sifting Limit Β(k) / 1.3.6：
Composition of Sieves / 1.3.7：
Notes on Chapter 1 / 1.4：
Selberg's Upper Bound Method / 2：
The Sifting Apparatus / 2.1：
Selberg's Theorem / 2.1.1：
The Numbers (lambda)(d) / 2.1.2：
A Simple Application / 2.1.3：
General Estimates of G(x) and E(D, P) / 2.2：
An Estimate by Rankin's Device / 2.2.1：
Asymptotic Formulas / 2.2.2：
The Error Term / 2.2.3：
Applications / 2.3：
Prime Twins and Goldbach's Problem / 2.3.1：
Polynomial Sequences / 2.3.3：
Notes on Chapter 2 / 2.4：
Combinatorial Methods / 3：
The Construction of Combinatorial Sieves / 3.1：
Preliminary Discussion of Brun's Ideas / 3.1.1：
Fundamental Inequalities and Identities / 3.1.2：
Buchstab's Identity / 3.1.3：
The Combinatorial Sieve Lemma / 3.1.4：
Brun's Pure Sieve / 3.2：
Inequalities and Identities / 3.2.1：
The "Pure Sieve" Theorem / 3.2.2：
A Corollary / 3.2.3：
Prime Twins / 3.2.4：
A Modern Edition of Brun's Sieve / 3.3：
Rosser's Choice of X / 3.3.1：
A Technical Estimate / 3.3.2：
A Simplifying Approximation / 3.3.3：
A Combinatorial Sieve Theorem / 3.3.4：
Brun's Version of his Method / 3.3.5：
Brun's Choice of x / 3.4.1：
The Estimations / 3.4.2：
The Result / 3.4.3：
Notes on Chapter 3 / 3.5：
Rosser's Sieve / 4：
Approximations by Continuous Functions / 4.1：
The Recurrence Relations / 4.1.1：
Partial Summation / 4.1.2：
The Leading Terms / 4.1.3：
The Functions F and f / 4.2：
The Difference-Differential Equations / 4.2.1：
The Adjoint Equation and the Inner Product / 4.2.2：
Solutions of the Adjoint Equation / 4.2.3：
Particular Values of F(s) and f(s) / 4.2.4：
Asymptotic Analysis as k -> $(infinity$) / 4.2.5：
The Convergence Problem / 4.3：
The Auxiliary Functions / 4.3.1：
Adjoints and Inner Products / 4.3.2：
The Case k
A Sieve Theorem Following Rosser / 4.4：
The Case k >/= 1/2: a First Result / 4.4.1：
Theorem 1 when k
An Improved Version of Proposition 1 / 4.4.3：
A Two-Sided Estimate / 4.4.4：
Extremal Examples / 4.5：
The Linear Case / 4.5.1：
The Case k=1/2 / 4.5.2：
Notes on Chapter 4 / 4.6：
The Sieve with Weights / 5：
Simpler Weighting Devices / 5.1：
Logarithmic Weights / 5.1.1：
Modified Logarithmic Weights / 5.1.2：
Some Applications / 5.1.3：
More Elaborate Weighted Sieves / 5.2：
An Improved Weighting Device / 5.2.1：
Buchstab's Weights / 5.2.2：
A Weighted Sieve Following Rosser / 5.3：
Combining Sieving and Weighting / 5.3.1：
The Reduction Identities / 5.3.2：
An Identity for the Main Term / 5.3.3：
The Estimate for the Main Term / 5.3.4：
Notes on Chapter 5 / 5.4：
The Remainder Term in the Linear Sieve / 6：
The Bilinear Nature of Rosser's Construction / 6.1：
The Factorisation of x.d / 6.1.1：
Discretisations of Rosser's Sieve / 6.1.2：
Specification of Details / 6.1.3：
The Leading Contributions to the Main Term / 6.1.4：
The Remainder Term / 6.1.5：
Sifting Short Intervals / 6.2：
The Smoothed Formulation / 6.2.1：
The Remainder Sums / 6.2.2：
Trigonometrical Sums / 6.2.3：
Notes on Chapter 6 / 6.3：
Lower Bound Sieves when k > 1 / 7：
An Extension of Selberg's Upper Bound / 7.1：
The Integral Equation and the Function $(sigma$) (s) / 7.1.1：
The Estimation of G(s) / 7.1.2：
A Lower Bound Sieve via Buchstab's Identity / 7.2：
Buchstab's Iterations / 7.2.1：
The Buchstab Transform of the $(lambda$)2 Method / 7.2.2：
The Sifting Limit as k -> $(infinity$) / 7.2.3：
Selberg's a2 a" Method / 7.3：
The Improved Sifting Limit for Large k / 7.3.1：
Notes on Chapter 7 / 7.4：
References
Index
Introduction
The Structure of Sifting Arguments / 1：
The Sieves of Eratosthenes and Legendre / 1.1：
13.

図書
図書
13. Nonlinear potential theory and weighted Sobolev spaces
Bengt Ove Turesson
出版情報: Berlin : Springer, c2000  xiv, 173 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1736
所蔵情報: loading…
目次情報: 続きを見る
Introduction
Preliminaries / 1：
Notation and conventions / 1.1：
Basic results concerning weights / 1.2：
General weights / 1.2.1：
Ap weights / 1.2.2：
Doubling weights / 1.2.3：
A∞ weights / 1.2.4：
Proof of Muckenhoupt's maximal theorem / 1.2.5：
Boundedness of singular integrals / 1.2.6：
Two theorems by Muckenhoupt and Wheeden / 1.2.7：
Sobolev spaces / 2：
The Sobolev space <$$> / 2.1：
Approximation results / 2.1.1：
Extension theorems / 2.1.2：
An interpolation inequality / 2.1.3：
Hausdorff measures / 2.2：
Isoperimetric inequalities / 2.4：
Preliminary lemmas / 2.4.1：
Extensions of some results by David and Semmes / 2.4.2：
Isoperimetric inequalities involving lower Minkowski content / 2.4.3：
Isoperimetric inequalities with Hausdorff measures / 2.4.4：
A boxing inequality / 2.4.5：
Some Sobolev type inequalities / 2.5：
Embeddings into <$$> / 2.6：
Embedding theorems / 2.6.1：
Potential theory / 3：
Norm inequalities for fractional integrals and maximal functions / 3.1：
Proof of the main inequality and some corollaries / 3.1.1：
An inequality for Bessel potentials / 3.1.2：
Meyers' theory for Incapacities / 3.2：
Outline of Meyers'theory / 3.2.1：
Capacitary measures and capacitary potentials / 3.2.2：
Bessel and Riesz capacities / 3.3：
Basic properties / 3.3.1：
Adams' formula for the capacity of a ball / 3.3.2：
Hausdorff capacities / 3.4：
The capacity of a ball / 3.4.1：
Non-triviality of <$$> / 3.4.3：
Local equivalence between <$$> and <$$> / 3.4.4：
Continuity properties / 3.4.5：
Prostman's lemma / 3.4.6：
Variational capacities / 3.5：
The case 1 < p < ∞ / 3.5.1：
The case p = 1 / 3.5.2：
An embedding theorem / 3.5.3：
Thinness: The case 1 < p < ∞ / 3.6：
Preliminary considerations / 3.6.1：
A Wolff type inequality / 3.6.2：
Proof of the Kellogg property / 3.6.3：
A concept of thinness based on a condensor capacity / 3.6.4：
Thinness: The case p = 1 / 3.7：
Applications of potential theory to Sobolev spaces / 4：
Quasicontinuity / 4.1：
Measures in the dual of <$$$> / 4.1.1：
Poincare type inequalities / 4.2.1：
Spectral synthesis / 4.3.1：
References / 4.4.1：
Index
Introduction
Preliminaries / 1：
Notation and conventions / 1.1：
14.

図書
図書
14. Introduction to Fourier analysis and wavelets
Mark A. Pinsky
出版情報: Australia : Brooks/Cole, c2002  xviii, 376 p. ; 25 cm
シリーズ名: Brooks/Cole series in advanced mathematics
所蔵情報: loading…
目次情報: 続きを見る
Fourier Series on the Circle / 1：
Motivation and Heuristics / 1.1：
Motivation from Physics / 1.1.1：
The Vibrating String / 1.1.1.1：
Heat Flow in Solids / 1.1.1.2：
Absolutely Convergent Trigonometric Series / 1.1.2：
Examples of Factorial and Bessel Functions / 1.1.3：
Poisson Kernel Example / 1.1.4：
Proof of Laplace's Method / 1.1.5：
Nonabsolutely Convergent Trigonometric Series / 1.1.6：
Formulation of Fourier Series / 1.2：
Fourier Coefficients and Their Basic Properties / 1.2.1：
Fourier Series of Finite Measures / 1.2.2：
Rates of Decay of Fourier Coefficients / 1.2.3：
Piecewise Smooth Functions / 1.2.3.1：
Fourier Characterization of Analytic Functions / 1.2.3.2：
Sine Integral / 1.2.4：
Other Proofs That Si([infinity]) = 1 / 1.2.4.1：
Pointwise Convergence Criteria / 1.2.5：
Integration of Fourier Series / 1.2.6：
Convergence of Fourier Series of Measures / 1.2.6.1：
Riemann Localization Principle / 1.2.7：
Gibbs-Wilbraham Phenomenon / 1.2.8：
The General Case / 1.2.8.1：
Fourier Series in L[superscript 2] / 1.3：
Mean Square Approximation--Parseval's Theorem / 1.3.1：
Application to the Isoperimetric Inequality / 1.3.2：
Rates of Convergence in L[superscript 2] / 1.3.3：
Application to Absolutely-Convergent Fourier Series / 1.3.3.1：
Norm Convergence and Summability / 1.4：
Approximate Identities / 1.4.1：
Almost-Everywhere Convergence of the Abel Means / 1.4.1.1：
Summability Matrices / 1.4.2：
Fejer Means of a Fourier Series / 1.4.3：
Wiener's Closure Theorem on the Circle / 1.4.3.1：
Equidistribution Modulo One / 1.4.4：
Hardy's Tauberian Theorem / 1.4.5：
Improved Trigonometric Approximation / 1.5：
Rates of Convergence in C (T) / 1.5.1：
Approximation with Fejer Means / 1.5.2：
Jackson's Theorem / 1.5.3：
Higher-Order Approximation / 1.5.4：
Converse Theorems of Bernstein / 1.5.5：
Divergence of Fourier Series / 1.6：
The Example of du Bois-Reymond / 1.6.1：
Analysis via Lebesgue Constants / 1.6.2：
Divergence in the Space L[superscript 1] / 1.6.3：
Appendix: Complements on Laplace's Method / 1.7：
First Variation on the Theme-Gaussian Approximation / 1.7.0.1：
Second Variation on the Theme-Improved Error Estimate / 1.7.0.2：
Application to Bessel Functions / 1.7.1：
The Local Limit Theorem of DeMoivre-Laplace / 1.7.2：
Appendix: Proof of the Uniform Boundedness Theorem / 1.8：
Appendix: Higher-Order Bessel functions / 1.9：
Appendix: Cantor's Uniqueness Theorem / 1.10：
Fourier Transforms on the Line And Space / 2：
Basic Properties of the Fourier Transform / 2.1：
Riemann-Lebesgue Lemma / 2.2.1：
Approximate Identities and Gaussian Summability / 2.2.2：
Improved Approximate Identities for Pointwise Convergence / 2.2.2.1：
Application to the Fourier Transform / 2.2.2.2：
The n-Dimensional Poisson Kernel / 2.2.2.3：
Fourier Transforms of Tempered Distributions / 2.2.3：
Characterization of the Gaussian Density / 2.2.4：
Wiener's Density Theorem / 2.2.5：
Fourier Inversion in One Dimension / 2.3：
Dirichlet Kernel and Symmetric Partial Sums / 2.3.1：
Example of the Indicator Function / 2.3.2：
Dini Convergence Theorem / 2.3.3：
Extension to Fourier's Single Integral / 2.3.4.1：
Smoothing Operations in R[superscript 1]-Averaging and Summability / 2.3.5：
Averaging and Weak Convergence / 2.3.6：
Cesaro Summability / 2.3.7：
Approximation Properties of the Fejer Kernel / 2.3.7.1：
Bernstein's Inequality / 2.3.8：
One-Sided Fourier Integral Representation / 2.3.9：
Fourier Cosine Transform / 2.3.9.1：
Fourier Sine Transform / 2.3.9.2：
Generalized h-Transform / 2.3.9.3：
L[superscript 2] Theory in R[superscript n] / 2.4：
Plancherel's Theorem / 2.4.1：
Bernstein's Theorem for Fourier Transforms / 2.4.2：
The Uncertainty Principle / 2.4.3：
Uncertainty Principle on the Circle / 2.4.3.1：
Spectral Analysis of the Fourier Transform / 2.4.4：
Hermite Polynomials / 2.4.4.1：
Eigenfunction of the Fourier Transform / 2.4.4.2：
Orthogonality Properties / 2.4.4.3：
Completeness / 2.4.4.4：
Spherical Fourier Inversion in R[superscript n] / 2.5：
Bochner's Approach / 2.5.1：
Piecewise Smooth Viewpoint / 2.5.2：
Relations with the Wave Equation / 2.5.3：
The Method of Brandolini and Colzani / 2.5.3.1：
Bochner-Riesz Summability / 2.5.4：
A General Theorem on Almost-Everywhere Summability / 2.5.4.1：
Bessel Functions / 2.6：
Fourier Transforms of Radial Functions / 2.6.1：
L[superscript 2]-Restriction Theorems for the Fourier Transform / 2.6.2：
An Improved Result / 2.6.2.1：
Limitations on the Range of p / 2.6.2.2：
The Method of Stationary Phase / 2.7：
Statement of the Result / 2.7.1：
Proof of the Method of Stationary Phase / 2.7.2：
Abel's Lemma / 2.7.4：
Fourier Analysis in L[superscript p] Spaces / 3：
The M. Riesz-Thorin Interpolation Theorem / 3.1：
Generalized Young's Inequality / 3.2.0.1：
The Hausdorff-Young Inequality / 3.2.0.2：
Stein's Complex Interpolation Theorem / 3.2.1：
The Conjugate Function or Discrete Hilbert Transform / 3.3：
L[superscript p] Theory of the Conjugate Function / 3.3.1：
L[superscript 1] Theory of the Conjugate Function / 3.3.2：
Identification as a Singular Integral / 3.3.2.1：
The Hilbert Transform on R / 3.4：
L[superscript 2] Theory of the Hilbert Transform / 3.4.1：
L[superscript p] Theory of the Hilbert Transform, 1 [ p [ [infinity] / 3.4.2：
Applications to Convergence of Fourier Integrals / 3.4.2.1：
L[superscript 1] Theory of the Hilbert Transform and Extensions / 3.4.3：
Kolmogorov's Inequality for the Hilbert Transform / 3.4.3.1：
Application to Singular Integrals with Odd Kernels / 3.4.4：
Hardy-Littlewood Maximal Function / 3.5：
Application to the Lebesgue Differentiation Theorem / 3.5.1：
Application to Radial Convolution Operators / 3.5.2：
Maximal Inequalities for Spherical Averages / 3.5.3：
The Marcinkiewicz Interpolation Theorem / 3.6：
Calderon-Zygmund Decomposition / 3.7：
A Class of Singular Integrals / 3.8：
Properties of Harmonic Functions / 3.9：
General Properties / 3.9.1：
Representation Theorems in the Disk / 3.9.2：
Representation Theorems in the Upper Half-Plane / 3.9.3：
Herglotz/Bochner Theorems and Positive Definite Functions / 3.9.4：
Poisson Summation Formula And Multiple Fourier Series / 4：
The Poisson Summation Formula in R[superscript 1] / 4.1：
Periodization of a Function / 4.2.1：
Statement and Proof / 4.2.2：
Shannon Sampling / 4.2.3：
Multiple Fourier Series / 4.3：
Basic L[superscript 1] Theory / 4.3.1：
Pointwise Convergence for Smooth Functions / 4.3.1.1：
Representation of Spherical Partial Sums / 4.3.1.2：
Basic L[superscript 2] Theory / 4.3.2：
Restriction Theorems for Fourier Coefficients / 4.3.3：
Poisson Summation Formula in R[superscript d] / 4.4：
Simultaneous Nonlocalization / 4.4.1：
Application to Lattice Points / 4.5：
Kendall's Mean Square Error / 4.5.1：
Landau's Asymptotic Formula / 4.5.2：
Application to Multiple Fourier Series / 4.5.3：
Three-Dimensional Case / 4.5.3.1：
Higher-Dimensional Case / 4.5.3.2：
Schrodinger Equation and Gauss Sums / 4.6：
Distributions on the Circle / 4.6.1：
The Schrodinger Equation on the Circle / 4.6.2：
Recurrence of Random Walk / 4.7：
Applications to Probability Theory / 5：
Basic Definitions / 5.1：
The Central Limit Theorem / 5.2.1：
Restatement in Terms of Independent Random Variables / 5.2.1.1：
Extension to Gap Series / 5.3：
Extension to Abel Sums / 5.3.1：
Weak Convergence of Measures / 5.4：
An Improved Continuity Theorem / 5.4.1：
Another Proof of Bochner's Theorem / 5.4.1.1：
Convolution Semigroups / 5.5：
The Berry-Esseen Theorem / 5.6：
Extension to Different Distributions / 5.6.1：
The Law of the Iterated Logarithm / 5.7：
Introduction to Wavelets / 6：
Heuristic Treatment of the Wavelet Transform / 6.1：
Wavelet Transform / 6.2：
Wavelet Characterization of Smoothness / 6.2.0.1：
Haar Wavelet Expansion / 6.3：
Haar Functions and Haar Series / 6.3.1：
Haar Sums and Dyadic Projections / 6.3.2：
Completeness of the Haar Functions / 6.3.3：
Haar Series in C[subscript 0] and L[subscript p] Spaces / 6.3.3.1：
Pointwise Convergence of Haar Series / 6.3.3.2：
Construction of Standard Brownian Motion / 6.3.4：
Haar Function Representation of Brownian Motion / 6.3.5：
Proof of Continuity / 6.3.6：
Levy's Modulus of Continuity / 6.3.7：
Multiresolution Analysis / 6.4：
Orthonormal Systems and Riesz Systems / 6.4.1：
Scaling Equations and Structure Constants / 6.4.2：
From Scaling Function to MRA / 6.4.3：
Additional Remarks / 6.4.3.1：
Meyer Wavelets / 6.4.4：
From Scaling Function to Orthonormal Wavelet / 6.4.5：
Direct Proof that V[subscript 1] [minus sign in circle] V[subscript 0] Is Spanned by {[Psi](t - k)}[subscript k[set membership]Z] / 6.4.5.1：
Null Integrability of Wavelets Without Scaling Functions / 6.4.5.2：
Wavelets with Compact Support / 6.5：
From Scaling Filter to Scaling Function / 6.5.1：
Explicit Construction of Compact Wavelets / 6.5.2：
Daubechies Recipe / 6.5.2.1：
Hernandez-Weiss Recipe / 6.5.2.2：
Smoothness of Wavelets / 6.5.3：
A Negative Result / 6.5.3.1：
Cohen's Extension of Theorem 6.5.1 / 6.5.4：
Convergence Properties of Wavelet Expansions / 6.6：
Wavelet Series in L[superscript p] Spaces / 6.6.1：
Large Scale Analysis / 6.6.1.1：
Almost-Everywhere Convergence / 6.6.1.2：
Convergence at a Preassigned Point / 6.6.1.3：
Jackson and Bernstein Approximation Theorems / 6.6.2：
Wavelets in Several Variables / 6.7：
Two Important Examples / 6.7.1：
Tensor Product of Wavelets / 6.7.1.1：
General Formulation of MRA and Wavelets in R[superscript d] / 6.7.2：
Notations for Subgroups and Cosets / 6.7.2.1：
Riesz Systems and Orthonormal Systems in R[superscript d] / 6.7.2.2：
Scaling Equation and Structure Constants / 6.7.2.3：
Existence of the Wavelet Set / 6.7.2.4：
Proof That the Wavelet Set Spans V[subscript 1] [minus sign in circle] V[subscript 0] / 6.7.2.5：
Cohen's Theorem in R[superscript d] / 6.7.2.6：
Examples of Wavelets in R[superscript d] / 6.7.3：
References
Notations
Index
Fourier Series on the Circle / 1：
Motivation and Heuristics / 1.1：
Motivation from Physics / 1.1.1：
15.

図書
図書
15. Lecture notes on Chern-Simons-Witten theory (: pbk)
Sen Hu
出版情報: Singapore ; London : World Scientific, c2001  xii, 200 p. ; 22 cm
所蔵情報: loading…
目次情報: 続きを見る
Preface
Examples of Quantizations / Chapter 1：
Quantization of R[superscript 2] / 1.1：
Classical mechanics / 1.1.1：
Symplectic method / 1.1.2：
Holomorphic method / 1.1.3：
Holomorphic representation of symplectic quotients and its quantization / 1.2：
An example of circle action / 1.2.1：
Moment map of symplectic actions / 1.2.2：
Some geometric invariant theory / 1.2.3：
Grassmanians / 1.2.4：
Calabi-Yau/Ginzburg-Landau correspondence / 1.2.5：
Quantization of symplectic quotients / 1.2.6：
Classical Solutions of Gauge Field Theory / Chapter 2：
Moduli space of classical solutions of Chern-Simons action / 2.1：
Symplectic reduction of gauge fields over a Riemann surface / 2.1.1：
Chern-Simons action on a three manifold / 2.1.2：
Maxwell equations and Yang-Mills equations / 2.2：
Maxwell equations / 2.2.1：
Yang-Mills equations / 2.2.2：
Vector bundle, Chern classes and Chern-Weil theory / 2.3：
Vector bundle and connection / 2.3.1：
Curvature, Chern classes and Chern-Weil theory / 2.3.2：
Quantization of Chern-Simons Action / Chapter 3：
Introduction / 3.1：
Some formal discussions on quantization / 3.2：
Pre-quantization / 3.3：
M as a complex variety / 3.3.1：
Quillen's determinant bundle on M and the Laplacian / 3.3.2：
Some Lie groups / 3.4：
G = R / 3.4.1：
G = S[superscript 1] = R/2[pi]Z / 3.4.2：
T*G / 3.4.3：
Compact Lie groups, G = SU (2) / 3.5：
Genus one / 3.5.1：
Riemann sphere with punctures / 3.5.2：
Higher genus Riemann surface / 3.5.3：
Relation with WZW model and conformal field theory / 3.5.4：
Independence of complex structures / 3.6：
Borel-Weil-Bott theorem of representation of Lie groups / 3.7：
Chern-Simons-Witten Theory and Three Manifold Invariant / Chapter 4：
Representation of mapping class group and three manifold invariant / 4.1：
Knizhik-Zamolodchikov equations and conformal blocks / 4.1.1：
Braiding and fusing matrices / 4.1.2：
Projective representation of mapping class group / 4.1.3：
Three-dimensional manifold invariants via Heegard decomposition / 4.1.4：
Calculations by topological quantum field theory / 4.2：
Atiyah's axioms / 4.2.1：
An example: connected sum / 4.2.2：
Jones polynomials / 4.2.3：
Surgery / 4.2.4：
Verlinde's conjecture and its proof / 4.2.5：
A brief survey on quantum group method / 4.3：
Algebraic representation of knot / 4.3.1：
Hopf algebra and quantum groups / 4.3.2：
Chern-Simons theory and quantum groups / 4.3.3：
Renormalized Perturbation Series of Chern-Simons-Witten Theory / Chapter 5：
Path integral and morphism of Hilbert spaces / 5.1：
One-dimensional quantum field theory / 5.1.1：
Schroedinger operator / 5.1.2：
Spectrum and determinant / 5.1.3：
Asymptotic expansion and Feynman diagrams / 5.2：
Asymptotic expansion of integrals, finite dimensional case / 5.2.1：
Integration on a sub-variety / 5.2.2：
Partition function and topological invariants / 5.3：
Gauge fixing and Faddeev-Popov ghosts / 5.3.1：
The leading term / 5.3.2：
Wilson line and link invariants / 5.3.3：
A brief introduction on renormalization of Chern-Simons theory / 5.4：
A regulization scheme / 5.4.1：
The Feynman rules / 5.4.2：
Topological Sigma Model and Localization / Chapter 6：
Constructing knot invariants from open string theory / 6.1：
A topological sigma model / 6.1.1：
Localization principle / 6.1.3：
Large N expansion of Chern-Simons gauge theory / 6.1.4：
Equivariant cohomology and localization / 6.2：
Equivariant cohomology / 6.2.1：
Localization, finite dimensional case / 6.2.2：
Atiyah-Bott's residue formula and Duistermaat-Heckman formula / 6.3：
Complex case, Atiyah-Bott's residue formula / 6.3.1：
Symplectic case, Duistermaat-Heckman formula / 6.3.2：
2D Yang-Mills theory by localization principle / 6.4：
Cohomological Yang-Mills field theory / 6.4.1：
Relation with physical Yang-Mills theory / 6.4.2：
Evaluation of Yang-Mills theory / 6.4.3：
Combinatorial approach to 2D Yang-Mills theory / 6.5：
Complex Manifold Without Potential Theory / S. S. Chern
Geometric Quantization of Chern-Simons Gauge Theory / S. Axelrod ; S. D. Pietra ; E. Witten
On Holomorphic Factorization of WZW and Coset Models
Bibliography
Index
Afterwards
Preface
Examples of Quantizations / Chapter 1：
Quantization of R[superscript 2] / 1.1：
16.

図書
図書
16. Statistical physics : an advanced approach with applications : web-enhanced with problems and solutions. 2nd ed.
Josef Honerkamp
出版情報: Berlin : Springer, c2002  xiv, 515 p. ; 24 cm
シリーズ名: Advanced texts in physics
所蔵情報: loading…
目次情報: 続きを見る
Statistical Physics Is More than Statistical Mechanics / 1：
Modeling of Statistical Systems / Part I：
Random Variables: Fundamentals of Probability Theory and Statistics / 2：
Probability and Random Variables / 2.1：
The Space of Events / 2.1.1：
Introduction of Probability / 2.1.2：
Random Variables / 2.1.3：
Multivariate Random Variables and Conditional Probabilities / 2.2：
Multidimensional Random Variables / 2.2.1：
Marginal Densities / 2.2.2：
Conditional Probabilities and Bayes' Theorem / 2.2.3：
Moments and Quantiles / 2.3：
Moments / 2.3.1：
Quantiles / 2.3.2：
The Entropy / 2.4：
Entropy for a Discrete Set of Events / 2.4.1：
Entropy for a Continuous Space of Events / 2.4.2：
Relative Entropy / 2.4.3：
Remarks / 2.4.4：
Applications / 2.4.5：
Computations with Random Variables / 2.5：
Addition and Multiplication of Random Variables / 2.5.1：
Further Important Random Variables / 2.5.2：
Limit Theorems / 2.5.3：
Stable Random Variables and Renormalization Transformations / 2.6：
Stable Random Variables / 2.6.1：
The Renormalization Transformation / 2.6.2：
Stability Analysis / 2.6.3：
Scaling Behavior / 2.6.4：
The Large Deviation Property for Sums of Random Variables / 2.7：
Random Variables in State Space: Classical Statistical Mechanics of Fluids / 3：
The Microcanonical System / 3.1：
Systems in Contact / 3.2：
Thermal Contact / 3.2.1：
Systems with Exchange of Volume and Energy / 3.2.2：
Systems with Exchange of Particles and Energy / 3.2.3：
Thermodynamic Potentials / 3.3：
Susceptibilities / 3.4：
Heat Capacities / 3.4.1：
Isothermal Compressibility / 3.4.2：
Isobaric Expansivity / 3.4.3：
Isochoric Tension Coefficient and Adiabatic Compressibility / 3.4.4：
A General Relation Between Response Functions / 3.4.5：
The Equipartition Theorem / 3.5：
The Radial Distribution Function / 3.6：
Approximation Methods / 3.7：
The Virial Expansion / 3.7.1：
Integral Equations for the Radial Distribution Function / 3.7.2：
Perturbation Theory / 3.7.3：
The van der Waals Equation / 3.8：
The Isotherms / 3.8.1：
The Maxwell Construction / 3.8.2：
Corresponding States / 3.8.3：
Critical Exponents / 3.8.4：
Some General Remarks about Phase Transitions and Phase Diagrams / 3.9：
Random Fields: Textures and Classical Statistical Mechanics of Spin Systems / 4：
Discrete Stochastic Fields / 4.1：
Markov Fields / 4.1.1：
Gibbs Fields / 4.1.2：
Equivalence of Gibbs and Markov Fields / 4.1.3：
Examples of Markov Random Fields / 4.2：
Model with Independent Random Variables / 4.2.1：
Auto Model / 4.2.2：
Multilevel Logistic Model / 4.2.3：
Gauss Model / 4.2.4：
Characteristic Quantities of Densities for Random Fields / 4.3：
Simple Random Fields / 4.4：
The White Random Field or the Ideal Paramagnetic System / 4.4.1：
The One-Dimensional Ising Model / 4.4.2：
Random Fields with Phase Transitions / 4.5：
The Curie-Weiss Model / 4.5.1：
The Mean Field Approximation / 4.5.2：
The Two-Dimensional Ising Model / 4.5.3：
The Landau Free Energy / 4.6：
The Renormalization Group Method for Random Fields and Scaling Laws / 4.7：
Scaling Laws / 4.7.1：
Time-Dependent Random Variables: Classical Stochastic Processes / 5：
Markov Processes / 5.1：
The Master Equation / 5.2：
Examples of Master Equations / 5.3：
Analytic Solutions of Master Equations / 5.4：
Equations for the Moments / 5.4.1：
The Equation for the Characteristic Function / 5.4.2：
Examples / 5.4.3：
Simulation of Stochastic Processes and Fields / 5.5：
The Fokker-Planck Equation / 5.6：
Fokker-Planck Equation with Linear Drift Term and Additive Noise / 5.6.1：
The Linear Response Function and the Fluctuation-Dissipation Theorem / 5.7：
The [Omega] Expansion / 5.8：
The One-Particle Picture / 5.8.2：
More General Stochastic Processes / 5.9：
Self-Similar Processes / 5.9.1：
Fractal Brownian Motion / 5.9.2：
Stable Levy Processes / 5.9.3：
Autoregressive Processes / 5.9.4：
Quantum Random Systems / 6：
Quantum-Mechanical Description of Statistical Systems / 6.1：
Ideal Quantum Systems: General Considerations / 6.2：
Expansion in the Classical Regime / 6.2.1：
First Quantum-Mechanical Correction Term / 6.2.2：
Relations Between the Thermodynamic Potential and Other System Variables / 6.2.3：
The Ideal Fermi Gas / 6.3：
The Fermi-Dirac Distribution / 6.3.1：
Determination of the System Variables at Low Temperatures / 6.3.2：
Applications of the Fermi-Dirac Distribution / 6.3.3：
The Ideal Bose Gas / 6.4：
Particle Number and the Bose-Einstein Distribution / 6.4.1：
Bose-Einstein Condensation / 6.4.2：
Pressure / 6.4.3：
Energy and Specific Heat / 6.4.4：
Entropy / 6.4.5：
Applications of Bose Statistics / 6.4.6：
The Photon Gas and Black Body Radiation / 6.5：
The Kirchhoff Law / 6.5.1：
The Stefan-Boltzmann Law / 6.5.2：
The Pressure of Light / 6.5.3：
The Total Radiative Power of the Sun / 6.5.4：
The Cosmic Background Radiation / 6.5.5：
Lattice Vibrations in Solids: The Phonon Gas / 6.6：
Systems with Internal Degrees of Freedom: Ideal Gases of Molecules / 6.7：
Magnetic Properties of Fermi Systems / 6.8：
Diamagnetism / 6.8.1：
Paramagnetism / 6.8.2：
Quasi-particles / 6.9：
Models for the Magnetic Properties of Solids / 6.9.1：
Superfluidity / 6.9.2：
Changes of External Conditions / 7：
Reversible State Transformations, Heat, and Work / 7.1：
Cyclic Processes / 7.2：
Exergy and Relative Entropy / 7.3：
Time Dependence of Statistical Systems / 7.4：
Analysis of Statistical Systems / Part II：
Estimation of Parameters / 8：
Samples and Estimators / 8.1：
Confidence Intervals / 8.2：
Propagation of Errors / 8.3：
The Maximum Likelihood Estimator / 8.4：
The Least-Squares Estimator / 8.5：
Signal Analysis: Estimation of Spectra / 9：
The Discrete Fourier Transform and the Periodogram / 9.1：
Filters / 9.2：
Filters and Transfer Functions / 9.2.1：
Filter Design / 9.2.2：
Consistent Estimation of Spectra / 9.3：
Frequency Distributions for Nonstationary Time Series / 9.4：
Filter Banks and Discrete Wavelet Transformations / 9.5：
Wavelets / 9.6：
Wavelets as Base Functions in Function Spaces / 9.6.1：
Wavelets and Filter Banks / 9.6.2：
Solutions of the Dilation Equation / 9.6.3：
Estimators Based on a Probability Distribution for the Parameters / 10：
Bayesian Estimator and Maximum a Posteriori Estimator / 10.1：
Marginalization of Nuisance Parameters / 10.2：
Numerical Methods for Bayesian Estimators / 10.3：
Identification of Stochastic Models from Observations / 11：
Hidden Systems / 11.1：
The Maximum a Posteriori (MAP) Estimator for the Inverse Problem / 11.2：
The Least-Squares Estimator as a Special MAP Estimator / 11.2.1：
Strategies for Choosing the Regularization Parameter / 11.2.2：
The Regularization Method / 11.2.3：
Examples of Estimating a Distribution Function by a Regularization Method / 11.2.4：
Estimating the Realization of a Hidden Process / 11.3：
The Viterbi Algorithm / 11.3.1：
The Kalman Filter / 11.3.2：
Estimating the Parameters of a Hidden Stochastic Model / 12：
The Expectation Maximization Method (EM Method) / 12.1：
Use of the EM Method for Estimation of the Parameters in Hidden Systems / 12.2：
Estimating the Parameters of a Hidden Markov Model / 12.3：
The Forward Algorithm / 12.3.1：
The Backward Algorithm / 12.3.2：
The Estimation Formulas / 12.3.3：
Estimating the Parameters in a State Space Model / 12.4：
Statistical Tests and Classification Methods / 13：
General Comments Concerning Statistical Tests / 13.1：
Test Quantity and Significance Level / 13.1.1：
Empirical Moments for a Test Quantity: The Bootstrap Method / 13.1.2：
The Power of a Test / 13.1.3：
Some Useful Tests / 13.2：
The z- and the t-Test / 13.2.1：
Test for the Equality of the Variances of Two Sets of Measurements, the F-Test / 13.2.2：
The x[superscript 2]-Test / 13.2.3：
The Kolmogorov-Smirnov Test / 13.2.4：
The F-Test for Least-Squares Estimators / 13.2.5：
The Likelihood-Ratio Test / 13.2.6：
Classification Methods / 13.3：
Classifiers / 13.3.1：
Estimation of Parameters That Arise in Classifiers / 13.3.2：
Automatic Classification (Cluster Analysis) / 13.3.3：
Random Number Generation for Simulating Realizations of Random Variables / Appendix：
Problems
Hints and Solutions
References
Index
Statistical Physics Is More than Statistical Mechanics / 1：
Modeling of Statistical Systems / Part I：
Random Variables: Fundamentals of Probability Theory and Statistics / 2：
17.

図書
図書
17. Tools for computational finance (: pbk)
Rüdiger Seydel
出版情報: Berlin : Tokyo : Springer, c2002  xiv, 224 p. ; 24 cm
シリーズ名: Universitext
所蔵情報: loading…
目次情報: 続きを見る
Prefaces
Contents
Notation
Modeling Tools for Financial Options / Chapter 1：
Options / 1.1：
Model of the Financial Market / 1.2：
Numerical Methods / 1.3：
The Binomial Method / 1.4：
Risk-Neutral Valuation / 1.5：
Stochastic Processes / 1.6：
Wiener Process / 1.6.1：
Stochastic Integral / 1.6.2：
Stochastic Differential Equations / 1.7：
Ito Process / 1.7.1：
Application to the Stock Market / 1.7.2：
Ito Lemma and Implications / 1.8：
Jump Processes / 1.9：
Notes and Comments
Exercises
Generating Random Numbers with Specified Distributions / Chapter 2：
Pseudo-Random Numbers / 2.1：
Linear Congruential Generators / 2.1.1：
Random Vectors / 2.1.2：
Fibonacci Generators / 2.1.3：
Transformed Random Variables / 2.2：
Inversion / 2.2.1：
Transformation in IR[superscript 1] / 2.2.2：
Transformation in IR[superscript n] / 2.2.3：
Normally Distributed Random Variables / 2.3：
Method of Box and Muller / 2.3.1：
Variant of Marsaglia / 2.3.2：
Correlated Random Variables / 2.3.3：
Sequences of Numbers with Low Discrepancy / 2.4：
Monte Carlo Integration / 2.4.1：
Discrepancy / 2.4.2：
Examples of Low-Discrepancy Sequences / 2.4.3：
Numerical Integration of Stochastic Differential Equations / Chapter 3：
Approximation Error / 3.1：
Stochastic Taylor Expansion / 3.2：
Examples of Numerical Methods / 3.3：
Intermediate Values / 3.4：
Monte Carlo Simulation / 3.5：
The Basic Version / 3.5.1：
Variance Reduction / 3.5.2：
Finite Differences and Standard Options / Chapter 4：
Preparations / 4.1：
Foundations of Finite-Difference Methods / 4.2：
Difference Approximation / 4.2.1：
The Grid / 4.2.2：
Explicit Method / 4.2.3：
Stability / 4.2.4：
Implicit Method / 4.2.5：
Crank-Nicolson Method / 4.3：
Boundary Conditions / 4.4：
American Options as Free Boundary-Value Problems / 4.5：
Free Boundary-Value Problems / 4.5.1：
Black-Scholes Inequality / 4.5.2：
Obstacle Problems / 4.5.3：
Linear Complementarity for American Put Options / 4.5.4：
Computation of American Options / 4.6：
Discretization with Finite Differences / 4.6.1：
Iterative Solution / 4.6.2：
Algorithm for Calculating American Options / 4.6.3：
On the Accuracy / 4.7：
Finite-Element Methods / Chapter 5：
Weighted Residuals / 5.1：
The Principle of Weighted Residuals / 5.1.1：
Examples of Weighting Functions / 5.1.2：
Examples of Basis Functions / 5.1.3：
Galerkin Approach with Hat Functions / 5.2：
Hat Functions / 5.2.1：
A Simple Application / 5.2.2：
Application to Standard Options / 5.3：
Error Estimates / 5.4：
Classical and Weak Solutions / 5.4.1：
Approximation on Finite-Dimensional Subspaces / 5.4.2：
Cea's Lemma / 5.4.3：
Pricing of Exotic Options / Chapter 6：
Exotic Options / 6.1：
Asian Options / 6.2：
The Payoff / 6.2.1：
Modeling in the Black-Scholes Framework / 6.2.2：
Reduction to a One-Dimensional Equation / 6.2.3：
Discrete Monitoring / 6.2.4：
Numerical Aspects / 6.3：
Convection-Diffusion Problems / 6.3.1：
Von Neumann Stability Analysis / 6.3.2：
Upwind Schemes and Other Methods / 6.4：
Upwind Scheme / 6.4.1：
Dispersion / 6.4.2：
High-Resolution Methods / 6.5：
The Lax-Wendroff Method / 6.5.1：
Total Variation Diminishing / 6.5.2：
Numerical Dissipation / 6.5.3：
Appendices
Financial Derivatives / A1：
Essentials of Stochastics / A2：
The Black-Scholes Equation / A3：
Iterative Methods for Ax = b / A4：
Function Spaces / A6：
Complementary Formula / A7：
References
Index
Prefaces
Contents
Notation
18.

図書
図書
18. Algebraic geometry and arithmetic curves
Qing Liu ; translated by Reinie Erné
出版情報: Oxford : Oxford University Press, 2002  xv, 576 p. ; 24 cm
シリーズ名: Oxford graduate texts in mathematics ; 6
所蔵情報: loading…
目次情報: 続きを見る
Some topics in commutative algebra / 1：
Tensor products / 1.1：
Tensor product of modules / 1.1.1：
Right-exactness of the tensor product / 1.1.2：
Tensor product of algebras / 1.1.3：
Flatness / 1.2：
Left-exactness: flatness / 1.2.1：
Local nature of flatness / 1.2.2：
Faithful flatness / 1.2.3：
Formal completion / 1.3：
Inverse limits and completions / 1.3.1：
The Artin-Rees lemma and applications / 1.3.2：
The case of Noetherian local rings / 1.3.3：
General properties of schemes / 2：
Spectrum of a ring / 2.1：
Zariski topology / 2.1.1：
Algebraic sets / 2.1.2：
Ringed topological spaces / 2.2：
Sheaves / 2.2.1：
Schemes / 2.2.2：
Definition of schemes and examples / 2.3.1：
Morphisms of schemes / 2.3.2：
Projective schemes / 2.3.3：
Noetherian schemes, algebraic varieties / 2.3.4：
Reduced schemes and integral schemes / 2.4：
Reduced schemes / 2.4.1：
Irreducible components / 2.4.2：
Integral schemes / 2.4.3：
Dimension / 2.5：
Dimension of schemes / 2.5.1：
The case of Noetherian schemes / 2.5.2：
Dimension of algebraic varieties / 2.5.3：
Morphisms and base change / 3：
The technique of base change / 3.1：
Fibered product / 3.1.1：
Base change / 3.1.2：
Applications to algebraic varieties / 3.2：
Morphisms of finite type / 3.2.1：
Algebraic varieties and extension of the base field / 3.2.2：
Points with values in an extension of the base field / 3.2.3：
Frobenius / 3.2.4：
Some global properties of morphisms / 3.3：
Separated morphisms / 3.3.1：
Proper morphisms / 3.3.2：
Projective morphisms / 3.3.3：
Some local properties / 4：
Normal schemes / 4.1：
Normal schemes and extensions of regular functions / 4.1.1：
Normalization / 4.1.2：
Regular schemes / 4.2：
Tangent space to a scheme / 4.2.1：
Regular schemes and the Jacobian criterion / 4.2.2：
Flat morphisms and smooth morphisms / 4.3：
Flat morphisms / 4.3.1：
Etale morphisms / 4.3.2：
Smooth morphisms / 4.3.3：
Zariski's 'Main Theorem' and applications / 4.4：
Coherent sheaves and Cech cohomology / 5：
Coherent sheaves on a scheme / 5.1：
Sheaves of modules / 5.1.1：
Quasi-coherent sheaves on an affine scheme / 5.1.2：
Coherent sheaves / 5.1.3：
Quasi-coherent sheaves on a projective scheme / 5.1.4：
Cech cohomology / 5.2：
Differential modules and cohomology with values in a sheaf / 5.2.1：
Cech cohomology on a separated scheme / 5.2.2：
Higher direct image and flat base change / 5.2.3：
Cohomology of projective schemes / 5.3：
Direct image theorem / 5.3.1：
Connectedness principle / 5.3.2：
Cohomology of the fibers / 5.3.3：
Sheaves of differentials / 6：
Kahler differentials / 6.1：
Modules of relative differential forms / 6.1.1：
Sheaves of relative differentials (of degree 1) / 6.1.2：
Differential study of smooth morphisms / 6.2：
Smoothness criteria / 6.2.1：
Local structure and lifting of sections / 6.2.2：
Local complete intersection / 6.3：
Regular immersions / 6.3.1：
Local complete intersections / 6.3.2：
Duality theory / 6.4：
Determinant / 6.4.1：
Canonical sheaf / 6.4.2：
Grothendieck duality / 6.4.3：
Divisors and applications to curves / 7：
Cartier divisors / 7.1：
Meromorphic functions / 7.1.1：
Inverse image of Cartier divisors / 7.1.2：
Weil divisors / 7.2：
Cycles of codimension 1 / 7.2.1：
Van der Waerden's purity theorem / 7.2.2：
Riemann-Roch theorem / 7.3：
Degree of a divisor / 7.3.1：
Riemann-Roch for projective curves / 7.3.2：
Algebraic curves / 7.4：
Classification of curves of small genus / 7.4.1：
Hurwitz formula / 7.4.2：
Hyperelliptic curves / 7.4.3：
Group schemes and Picard varieties / 7.4.4：
Singular curves, structure of Pic[superscript 0](X) / 7.5：
Birational geometry of surfaces / 8：
Blowing-ups / 8.1：
Definition and elementary properties / 8.1.1：
Universal property of blowing-up / 8.1.2：
Blowing-ups and birational morphisms / 8.1.3：
Normalization of curves by blowing-up points / 8.1.4：
Excellent schemes / 8.2：
Universally catenary schemes and the dimension formula / 8.2.1：
Cohen-Macaulay rings / 8.2.2：
Fibered surfaces / 8.2.3：
Properties of the fibers / 8.3.1：
Valuations and birational classes of fibered surfaces / 8.3.2：
Contraction / 8.3.3：
Desingularization / 8.3.4：
Regular surfaces / 9：
Intersection theory on a regular surface / 9.1：
Local intersection / 9.1.1：
Intersection on a fibered surface / 9.1.2：
Intersection with a horizontal divisor, adjunction formula / 9.1.3：
Intersection and morphisms / 9.2：
Factorization theorem / 9.2.1：
Projection formula / 9.2.2：
Birational morphisms and Picard groups / 9.2.3：
Embedded resolutions / 9.2.4：
Minimal surfaces / 9.3：
Exceptional divisors and Castelnuovo's criterion / 9.3.1：
Relatively minimal surfaces / 9.3.2：
Existence of the minimal regular model / 9.3.3：
Minimal desingularization and minimal embedded resolution / 9.3.4：
Applications to contraction; canonical model / 9.4：
Artin's contractability criterion / 9.4.1：
Determination of the tangent spaces / 9.4.2：
Canonical models / 9.4.3：
Weierstrass models and regular models of elliptic curves / 9.4.4：
Reduction of algebraic curves / 10：
Models and reductions / 10.1：
Models of algebraic curves / 10.1.1：
Reduction / 10.1.2：
Reduction map / 10.1.3：
Graphs / 10.1.4：
Reduction of elliptic curves / 10.2：
Reduction of the minimal regular model / 10.2.1：
Neron models of elliptic curves / 10.2.2：
Potential semi-stable reduction / 10.2.3：
Stable reduction of algebraic curves / 10.3：
Stable curves / 10.3.1：
Stable reduction / 10.3.2：
Some sufficient conditions for the existence of the stable model / 10.3.3：
Deligne-Mumford theorem / 10.4：
Simplifications on the base scheme / 10.4.1：
Proof of Artin-Winters / 10.4.2：
Examples of computations of the potential stable reduction / 10.4.3：
Bibliography
Index
Some topics in commutative algebra / 1：
Tensor products / 1.1：
Tensor product of modules / 1.1.1：
19.

図書
図書
19. Nonlinear diffusion equations
Zhuoqun Wu ... [et al.]
出版情報: Singapore : World Scientific, c2001  xvii, 502 p. ; 23 cm
所蔵情報: loading…
目次情報: 続きを見る
Preface
Newtonian Filtration Equations / Chapter 1：
Introduction / 1.1：
Physical examples / 1.1.1：
Definitions of generalized solutions / 1.1.2：
Special solutions / 1.1.3：
Existence and Uniqueness of Solutions: One Dimensional Case / 1.2：
Uniqueness of solutions / 1.2.1：
Existence of solutions / 1.2.2：
Comparison theorems / 1.2.3：
Some extensions / 1.2.4：
Existence and Uniqueness of Solutions: Higher Dimensional Case / 1.3：
Comparison theorem and uniqueness of solutions / 1.3.1：
Regularity of Solutions: One Dimensional Case / 1.3.2：
Lemma / 1.4.1：
Regularity of solutions / 1.4.2：
Regularity of Solutions: Higher Dimensional Case / 1.4.3：
Generalized class B[subscript 2] / 1.5.1：
Some lemmas / 1.5.2：
Properties of functions in the generalized class B[subscript 2] / 1.5.3：
Holder continuity of solutions / 1.5.4：
Properties of the Free Boundary: One Dimensional Case / 1.6：
Finite propagation of disturbances / 1.6.1：
Localization and extinction of disturbances / 1.6.2：
Differential equation on the free boundary / 1.6.3：
Continuously differentiability of the free boundary / 1.6.4：
Some further results / 1.6.5：
Properties of the Free Boundary: Higher Dimensional Case / 1.7：
Monotonicity and Holder continuity of the free boundary / 1.7.1：
Lipschitz continuity of the free boundary / 1.7.2：
Initial Trace of Solutions / 1.7.3：
Harnack inequality / 1.8.1：
Main result / 1.8.2：
Extension of existence and uniqueness theorem / 1.8.3：
Other Problems / 1.9：
Equations with strongly nonlinear sources / 1.9.1：
Asymptotic properties of solutions / 1.9.2：
Non-Newtonian Filtration Equations / Chapter 2：
Introduction Preliminary Knowledge / 2.1：
Introduction Physical example / 2.1.1：
Basic spaces and some lemmas / 2.1.2：
Existence of Solutions / 2.1.3：
The case u[subscript 0] [set membership] C[superscript [infinity] subscript 0](R[superscript N]) or u[subscript 0] [set membership] L[superscript 1](R[superscript N]) [intersection of] L[superscript [infinity](R[superscript N]) / 2.2.1：
The case u[subscript 0] [set membership] L[superscript 1 subscript loc](R[superscript N]) / 2.2.2：
Some remarks / 2.2.3：
Harnack Inequality and the Initial Trace of Solutions / 2.3：
Local Harnack inequality / 2.3.1：
Global Harnack inequality / 2.3.2：
Initial trace of solutions / 2.3.3：
Regularity of Solutions / 2.4：
Boundedness of solutions / 2.4.1：
Boundedness of the gradient of solutions / 2.4.2：
Holder continuity of the gradient of solutions / 2.4.3：
Uniqueness of Solutions / 2.5：
Auxiliary propositions / 2.5.1：
Uniqueness theorem and its proof / 2.5.2：
Properties of the Free Boundary / 2.6：
p-Laplacian equation with strongly nonlinear sources / 2.6.1：
General Quasilinear Equations of Second Order / 2.7.2：
Weakly Degenerate Equations in One Dimension / 3.1：
Uniqueness of bounded and measurable solutions / 3.2.1：
Existence of continuous solutions / 3.2.2：
Weakly Degenerate Equations in Higher Dimension / 3.2.3：
Existence of continuous solutions for equations with two points of degeneracy / 3.3.1：
Uniqueness of BV solutions / 3.3.2：
Existence of BV solutions / 3.3.3：
Strongly Degenerate Equations in One Dimension / 3.3.4：
Definitions of solutions with discontinuity / 3.4.1：
Interior discontinuity condition / 3.4.2：
Uniqueness of BV solutions of the Cauchy problem / 3.4.3：
Formulation of the boundary value problem / 3.4.4：
Boundary discontinuity condition / 3.4.5：
Uniqueness of BV solutions of the first boundary value problem / 3.4.6：
Existence of BV solutions of the first boundary value problem / 3.4.7：
Equations with degeneracy at infinity / 3.4.8：
Properties of the curves of discontinuity / 3.4.10：
Degenerate Equations in Higher Dimension without Terms of Lower Order / 3.5：
Uniqueness of bounded and integrable solutions / 3.5.1：
A lemma on weak convergence / 3.5.2：
General Strongly Degenerate Equations in Higher Dimension / 3.5.3：
Appendix Classes BV and BV[subscript x] / 3.6.1：
Nonlinear Diffusion Equations of Higher Order / Chapter 4：
Similarity Solutions of a Fourth Order Equation / 4.1：
Definition of similarity solutions / 4.2.1：
Existence and uniqueness of global solutions of the Cauchy problem / 4.2.2：
Properties of solutions at zero points / 4.2.3：
Properties of unbounded solutions / 4.2.5：
Bounded solutions on the half line / 4.2.6：
Bounded solutions on the whole line / 4.2.7：
Properties of solutions in typical cases k = 1,2,3,4 / 4.2.8：
Behavior of similarity solutions as t [right arrow] 0[superscript +] / 4.2.9：
Equations with Double-Degeneracy / 4.3：
Weighted energy equality of solutions / 4.3.1：
Some auxiliary inequalities / 4.3.4：
Asymptotic behavior of solutions / 4.3.5：
Extinction of solutions at finite time / 4.3.7：
Nonexistence of nonnegative solutions / 4.3.8：
Infinite propagation case / 4.3.9：
Cahn-Hilliard Equation with Constant Mobility / 4.4：
Existence of classical solutions / 4.4.1：
Blowing-up of solutions / 4.4.2：
Global existence of solutions for small initial value / 4.4.3：
Cahn-Hilliard Equations with Positive Concentration Dependent Mobility / 4.5：
A modified Campanato space / 4.5.1：
Holder norm estimates for a linear problem / 4.5.2：
Zero potential case / 4.5.3：
General case / 4.5.4：
Thin Film Equation / 4.6：
Definition of generalized solutions / 4.6.1：
Approximate solutions / 4.6.2：
Nonnegativity of solutions / 4.6.3：
Zeros of nonnegative solutions / 4.6.5：
Monotonicity of the support of solutions / 4.6.6：
Cahn-Hilliard Equation with Degenerate Mobility / 4.7：
Models with degenerate mobility / 4.7.1：
Definition of physical solutions / 4.7.2：
Physical solutions / 4.7.3：
Bibliography
Preface
Newtonian Filtration Equations / Chapter 1：
Introduction / 1.1：
20.

図書
図書
20. Random walks in the quarter-plane : algebraic methods, boundary value problems and applications (: hardcover)
Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
出版情報: Berlin ; New York : Springer, c1999  xv, 156 p. ; 25 cm
シリーズ名: Applications of mathematics ; 40
所蔵情報: loading…
目次情報: 続きを見る
Introduction and History
Probabilistic Background / 1：
Markov Chains / 1.1：
Random Walks in a Quarter Plane / 1.2：
Functional Equations for the Invariant Measure / 1.3：
Foundations of the Analytic Approach / 2：
Fundamental Notions and Definitions / 2.1：
Covering Manifolds / 2.1.1：
Algebraic Functions / 2.1.2：
Elements of Galois Theory / 2.1.3：
Universal Cover and Uniformization / 2.1.4：
Abelian Differentials and Divisors / 2.1.5：
Restricting the Equation to an Algebraic Curve / 2.2：
First Insight (Algebraic Functions) / 2.2.1：
Second Insight (Algebraic Curve) / 2.2.2：
Third Insight (Factorization) / 2.2.3：
Fourth Insight (Riemann Surfaces) / 2.2.4：
The Algebraic Curve Q(x,y) = 0 / 2.3：
Branches of the Algebraic Functions on the Unit Circle / 2.3.1：
Branch Points / 2.3.2：
Galois Automorphisms and the Group of the Random Walk / 2.4：
? and ? on S / 2.4.1：
Reduction of the Main Equation to the Riemann Torus / 2.5：
Analytic Continuation of the Unknown Functions in the Genus Case / 3：
Lifting the Fundamental Equation onto the Universal Covering / 3.1：
Lifting of the Branch Points / 3.1.1：
Lifting of the Automorphisms on the Universal Covering / 3.1.2：
Analytic Continuation / 3.2：
More about Uniformization / 3.3：
The Case of a Finite Group / 4：
On the Conditions for H to be Finite / 4.1：
Explicit Conditions for Groups of Order 4 or 6 / 4.1.1：
The General Case / 4.1.2：
Rational Solutions / 4.2：
The Case N(f) = 1 / 4.2.1：
Algebraic Solutions / 4.2.2：
Final Form of the General Solution / 4.3.1：
The Problem of the Poles and Examples / 4.5：
Reversible Random Walks / 4.5.1：
Simple Examples of Nonreversible Random Walks / 4.5.1.2：
One Parameter Families / 4.5.1.3：
Two Typical Situations / 4.5.1.4：
Ergodicity Conditions / 4.5.1.5：
Proof of Lemma 4.5.2 / 4.5.1.6：
An Example of Algebraic Solution by Flatto and Hahn / 4.6：
Two Queues in Tandem / 4.7：
Solution in the Case of an Arbitrary Group / 5：
Informal Reduction to a Riemann-Hilbert-Carleman BVP / 5.1：
Introduction to BVP in the Complex Plane / 5.2：
A Bit of History / 5.2.1：
The Sokhotski-Plemelj Formulae / 5.2.2：
The Riemann Boundary Value Problem for a Closed Con- tour / 5.2.3：
The Riemann BVP for an Open Contour / 5.2.4：
The Riemann-Carleman Problem with a Shift / 5.2.5：
Further Properties of the Branches Defined by Q(x,y) = 0 / 5.3：
Index and Solution of the BVP (5.1.5) / 5.4：
Complements / 5.5：
Computation of w / 5.5.1：
An Explicit Form via the Weierstrass P-Function / 5.5.2.1：
A Differential Equation / 5.5.2.2：
An Integral Equation / 5.5.2.3：
The Genus 0 Case / 6：
Properties of the Branches / 6.1：
Case 1: <$$$> / 6.2：
Case 3: <$$$> / 6.3：
Case 4: <$$$> / 6.4：
Integral Equation / 6.4.1：
Series Representation / 6.4.2：
Uniformization / 6.4.3：
Boundary Value Problem / 6.4.4：
Case 5: <$$$> / 6.5：
Miscellanea / 7：
About Explicit Solutions / 7.1：
Asymptotics / 7.2：
Large Deviations and Stationary Probabilities / 7.2.1：
Generalized Problems and Analytic Continuation / 7.3：
Outside Probability / 7.4：
References
Index
Introduction and History
Probabilistic Background / 1：
Markov Chains / 1.1：
21.

図書
図書
21. Fields, symmetries, and quarks. 2nd, rev. and enl. ed
Ulrich Mosel
出版情報: Berlin : Springer, c1999  xiii, 310 p. ; 25 cm
シリーズ名: Texts and monographs in physics
所蔵情報: loading…
目次情報: 続きを見る
Preliminaries / Part I：
Units and Metric / 1：
Units / 1.1：
Metric and Notation / 1.2：
Fundamentals of Field Theory / Part II：
Classical Fields / 2：
Equations of Motion / 2.1：
Examples / 2.1.1：
Symmetries and Conservation Laws / 2.2：
Geometrical Space-Time Symmetries / 2.2.1：
Internal Symmetries / 2.2.2：
Free Fields and Their Quantization / 3：
Classification of Fields / 3.1：
Scalar Fields / 3.2：
Quantization of the Hermitian Scalar Field / 3.2.1：
Quantization of the Charged Scalar Field / 3.2.2：
Vector Fields / 3.3：
Massive Vector Fields / 3.3.1：
Massless Vector Fields / 3.3.2：
Fermion Fields / 3.4：
Dirac Equation / 3.4.1：
Lagrangian for Fermion Fields / 3.4.2：
Quantization ofthe Dirac Field / 3.4.3：
Massless Fermions / 3.4.4：
Neutrinos / 3.4.5：
Transition Rates in Quantum Field Theory / 3.5：
Quantum Mechanical Consistency / 3.6：
GlobalSymmetries / Part III：
Symmetries of Meson and Baryon Systems / 4：
U(1) Symmetry / 4.1：
Properties of the Group U(1) / 4.1.1：
Structure of the Nucleon Lagrangian / 4.1.2：
SU(2) Symmetry / 4.2：
Properties of the Group SU(2) / 4.2.1：
General Definitions / 4.2.2：
Application to the Pion-Nucleon System / 4.2.3：
Structure of SU(2) Multiplets / 4.2.4：
SU(3) Symmetry / 4.3：
Properties of the Group SU(3) / 4.3.1：
Structure of SU(3) Multiplets / 4.3.2：
Assignments of Hadrons to SU(3) Multiplets / 4.3.3：
SU(3) Symmetry Breaking / 4.3.4：
Quarks / 5：
Construction of SU(3) Multiplets / 5.1：
Construction of the Representation <$>3 \otimes \bar {3}<$> / 5.1.1：
Construction of the Representation 3 ⊗ 3 ⊗ 3 / 5.1.2：
State Vectors for the Multiplets / 5.2：
Tensor Algebra / 5.2.1：
Hadron Multiplets / 5.2.2：
Color Degree of Freedom / 5.3：
Chiral Symmetry / 6：
Phenomenology of β-Decay / 6.1：
Leptonic β-Decay / 6.1.1：
Semileptonic β-Decay / 6.1.2：
Current Conservation in Strong Interactions / 6.2：
Vector Current Conservation / 6.2.1：
Axial Vector Current Conservation / 6.2.2：
Chiral Symmetry Group / 6.3：
Chiral Symmetry Transformations for the Fermions / 6.3.1：
Chiral Symmetry Transformations for the Mesons / 6.3.2：
Spontaneous Global Symmetry Breaking / 7：
Goldstone Theorem / 7.1：
Goldstone Bosons / 7.1.1：
Examples of the Goldstone Mechanism / 7.2：
Spontaneous Breaking of a Global Non-Abelian Symmetry / 7.2.1：
σ-Model / 7.2.2：
Nambu-Jona-Lasinio Model / 7.2.3：
Local Gauge Symmetries / Part IV：
Gauge Field Theories / 8：
Conserved Currents in QED / 8.1：
Local Abelian Gauge Invariance / 8.2：
Non-Abelian Gauge Fields / 8.3：
Lagrangian for Non-Abelian Gauge Field Theories / 8.3.1：
Properties of Non-Abelian Gauge Field Theories / 8.3.2：
Spontaneous Symmetry Breaking in Gauge Field Theories / 9：
Higgs Mechanism / 9.1：
Spontaneous Breaking of a Local Non-Abelian Symmetry / 9.2：
Summary of the Higgs Mechanism / 9.3：
Electroweak Interaction / Part V：
Weak Interactions of Quarks and Leptons / 10：
Phenomenological Introduction / 10.1：
Strangeness Changing Weak Decays / 10.1.1：
Neutral Currents / 10.1.2：
Intermediate Vector Bosons / 10.2：
Fundamentals of a Theory of Weak Interactions / 10.3：
Electroweak Interactions of Leptons / 11：
Leptonic Multiplets and Interactions / 11.1：
Electroweak Currents / 11.1.1：
Lepton Masses / 11.2：
Electroweak Interactions / 11.3：
Generalization to Other Leptons / 11.3.1：
Parameters of the Lagrangian / 11.4：
Charged Current Experiments / 11.4.1：
Neutral Current Experiments / 11.4.2：
Electroweak Interactions of Quarks / 12：
Hadronic Multiplets / 12.1：
Hadron Masses / 12.1.1：
Electroweak Interactions of Quarks and Leptons / 13：
Lagrangian of Electroweak Interactions / 13.1：
Standard Model / 13.2：
CP Invariance of Electroweak Interactions / 14：
Kobayashi-Maskawa Matrix / 14.1：
Unitarity of the KM Matrix / 14.2：
K0 Decay and CP Violation / 14.3：
CP Invariance and the KM Matrix / 14.4：
Strong Interaction / Part VI：
Quantum Chromodynamics / 15：
Gauge Group for Strong Interactions / 15.1：
QCD Lagrangian / 15.2：
Properties of QCD / 15.3：
Scale Invariance / 15.3.1：
Chiral Invariance / 15.3.2：
Antishielding and Confinement / 15.3.3：
Deconfinement Phase Transition / 15.3.4：
Hadron Structure / Part VII：
Bag Models of Hadrons / 16：
Potential Well in the Dirac Theory / 16.1：
The MIT Bag / 16.2：
Fermions in the MIT Bag / 16.2.1：
Gluons in the MIT Bag / 16.2.2：
Hyperfine Structure of Bag States / 16.2.4：
Magnetic Moments of the Nucleon / 16.2.5：
Axial Vector Current / 16.2.6：
Chiral Symmetry in the MIT Bag / 16.2.7：
Soliton Models of Hadrons / 17：
Skyrmion Model / 17.1：
Hybrid Chiral Bag Model / 17.2：
Linear 7-Model / 17.3：
Friedberg-Lee Soliton Bag Model / 17.4：
NJL Soliton Model / 17.5：
Appendices / Part VIII：
Solutions of the Free Dirac Equation / A：
Properties of Free Dirac States / A.1：
Dirac and Majorana Fields / A.2：
Explicit Quark States for Hadrons / B：
Table of Hadron Properties / C：
Bibliography by Subject
References
Index
Preliminaries / Part I：
Units and Metric / 1：
Units / 1.1：
22.

図書
図書
22. Generalized difference methods for differential equations : numerical analysis of finite volume methods
Ronghua Li, Zhongying Chen, Wei Wu
出版情報: New York : Marcel Dekker, c2000  xv, 442 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 226
所蔵情報: loading…
目次情報: 続きを見る
Preface
Preliminaries / 1：
Sobolev Spaces / 1.1：
Smooth approximations. Fundamental lemma of variational methods / 1.1.1：
Generalized derivatives and Sobolev spaces / 1.1.2：
Imbedding and trace theorems / 1.1.3：
Finite element spaces / 1.1.4：
Interpolation error estimates in Sobolev spaces / 1.1.5：
Variational Problems and Their Approximations / 1.2：
Abstract variational form / 1.2.1：
Green's formulas and variational problems / 1.2.2：
Well-posedness of variational problems / 1.2.3：
Approximation methods. A necessary and sufficient condition for approximate-solvability / 1.2.4：
Galerkin methods / 1.2.5：
Generalized Galerkin methods / 1.2.6：
Bibliography and Comments
Two Point Boundary Value Problems / 2：
Basic Ideas of the Generalized Difference Method / 2.1：
A variational form / 2.1.1：
Generalized Galerkin variational principles / 2.1.2：
Generalized difference methods / 2.1.4：
Linear Element Difference Schemes / 2.2：
Trial and test function spaces / 2.2.1：
Difference equations / 2.2.2：
Convergence estimates / 2.2.3：
Quadratic Element Difference Schemes / 2.3：
Trial and test spaces / 2.3.1：
Convergence order estimates / 2.3.2：
Cubic Element Difference Schemes / 2.4：
Some lemmas / 2.4.1：
Existence, uniqueness and stability / 2.4.4：
Numerical examples / 2.4.5：
Estimates in L[superscript 2] and Maximum Norms / 2.5：
L[superscript 2]-estimates / 2.5.1：
Maximum norm estimates / 2.5.2：
Superconvergence / 2.6：
Optimal stress points / 2.6.1：
Superconvergence for linear element difference schemes / 2.6.2：
Superconvergence for cubic element difference schemes / 2.6.3：
Generalized Difference Methods for a Fourth Order Equation / 2.7：
Generalized difference equations / 2.7.1：
Positive definiteness of a(u[subscript h], II*[subscript h] u[subscript h]) / 2.7.2：
Second Order Elliptic Equations / 2.7.3：
Introduction / 3.1：
Generalized Difference Methods on Triangular Meshes / 3.2：
Generalized difference equation / 3.2.1：
a priori estimates / 3.2.3：
Error estimates / 3.2.4：
Generalized Difference Methods on Quadrilateral Meshes / 3.3：
Numerical example / 3.3.1：
L[superscript 2] and Maximum Norm Estimates / 3.5：
L[superscript 2] estimates / 3.6.1：
A maximum estimate and some remarks / 3.6.2：
Superconvergences / 3.7：
Weak estimate of interpolations / 3.7.1：
Superconvergence estimates / 3.7.2：
Fourth Order and Nonlinear Elliptic Equations / 4：
Mixed Generalized Difference Methods Based on Ciarlet-Raviart Variational Principle / 4.1：
Mixed generalized difference equations / 4.1.1：
Mixed Generalized Difference Methods Based on Hermann-Miyoshi Variational Principle / 4.1.2：
Numerical experiments / 4.2.1：
Nonconforming Generalized Difference Method Based on Zienkiewicz Elements / 4.3：
Variational principle / 4.3.1：
Generalized difference schemes based on Zienkiewicz elements / 4.3.2：
Error analyses / 4.3.3：
Numerical experiment / 4.3.4：
Nonconforming Generalized Difference Methods Based on Adini Elements / 4.4：
Generalized difference scheme / 4.4.1：
Error estimate / 4.4.2：
Second Order Nonlinear Elliptic Equations / 4.4.3：
Parabolic Equations / 4.5.1：
Semi-discrete Generalized Difference Schemes / 5.1：
Problem and schemes / 5.1.1：
L[superscript 2]-error estimate / 5.1.2：
H[superscript 1]-error estimate / 5.1.4：
Fully-discrete Generalized Difference Schemes / 5.2：
Fully-discrete schemes / 5.2.1：
Error estimates for backward Euler generalized difference schemes / 5.2.2：
Error estimates for Crank-Nicolson generalized difference schemes / 5.2.3：
Mass Concentration Methods / 5.3：
Construction of schemes / 5.3.1：
Error estimates for semi-discrete schemes / 5.3.2：
Error estimates for fully-discrete schemes / 5.3.3：
High Order Element Difference Schemes / 5.4：
Cubic element difference schemes for one-dimensional parabolic equations / 5.4.1：
Quadratic element difference schemes for two-dimensional parabolic equations / 5.4.2：
Generalized Difference Methods for Nonlinear Parabolic Equations / 5.5：
Hyperbolic Equations / 5.5.1：
Generalized Difference Methods for Second Order Hyperbolic Equations / 6.1：
Semi-discrete generalized difference scheme / 6.1.1：
Fully-discrete generalized difference scheme / 6.1.2：
Generalized Upwind Schemes for First Order Hyperbolic Equations / 6.2：
Generalized upwind schemes / 6.2.1：
Semi-discrete error estimates / 6.2.2：
Fully-discrete error estimates / 6.2.3：
Generalized Upwind Schemes for First Order Hyperbolic Systems / 6.3：
Integral forms / 6.3.1：
Generalized upwind difference schemes / 6.3.2：
Estimation of a bilinear form / 6.3.3：
Some practical difference schemes / 6.3.4：
A numerical example / 6.3.5：
Finite Volume Methods for Nonlinear Conservative Hyperbolic Equations / 6.4：
Convection-Dominated Diffusion Problems / 7：
One-Dimensional Characteristic Difference Schemes / 7.1：
Difference methods based on algebraic interpolations / 7.1.1：
Upwind difference schemes / 7.1.2：
Generalized Upwind Difference Schemes for Steady-state Problems / 7.2：
Construction of the difference schemes / 7.2.1：
Convergence and error estimate / 7.2.2：
Extreme value theorem and uniform convergence / 7.2.3：
Mass conservation / 7.2.4：
Generalized Upwind Difference Schemes for Nonsteady-state Problems / 7.3：
Construction of difference schemes / 7.3.1：
Highly Accurate Generalized Upwind Schemes / 7.3.2：
Upwind Schemes for Nonlinear Convection Problems / 7.4.1：
Applications / 8：
Planar Elastic Problems / 8.1：
Displacement methods / 8.1.1：
Mixed methods / 8.1.2：
Computation of Electromagnetic Fields / 8.2：
Numerical Simulation of Underground Water Pollution / 8.3：
Upwind weighted multi-element balancing method / 8.3.1：
Stokes Equation / 8.4：
Nonconforming generalized difference method / 8.4.1：
Coupled Sound-Heat Problems / 8.4.2：
Regularized Long Wave Equations / 8.6：
Semi-discrete generalized difference schemes / 8.6.1：
Fully-discrete generalized difference schemes / 8.6.2：
Hierarchical Basis Methods / 8.6.3：
Hierarchical Basis / 8.7.1：
Application to difference equations / 8.7.2：
Iteration methods / 8.7.3：
Bibliography / 8.7.4：
Index
Preface
Preliminaries / 1：
Sobolev Spaces / 1.1：
23.

図書
図書
23. Prime numbers : a computational perspective
Richard Crandall, Carl Pomerance
出版情報: New York : Springer, c2001  xv, 547 p. ; 25 cm
所蔵情報: loading…
目次情報: 続きを見る
Preface
Primes! / 1：
Problems and progress / 1.1：
Fundamental theorem and fundamental problem / 1.1.1：
Technological and algorithmic progress / 1.1.2：
The infinitude of primes / 1.1.3：
Asymptotic relations and order nomenclature / 1.1.4：
How primes are distributed / 1.1.5：
Celebrated conjectures and curiosities / 1.2：
Twin primes / 1.2.1：
Prime k-tuples and hypothesis H / 1.2.2：
The Goldbach conjecture / 1.2.3：
The convexity question / 1.2.4：
Prime-producing formulae / 1.2.5：
Primes of special form / 1.3：
Mersenne primes / 1.3.1：
Fermat numbers / 1.3.2：
Certain presumably rare primes / 1.3.3：
Analytic number theory / 1.4：
The Riemann zeta function / 1.4.1：
Computational successes / 1.4.2：
Dirichlet L-functions / 1.4.3：
Exponential sums / 1.4.4：
Smooth numbers / 1.4.5：
Exercises / 1.5：
Research problems / 1.6：
Number-Theoretical Tools / 2：
Modular arithmetic / 2.1：
Greatest common divisor and inverse / 2.1.1：
Powers / 2.1.2：
Chinese remainder theorem / 2.1.3：
Polynomial arithmetic / 2.2：
Greatest common divisor for polynomials / 2.2.1：
Finite fields / 2.2.2：
Squares and roots / 2.3：
Quadratic residues / 2.3.1：
Square roots / 2.3.2：
Finding polynomial roots / 2.3.3：
Representation by quadratic forms / 2.3.4：
Recognizing Primes and Composites / 2.4：
Trial division / 3.1：
Divisibility tests / 3.1.1：
Practical considerations / 3.1.2：
Theoretical considerations / 3.1.4：
Sieving / 3.2：
Sieving to recognize primes / 3.2.1：
Eratosthenes pseudocode / 3.2.2：
Sieving to construct a factor table / 3.2.3：
Sieving to construct complete factorizations / 3.2.4：
Sieving to recognize smooth numbers / 3.2.5：
Sieving a polynomial / 3.2.6：
Recognizing smooth numbers / 3.2.7：
Pseudoprimes / 3.4：
Fermat pseudoprimes / 3.4.1：
Carmichael numbers / 3.4.2：
Probable primes and witnesses / 3.5：
The least witness for n / 3.5.1：
Lucas pseudoprimes / 3.6：
Fibonacci and Lucas pseudoprimes / 3.6.1：
Grantham's Frobenius test / 3.6.2：
Implementing the Lucas and quadratic Frobenius tests / 3.6.3：
Theoretical considerations and stronger tests / 3.6.4：
The general Frobenius test / 3.6.5：
Counting primes / 3.7：
Combinatorial method / 3.7.1：
Analytic method / 3.7.2：
Primality Proving / 3.8：
The n - 1 test / 4.1：
The Lucas theorem and Pepin test / 4.1.1：
Partial factorization / 4.1.2：
Succinct certificates / 4.1.3：
The n + 1 test / 4.2：
The Lucas-Lehmer test / 4.2.1：
An improved n + 1 test, and a combined n[superscript 2] - 1 test / 4.2.2：
Divisors in residue classes / 4.2.3：
The finite field primality test / 4.3：
Gauss and Jacobi sums / 4.4：
Gauss sums test / 4.4.1：
Jacobi sums test / 4.4.2：
The primality test of Agrawal, Kayal, and Saxena (AKS test) / 4.5：
Primality testing with roots of unity / 4.5.1：
The complexity of Algorithm 4.5.1 / 4.5.2：
Primality testing with Gaussian periods / 4.5.3：
A quartic time primality test / 4.5.4：
Exponential Factoring Algorithms / 4.6：
Squares / 5.1：
Fermat method / 5.1.1：
Lehman method / 5.1.2：
Factor sieves / 5.1.3：
Monte Carlo methods / 5.2：
Pollard rho method for factoring / 5.2.1：
Pollard rho method for discrete logarithms / 5.2.2：
Pollard lambda method for discrete logarithms / 5.2.3：
Baby-steps, giant-steps / 5.3：
Pollard p - 1 method / 5.4：
Polynomial evaluation method / 5.5：
Binary quadratic forms / 5.6：
Quadratic form fundamentals / 5.6.1：
Factoring with quadratic form representations / 5.6.2：
Composition and the class group / 5.6.3：
Ambiguous forms and factorization / 5.6.4：
Subexponential Factoring Algorithms / 5.7：
The quadratic sieve factorization method / 6.1：
Basic QS / 6.1.1：
Basic QS: A summary / 6.1.2：
Fast matrix methods / 6.1.3：
Large prime variations / 6.1.4：
Multiple polynomials / 6.1.5：
Self initialization / 6.1.6：
Zhang's special quadratic sieve / 6.1.7：
Number field sieve / 6.2：
Basic NFS: Strategy / 6.2.1：
Basic NFS: Exponent vectors / 6.2.2：
Basic NFS: Complexity / 6.2.3：
Basic NFS: Obstructions / 6.2.4：
Basic NFS: Square roots / 6.2.5：
Basic NFS: Summary algorithm / 6.2.6：
NFS: Further considerations / 6.2.7：
Rigorous factoring / 6.3：
Index-calculus method for discrete logarithms / 6.4：
Discrete logarithms in prime finite fields / 6.4.1：
Discrete logarithms via smooth polynomials and smooth algebraic integers / 6.4.2：
Elliptic Curve Arithmetic / 6.5：
Elliptic curve fundamentals / 7.1：
Elliptic arithmetic / 7.2：
The theorems of Hasse, Deuring, and Lenstra / 7.3：
Elliptic curve method / 7.4：
Basic ECM algorithm / 7.4.1：
Optimization of ECM / 7.4.2：
Counting points on elliptic curves / 7.5：
Shanks-Mestre method / 7.5.1：
Schoof method / 7.5.2：
Atkin-Morain method / 7.5.3：
Elliptic curve primality proving (ECPP) / 7.6：
Goldwasser-Kilian primality test / 7.6.1：
Atkin-Morain primality test / 7.6.2：
Fast primality-proving via ellpitic curves (fastECPP) / 7.6.3：
The Ubiquity of Prime Numbers / 7.7：
Cryptography / 8.1：
Diffie-Hellman key exchange / 8.1.1：
RSA cryptosystem / 8.1.2：
Elliptic curve cryptosystems (ECCs) / 8.1.3：
Coin-flip protocol / 8.1.4：
Random-number generation / 8.2：
Modular methods / 8.2.1：
Quasi-Monte Carlo (qMC) methods / 8.3：
Discrepancy theory / 8.3.1：
Specific qMC sequences / 8.3.2：
Primes on Wall Street? / 8.3.3：
Diophantine analysis / 8.4：
Quantum computation / 8.5：
Intuition on quantum Turing machines (QTMs) / 8.5.1：
The Shor quantum algorithm for factoring / 8.5.2：
Curious, anecdotal, and interdisciplinary references to primes / 8.6：
Fast Algorithms for Large-Integer Arithmetic / 8.7：
Tour of "grammar-school" methods / 9.1：
Multiplication / 9.1.1：
Squaring / 9.1.2：
Div and mod / 9.1.3：
Enhancements to modular arithmetic / 9.2：
Montgomery method / 9.2.1：
Newton methods / 9.2.2：
Moduli of special form / 9.2.3：
Exponentiation / 9.3：
Basic binary ladders / 9.3.1：
Enhancements to ladders / 9.3.2：
Enhancements for gcd and inverse / 9.4：
Binary gcd algorithms / 9.4.1：
Special inversion algorithms / 9.4.2：
Recursive-gcd schemes for very large operands / 9.4.3：
Large-integer multiplication / 9.5：
Karatsuba and Toom-Cook methods / 9.5.1：
Fourier transform algorithms / 9.5.2：
Convolution theory / 9.5.3：
Discrete weighted transform (DWT) methods / 9.5.4：
Number-theoretical transform methods / 9.5.5：
Schonhage method / 9.5.6：
Nussbaumer method / 9.5.7：
Complexity of multiplication algorithms / 9.5.8：
Application to the Chinese remainder theorem / 9.5.9：
Polynomial multiplication / 9.6：
Fast polynomial inversion and remaindering / 9.6.2：
Polynomial evaluation / 9.6.3：
Book Pseudocode / 9.7：
References
Preface
Primes! / 1：
Problems and progress / 1.1：
24.

図書
図書
24. Moment theory and some inverse problems in potential theory and heat conduction
Dang Dinh Ang ... [et al.]
出版情報: Berlin ; Tokyo : Springer, c2002  viii, 183 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1792
所蔵情報: loading…
目次情報: 続きを見る
Introduction
Mathematical preliminaries / 1：
Banach spaces / 1.1：
Hilbert spaces / 1.2：
Some useful function spaces / 1.3：
Spaces of continuous functions / 1.3.1：
Spaces of integrable functions / 1.3.2：
Sobolev spaces / 1.3.3：
Analytic functions and harmonic functions / 1.4：
Fourier transform and Laplace transform / 1.5：
Regularization of moment problems by truncated expansion and by the Tikhonov method / 2：
Method of truncated expansion / 2.1：
A construction of regularized solutions / 2.1.1：
Convergence of regularized solutions and error estimates / 2.1.2：
Error estimates using eigenvalues of the Laplacian / 2.1.3：
Method of Tikhonov / 2.2：
Case 1: exact solutions in L2(Ω) / 2.2.1：
Case 2: exact solutions in Lα* (Ω), 1 < α&infinity; < 8 / 2.2.2：
Case 3: exact solutions in H1(Ω) / 2.2.3：
Notes and remarks / 2.3：
Backus-Gilbert regularization of a moment problem / 3：
Backus-Gilbert solutions and their stability / 3.1：
Definition of the Backus-Gilbert solutions / 3.2.1：
Stability of the Backus-Gilbert solutions / 3.2.2：
Regularization via Backus-Gilbert solutions / 3.3：
Definitions and notations / 3.3.1：
Main results / 3.3.2：
The Hausdorff moment problem: regularization and error estimates / 4：
Finite moment approximation of (4.1) / 4.1：
Proof of Theorem 4.1 / 4.1.1：
Proof of Theorem 4.2 / 4.1.2：
A moment problem from Laplace transform / 4.2：
Analytic functions: reconstruction and Sinc approximations / 4.3：
Reconstruction of functions in H2(U): approximation by polynomials / 5.1：
Reconstruction of an analytic function: a problem of optimal recovery / 5.2：
Cardinal series representation and approximation: reformulation of moment problems / 5.3：
Two-dimensional Sinc theory / 5.3.1：
Approximation theorems / 5.3.2：
Regularization of some inverse problems in potential theory / 6：
Analyticity of harmonic functions / 6.1：
CauchyÆs problem for the Laplace equation / 6.2：
Surface temperature determination from borehole measurements (steady case) / 6.3：
Regularization of some inverse problems in heat conduction147 / 7：
The backward heat equation / 7.1：
Surface temperature determination from borehole measurements: a two-dimensional problem / 7.2：
An inverse two-dimensional Stefan problem: identification of boundary values / 7.3：
Epilogue / 7.4：
References
Index
Introduction
Mathematical preliminaries / 1：
Banach spaces / 1.1：
25.

図書
図書
25. Curve and surface reconstruction : algorithms with mathematical analysis
Tamal K. Dey
出版情報: New York : Cambridge University Press, 2007  xiii, 214 p. ; 24 cm
シリーズ名: Cambridge monographs on applied and computational mathematics ; 23
所蔵情報: loading…
目次情報: 続きを見る
Preface
Basics / 1：
Shapes / 1.1：
Spaces and Maps / 1.1.1：
Manifolds / 1.1.2：
Complexes / 1.1.3：
Feature Size and Sampling / 1.2：
Medial Axis / 1.2.1：
Local Feature Size / 1.2.2：
Sampling / 1.2.3：
Voronoi Diagram and Delaunay Triangulation / 1.3：
Two Dimensions / 1.3.1：
Three Dimensions / 1.3.2：
Notes and Exercises / 1.4：
Exercises
Curve Reconstruction / 2：
Consequences of [epsilon]-Sampling / 2.1：
Crust / 2.2：
Algorithm / 2.2.1：
Correctness / 2.2.2：
NN-Crust / 2.3：
Surface Samples / 2.3.1：
Normals / 3.1：
Approximation of Normals / 3.1.1：
Normal Variation / 3.1.2：
Edge and Triangle Normals / 3.1.3：
Topology / 3.2：
Topological Ball Property / 3.2.1：
Voronoi Faces / 3.2.2：
Surface Reconstruction / 3.3：
Poles and Cocones / 4.1：
Cocone Triangles / 4.1.2：
Pruning / 4.1.3：
Manifold Extraction / 4.1.4：
Geometric Guarantees / 4.2：
Additional Properties / 4.2.1：
Topological Guarantee / 4.3：
The Map [nu] / 4.3.1：
Homeomorphism Proof / 4.3.2：
Undersampling / 4.4：
Samples and Boundaries / 5.1：
Boundary Sample Points / 5.1.1：
Flat Sample Points / 5.1.2：
Flatness Analysis / 5.2：
Boundary Detection / 5.3：
Justification / 5.3.1：
Reconstruction / 5.3.2：
Watertight Reconstructions / 5.4：
Power Crust / 6.1：
Definition / 6.1.1：
Proximity / 6.1.2：
Homeomorphism and Isotopy / 6.1.3：
Tight Cocone / 6.1.4：
Marking / 6.2.1：
Peeling / 6.2.2：
Experimental Results / 6.3：
Noisy Samples / 6.4：
Noise Model / 7.1：
Empty Balls / 7.2：
Normal Approximation / 7.3：
Analysis / 7.3.1：
Feature Approximation / 7.3.2：
Noise and Reconstruction / 7.4.1：
Preliminaries / 8.1：
Union of Balls / 8.2：
Topological Equivalence / 8.3：
Labeling / 8.4.1：
Implicit Surface-Based Reconstructions / 8.4.2：
Generic Approach / 9.1：
Implicit Function Properties / 9.1.1：
MLS Surfaces / 9.1.2：
Adaptive MLS Surfaces / 9.2.1：
Sampling Assumptions and Consequences / 9.3：
Influence of Samples / 9.3.1：
Surface Properties / 9.4：
Hausdorff Property / 9.4.1：
Gradient Property / 9.4.2：
Algorithm and Implementation / 9.5：
Normal and Feature Approximation / 9.5.1：
Projection / 9.5.2：
Other MLS Surfaces / 9.6：
Projection MLS / 9.6.1：
Variation / 9.6.2：
Computational Issues / 9.6.3：
Voronoi-Based Implicit Surface / 9.7：
Morse Theoretic Reconstructions / 9.8：
Morse Functions and Flows / 10.1：
Discretization / 10.2：
Vector Field / 10.2.1：
Discrete Flow / 10.2.2：
Relations to Voronoi/Delaunay Diagrams / 10.2.3：
Reconstruction with Flow Complex / 10.3：
Flow Complex Construction / 10.3.1：
Merging / 10.3.2：
Critical Point Separation / 10.3.3：
Reconstruction with a Delaunay Subcomplex / 10.4：
Distance from Delaunay Balls / 10.4.1：
Classifying and Ordering Simplices / 10.4.2：
Bibliography / 10.4.3：
Index
Preface
Basics / 1：
Shapes / 1.1：
26.

図書
図書
26. Stochastic processes for insurance and finance
Tomasz Rolski ... [et al.]
出版情報: Chichester : J. Wiley, c1999  xviii, 654 p. ; 24 cm
シリーズ名: Wiley series in probability and mathematical statistics
所蔵情報: loading…
目次情報: 続きを見る
Preface
List of Principal Notation
Concepts from Insurance and Finance / 1：
Introduction / 1.1：
The Claim Number Process / 1.2：
Renewal Processes / 1.2.1：
Mixed Poisson Processes / 1.2.2：
Some Other Models / 1.2.3：
The Claim Size Process / 1.3：
Dangerous Risks / 1.3.1：
The Aggregate Claim Amount / 1.3.2：
Comparison of Risks / 1.3.3：
Solvability of the Portfolio / 1.4：
Premiums / 1.4.1：
The Risk Reserve / 1.4.2：
Economic Environment / 1.4.3：
Reinsurance / 1.5：
Need for Reinsurance / 1.5.1：
Types of Reinsurance / 1.5.2：
Ruin Problems / 1.6：
Related Financial Topics / 1.7：
Investment of Surplus / 1.7.1：
Diffusion Processes / 1.7.2：
Equity Linked Life Insurance / 1.7.3：
Probability Distributions / 2：
Random Variables and Their Characteristics / 2.1：
Distributions of Random Variables / 2.1.1：
Basic Characteristics / 2.1.2：
Independence and Conditioning / 2.1.3：
Convolution / 2.1.4：
Transforms / 2.1.5：
Parametrized Families of Distributions / 2.2：
Discrete Distributions / 2.2.1：
Absolutely Continuous Distributions / 2.2.2：
Parametrized Distributions with Heavy Tail / 2.2.3：
Operations on Distributions / 2.2.4：
Some Special Functions / 2.2.5：
Associated Distributions / 2.3：
Distributions with Monotone Hazard Rates / 2.4：
Heavy-Tailed Distributions / 2.4.1：
Definition and Basic Properties / 2.5.1：
Subexponential Distributions / 2.5.2：
Criteria for Subexponentiality and the Class S / 2.5.3：
Pareto Mixtures of Exponentials / 2.5.4：
Detection of Heavy-Tailed Distributions / 2.6：
Large Claims / 2.6.1：
Quantile Plots / 2.6.2：
Mean Residual Hazard Function / 2.6.3：
Extreme Value Statistics / 2.6.4：
Premiums and Ordering of Risks / 3：
Premium Calculation Principles / 3.1：
Desired Properties of "Good" Premiums / 3.1.1：
Basic Premium Principles / 3.1.2：
Quantile Function: Two More Premium Principles / 3.1.3：
Ordering of Distributions / 3.2：
Concepts of Utility Theory / 3.2.1：
Stochastic Order / 3.2.2：
Stop-Loss Order / 3.2.3：
The Zero Utility Principle / 3.2.4：
Some Aspects of Reinsurance / 3.3：
Distributions of Aggregate Claim Amount / 4：
Individual and Collective Model / 4.1：
Compound Distributions / 4.2：
Definition and Elementary Properties / 4.2.1：
Three Special Cases / 4.2.2：
Some Actuarial Applications / 4.2.3：
Ordering of Compounds / 4.2.4：
The Larger Claims in the Portfolio / 4.2.5：
Claim Number Distributions / 4.3：
Classical Examples; Panjer's Recurrence Relation / 4.3.1：
Discrete Compound Poisson Distributions / 4.3.2：
Mixed Poisson Distributions / 4.3.3：
Recursive Computation Methods / 4.4：
The Individual Model: De Pril's Algorithm / 4.4.1：
The Collective Model: Panjer's Algorithm / 4.4.2：
A Continuous Version of Panjer's Algorithm / 4.4.3：
Lundberg Bounds / 4.5：
Geometric Compounds / 4.5.1：
More General Compound Distributions / 4.5.2：
Estimation of the Adjustment Coefficient / 4.5.3：
Approximation by Compound Distributions / 4.6：
The Total Variation Distance / 4.6.1：
The Compound Poisson Approximation / 4.6.2：
Homogeneous Portfolio / 4.6.3：
Higher-Order Approximations / 4.6.4：
Inverting the Fourier Transform / 4.7：
Risk Processes / 5：
Time-Dependent Risk Models / 5.1：
The Ruin Problem / 5.1.1：
Computation of the Ruin Function / 5.1.2：
A Dual Queueing Model / 5.1.3：
A Risk Model in Continuous Time / 5.1.4：
Poisson Arrival Processes / 5.2：
Homogeneous Poisson Processes / 5.2.1：
Compound Poisson Processes / 5.2.2：
Ruin Probabilities: The Compound Poisson Model / 5.3：
An Integro-Differential Equation / 5.3.1：
An Integral Equation / 5.3.2：
Laplace Transforms, Pollaczek-Khinchin Formula / 5.3.3：
Severity of Ruin / 5.3.4：
Bounds, Asymptotics and Approximations / 5.4：
The Cramer-Lundberg Approximation / 5.4.1：
Subexponential Claim Sizes / 5.4.3：
Approximation by Moment Fitting / 5.4.4：
Ordering of Ruin Functions / 5.4.5：
Numerical Evaluation of Ruin Functions / 5.5：
Finite-Horizon Ruin Probabilities / 5.6：
Deterministic Claim Sizes / 5.6.1：
Seal's Formulae / 5.6.2：
Exponential Claim Sizes / 5.6.3：
Renewal Processes and Random Walks / 6：
The Renewal Function; Delayed Renewal Processes / 6.1：
Renewal Equations and Lorden's Inequality / 6.1.3：
Key Renewal Theorem / 6.1.4：
Another Look at the Aggregate Claim Amount / 6.1.5：
Extensions and Actuarial Applications / 6.2：
Weighted Renewal Functions / 6.2.1：
A Blackwell-Type Renewal Theorem / 6.2.2：
Approximation to the Aggregate Claim Amount / 6.2.3：
Lundberg-Type Bounds / 6.2.4：
Random Walks / 6.3：
Ladder Epochs / 6.3.1：
Random Walks with and without Drift / 6.3.2：
Ladder Heights; Negative Drift / 6.3.3：
The Wiener-Hopf Factorization / 6.4：
General Representation Formulae / 6.4.1：
An Analytical Factorization; Examples / 6.4.2：
Ladder Height Distributions / 6.4.3：
Ruin Probabilities: Sparre Andersen Model / 6.5：
Formulae of Pollaczek-Khinchin Type / 6.5.1：
Compound Poisson Model with Aggregate Claims / 6.5.2：
Markov Chains / 6.5.5：
Initial Distribution and Transition Probabilities / 7.1：
Computation of the n-Step Transition Matrix / 7.1.2：
Recursive Stochastic Equations / 7.1.3：
Bonus-Malus Systems / 7.1.4：
Stationary Markov Chains / 7.2：
Long-Run Behaviour / 7.2.1：
Application of the Perron-Frobenius Theorem / 7.2.2：
Irreducibility and Aperiodicity / 7.2.3：
Stationary Initial Distributions / 7.2.4：
Markov Chains with Rewards / 7.3：
Interest and Discounting / 7.3.1：
Discounted and Undiscounted Rewards / 7.3.2：
Efficiency of Bonus-Malus Systems / 7.3.3：
Monotonicity and Stochastic Ordering / 7.4：
Monotone Transition Matrices / 7.4.1：
Comparison of Markov Chains / 7.4.2：
Application to Bonus-Malus Systems / 7.4.3：
An Actuarial Application of Branching Processes / 7.5：
Continuous-Time Markov Models / 8：
Homogeneous Markov Processes / 8.1：
Matrix Transition Function / 8.1.1：
Kolmogorov Differential Equations / 8.1.2：
An Algorithmic Approach / 8.1.3：
Monotonicity of Markov Processes / 8.1.4：
Phase-Type Distributions / 8.1.5：
Some Matrix Algebra and Calculus / 8.2.1：
Absorption Time / 8.2.2：
Operations on Phase-Type Distributions / 8.2.3：
Risk Processes with Phase-Type Distributions / 8.3：
The Compound Poisson Model / 8.3.1：
Numerical Issues / 8.3.2：
Nonhomogeneous Markov Processes / 8.4：
Construction of Nonhomogeneous Markov Processes / 8.4.1：
Application to Life and Pension Insurance / 8.4.3：
Markov Processes with Infinite State Space / 8.5：
Mixed Poisson Processes as Pure Birth Processes / 8.5.3：
The Claim Arrival Epochs / 8.5.4：
The Inter-Occurrence Times / 8.5.5：
Examples / 8.5.6：
Martingale Techniques I / 9：
Discrete-Time Martingales / 9.1：
Fair Games / 9.1.1：
Filtrations and Stopping Times / 9.1.2：
Martingales, Sub- and Supermartingales / 9.1.3：
Life-Insurance Model with Multiple Decrements / 9.1.4：
Convergence Results / 9.1.5：
Optional Sampling Theorems / 9.1.6：
Doob's Inequality / 9.1.7：
The Doob-Meyer Decomposition / 9.1.8：
Change of the Probability Measure / 9.2：
The Likelihood Ratio Martingale / 9.2.1：
Kolmogorov's Extension Theorem / 9.2.2：
Exponential Martingales for Random Walks / 9.2.3：
Simulation of Ruin Probabilities / 9.2.4：
Martingale Techniques II / 10：
Continuous-Time Martingales / 10.1：
Stochastic Processes and Filtrations / 10.1.1：
Stopping Times / 10.1.2：
Brownian Motion and Related Processes / 10.1.3：
Uniform Integrability / 10.1.5：
Some Fundamental Results / 10.2：
Ruin Probabilities and Martingales / 10.2.1：
Ruin Probabilities for Additive Processes / 10.3.1：
Law of Large Numbers for Additive Processes / 10.3.2：
An Identity for Finite-Horizon Ruin Probabilities / 10.3.4：
Piecewise Deterministic Markov Processes / 11：
Markov Processes with Continuous State Space / 11.1：
Transition Kernels / 11.1.1：
The Infinitesimal Generator / 11.1.2：
Dynkin's Formula / 11.1.3：
The Full Generator / 11.1.4：
Construction and Properties of PDMP / 11.2：
Behaviour between Jumps / 11.2.1：
The Jump Mechanism / 11.2.2：
The Generator of a PDMP / 11.2.3：
An Application to Health Insurance / 11.2.4：
The Compound Poisson Model Revisited / 11.3：
Exponential Martingales via PDMP / 11.3.1：
Cramer-Lundberg Approximation / 11.3.2：
A Stopped Risk Reserve Process / 11.3.4：
Characteristics of the Ruin Time / 11.3.5：
Compound Poisson Model in an Economic Environment / 11.4：
A Discounted Risk Reserve Process / 11.4.1：
The Adjustment Coefficient / 11.4.3：
Decreasing Economic Factor / 11.4.4：
Exponential Martingales: the Sparre Andersen Model / 11.5：
Backward Markovization Technique / 11.5.1：
Forward Markovization Technique / 11.5.3：
Point Processes / 12：
Stationary Point Processes / 12.1：
Palm Distributions and Campbell's Formula / 12.1.1：
Ergodic Theorems / 12.1.3：
Marked Point Processes / 12.1.4：
Ruin Probabilities in the Time-Stationary Model / 12.1.5：
Mixtures and Compounds of Point Processes / 12.2：
Nonhomogeneous Poisson Processes / 12.2.1：
Cox Processes / 12.2.2：
Compounds of Point Processes / 12.2.3：
Comparison of Ruin Probabilities / 12.2.4：
The Markov-Modulated Risk Model via PDMP / 12.3：
A System of Integro-Differential Equations / 12.3.1：
Law of Large Numbers / 12.3.2：
The Generator and Exponential Martingales / 12.3.3：
Periodic Risk Model / 12.3.4：
The Bjork-Grandell Model via PDMP / 12.5：
General Results / 12.5.1：
Poisson Cluster Arrival Processes / 12.6.2：
Superposition of Renewal Processes / 12.6.3：
The Markov-Modulated Risk Model / 12.6.4：
The Bjork-Grandell Risk Model / 12.6.5：
Diffusion Models / 13：
Stochastic Differential Equations / 13.1：
Stochastic Integrals and Ito's Formula / 13.1.1：
Levy's Characterization Theorem / 13.1.2：
Perturbed Risk Processes / 13.2：
Modified Ladder Heights / 13.2.1：
Other Applications to Insurance and Finance / 13.2.3：
The Black-Scholes Model / 13.3.1：
Stochastic Interest Rates in Life Insurance / 13.3.2：
Simple Interest Rate Models / 13.4：
Zero-Coupon Bonds / 13.4.1：
The Vasicek Model / 13.4.2：
The Cox-Ingersoll-Ross Model / 13.4.3：
Distribution Tables
References
Index
Preface
List of Principal Notation
Concepts from Insurance and Finance / 1：
27.

図書
図書
27. Primes of the form x[2] + ny[2] : Fermat, class field theory, and complex multiplication (: pbk)
David A. Cox
出版情報: New York : Wiley, c1989  xi, 351 p.
所蔵情報: loading…
目次情報: 続きを見る
From Fermat to Gauss
Fermat, Euler and Quadratic Reciprocity
Lagrange, Legendre and Quadratic Forms
Gauss, Composition and Genera
Cubic and Biquadratic Reciprocity
Class Field Theory
The Hilbert Class Field and p = x"2 + ny"2
The Hilbert Class Field and Genus Theory
Orders in Imaginary Quadratic Fields
Class Fields Theory and the Cebotarev Density Theorem
Ring Class Field and p = x"2 + ny"2
Complex Multiplication
Elliptic Functions and Complex Multiplication
Modular Functions and Ring Class Fields
Modular Functions and Singular j-Invariants
The Class Equation
Ellpitic Curves
References
Index
From Fermat to Gauss
Fermat, Euler and Quadratic Reciprocity
Lagrange, Legendre and Quadratic Forms
28.

図書
図書
28. Graphs on surfaces and their applications
Sergei K. Lando, Alexander K. Zvonkin ; appendix by Don B. Zagier
出版情報: Berlin ; Tokyo : Springer, c2004  xv, 455 p. ; 25 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 141 . Low-dimensional topology ; 2
所蔵情報: loading…
目次情報: 続きを見る
Introduction: What is This Book About / 0：
New Life of an Old Theory / 0.1：
Plan of the Book / 0.2：
What You Will Not Find in this Book / 0.3：
Constellations, Coverings, and Maps / 1：
Constellations / 1.1：
Ramified Coverings of the Sphere / 1.2：
First Definitions / 1.2.1：
Coverings and Fundamental Groups / 1.2.2：
Ramified Coverings of the Sphere and Constellations / 1.2.3：
Surfaces / 1.2.4：
Maps / 1.3：
Graphs Versus Maps / 1.3.1：
Maps: Topological Definition / 1.3.2：
Maps: Permutational Model / 1.3.3：
Cartographic Groups / 1.4：
Hypermaps / 1.5：
Hypermaps and Bipartite Maps / 1.5.1：
Trees / 1.5.2：
Appendix: Finite Linear Groups / 1.5.3：
Canonical Triangulation / 1.5.4：
More Than Three Permutations / 1.6：
Preimages of a Star or of a Polygon / 1.6.1：
Cacti / 1.6.2：
Preimages of a Jordan Curve / 1.6.3：
Further Discussion / 1.7：
Coverings of Surfaces of Higher Genera / 1.7.1：
Ritt's Theorem / 1.7.2：
Symmetric and Regular Constellations / 1.7.3：
Review of Riemann Surfaces / 1.8：
Dessins d'Enfants / 2：
Introduction: The Belyi Theorem / 2.1：
Plane Trees and Shabat Polynomials / 2.2：
General Theory Applied to Trees / 2.2.1：
Simple Examples / 2.2.2：
More Advanced Examples / 2.2.3：
Belyi Functions and Belyi Pairs / 2.3：
Galois Action and Its Combinatorial Invariants / 2.4：
Preliminaries / 2.4.1：
Galois Invariants / 2.4.2：
Two Theorems on Trees / 2.4.3：
Several Facets of Belyi Functions / 2.5：
A Bound of Davenport-Stothers-Zannier / 2.5.1：
Jacobi Polynomials / 2.5.2：
Fermat Curve / 2.5.3：
The abc Conjecture / 2.5.4：
Julia Sets / 2.5.5：
Pell Equation for Polynomials / 2.5.6：
Proof of the Belyi Theorem / 2.6：
The "Only If" Part of the Belyi Theorem / 2.6.1：
Comments to the Proof of the "Only If" Part / 2.6.2：
The "If", or the "Obvious" Part of the Belyi Theorem / 2.6.3：
Introduction to the Matrix Integrals Method / 3：
Model Problem: One-Face Maps / 3.1：
Gaussian Integrals / 3.2：
The Gaussian Measure on the Line / 3.2.1：
Gaussian Measures in <$>{\op R}^k<$> / 3.2.2：
Integrals of Polynomials and the Wick Formula / 3.2.3：
A Gaussian Measure on the Space of Hermitian Matrices / 3.2.4：
Matrix Integrals and Polygon Gluings / 3.2.5：
Computing Gaussian Integrals. Unitary Invariance / 3.2.6：
Computation of the Integral for One Face Gluings / 3.2.7：
Matrix Integrals for Multi-Faced Maps / 3.3：
Feynman Diagrams / 3.3.1：
The Matrix Integral for an Arbitrary Gluing / 3.3.2：
Getting Rid of Disconnected Graphs / 3.3.3：
Enumeration of Colored Graphs / 3.4：
Two-Matrix Integrals and the Ising Model / 3.4.1：
The Gauss Problem / 3.4.2：
Meanders / 3.4.3：
On Enumeration of Meanders / 3.4.4：
Computation of Matrix Integrals / 3.5：
Example: Computing the Volume of the Unitary Group / 3.5.1：
Generalized Hermite Polynomials / 3.5.2：
Planar Approximations / 3.5.3：
Korteweg-de Vries (KdV) Hierarchy for the Universal One-Matrix Model / 3.6：
Singular Behavior of Generating Functions / 3.6.1：
The Operator of Multiplication by λ in the Double Scaling Limit / 3.6.2：
The One-Matrix Model and the KdV Hierarchy / 3.6.3：
Constructing Solutions to the KdV Hierarchy from the Sato Grassmanian / 3.6.4：
Physical Interpretation / 3.7：
Mathematical Relations Between Physical Models / 3.7.1：
Feynman Path Integrals and String Theory / 3.7.2：
Quantum Field Theory Models / 3.7.3：
Other Models / 3.7.4：
Appendix / 3.8：
Generating Functions / 3.8.1：
Connected and Disconnected Objects / 3.8.2：
Logarithm of a Power Series and Wick's Formula / 3.8.3：
Geometry of Moduli Spaces of Complex Curves / 4：
Generalities on Nodal Curves and Orbifolds / 4.1：
Differentials and Nodal Curves / 4.1.1：
Quadratic Differentials / 4.1.2：
Orbifolds / 4.1.3：
Moduli Spaces of Complex Structures / 4.2：
The Deligne-Mumford Compactification / 4.3：
Combinatorial Models of the Moduli Spaces of Curves / 4.4：
Orbifold Euler Characteristic of the Moduli Spaces / 4.5：
Intersection Indices on Moduli Spaces and the String and Dilaton Equations / 4.6：
KdV Hierarchy and Witten's Conjecture / 4.7：
The Kontsevich Model / 4.8：
A Sketch of Kontsevich's Proof of Witten's Conjecture / 4.9：
The Generating Function for the Kontsevich Model / 4.9.1：
The Kontsevich Model and Intersection Theory / 4.9.2：
The Kontsevich Model and the KdV Equation / 4.9.3：
Meromorphic Functions and Embedded Graphs / 5：
The Lyashko-Looijenga Mapping and Rigid Classification of Generic Polynomials / 5.1：
The Lyashko-Looijenga Mapping / 5.1.1：
Construction of the LL Mapping on the Space of Generic Polynomials / 5.1.2：
Proof of the Lyashko-Looijenga Theorem / 5.1.3：
Rigid Classification of Nongeneric Polynomials and the Geometry of the Discriminant / 5.2：
The Discriminant in the Space of Polynomials and Its Stratification / 5.2.1：
Statement of the Enumeration Theorem / 5.2.2：
Primitive Strata / 5.2.3：
Proof of the Enumeration Theorem / 5.2.4：
Rigid Classification of Generic Meromorphic Functions and Geometry of Moduli Spaces of Curves / 5.3：
Calculations: Genus 0 and Genus 1 / 5.3.1：
Cones and Their Segre Classes / 5.3.3：
Cones of Principal Parts / 5.3.4：
Hurwitz Spaces / 5.3.5：
Completed Hurwitz Spaces and Stable Mappings / 5.3.6：
Extending the LL Mapping to Completed Hurwitz Spaces / 5.3.7：
Computing the Top Segre Class; End of the Proof / 5.3.8：
The Braid Group Action / 5.4：
Braid Groups / 5.4.1：
Braid Group Action on Cacti: Generalities / 5.4.2：
Experimental Study / 5.4.3：
Primitive and Imprimitive Monodromy Groups / 5.4.4：
Perspectives / 5.4.5：
Megamaps / 5.5：
Hurwitz Spaces of Coverings with Four Ramification Points / 5.5.1：
Representation of <$>\overline {H}<$> as a Dessin d'Enfant / 5.5.2：
Examples / 5.5.3：
Algebraic Structures Associated with Embedded Graphs / 6：
The Bialgebra of Chord Diagrams / 6.1：
Chord Diagrams and Arc Diagrams / 6.1.1：
The 4-Term Relation / 6.1.2：
Multiplying Chord Diagrams / 6.1.3：
A Bialgebra Structure / 6.1.4：
Structure Theorem for the Bialgebra <$>{\cal M}<$> / 6.1.5：
Primitive Elements of the Bialgebra of Chord Diagrams / 6.1.6：
Knot Invariants and Origins of Chord Diagrams / 6.2：
Knot Invariants and their Extension to Singular Knots / 6.2.1：
Invariants of Finite Order / 6.2.2：
Deducing 1-Term and 4-Term Relations for Invariants / 6.2.3：
Chord Diagrams of Singular Links / 6.2.4：
Weight Systems / 6.3：
A Bialgebra Structure on the Module <$>{\cal V}<$> of Vassiliev Knot Invariants / 6.3.1：
Renormalization / 6.3.2：
Vassiliev Knot Invariants and Other Knot Invariants / 6.3.3：
Constructing Weight Systems via Intersection Graphs / 6.4：
The Intersection Graph of a Chord Diagram / 6.4.1：
Tutte Functions for Graphs / 6.4.2：
The 4-Bialgebra of Graphs / 6.4.3：
The Bialgebra of Weighted Graphs / 6.4.4：
Constructing Vassiliev Invariants from 4-Invariants / 6.4.5：
Constructing Weight Systems via Lie Algebras / 6.5：
Free Associative Algebras / 6.5.1：
Universal Enveloping Algebras of Lie Algebras / 6.5.2：
Some Other Algebras of Embedded Graphs / 6.5.3：
Circle Diagrams and Open Diagrams / 6.6.1：
The Algebra of 3-Graphs / 6.6.2：
The Temperley-Lieb Algebra / 6.6.3：
Applications of the Representation Theory of Finite Groups / Don ZagierA：
Representation Theory of Finite Groups / A.1：
Irreducible Representations and Characters / A.1.1：
Frobenius's Formula / A.1.2：
Applications / A.2：
Representations of Sn and Canonical Polynomials Associated to Partitions / A.2.1：
First Application: Enumeration of Polygon Gluings / A.2.2：
Second Application: the Goulden-Jackson Formula / A.2.4：
Third Application: "Mirror Symmetry" in Dimension One / A.2.5：
References
Index
Introduction: What is This Book About / 0：
New Life of an Old Theory / 0.1：
Plan of the Book / 0.2：
29.

図書
図書
29. System control and rough paths
Terry Lyons and Zhongmin Qian
出版情報: Oxford : Clarendon, 2002  x, 216 p. ; 25 cm
シリーズ名: Oxford mathematical monographs
所蔵情報: loading…
目次情報: 続きを見る
Introduction / 1：
Background and general description / 1.1：
Controlled systems / 1.1.1：
Vector systems / 1.1.2：
Iterated integral expansions / 1.1.3：
Mathematics of rough paths / 1.2：
Lipschitz paths / 2：
Several examples / 2.1：
Integration theory / 2.2：
Equations driven by Lipschitz paths / 2.3：
Existence of solutions / 2.3.1：
Uniqueness / 2.3.2：
Existence of solutions revisited / 2.3.3：
Continuity of the Ito map / 2.3.4：
Comments and notes on Chapter 2 / 2.4：
Rough paths / 3：
Basic definitions and properties / 3.1：
The binomial inequality / 3.1.1：
Several basic results / 3.1.2：
Almost rough paths / 3.2：
Spaces of rough paths / 3.3：
Variation distances and variation topology / 3.3.1：
Young's integration theory / 3.3.2：
Elementary operations on rough paths / 3.3.3：
Comments and notes on Chapter 3 / 3.4：
Brownian rough paths / 4：
Control variation distances / 4.1：
Dyadic polygonal approximations / 4.2：
Holder's condition / 4.3：
Processes with long-time memory / 4.4：
Gaussian processes / 4.5：
Wiener processes in Banach spaces / 4.6：
Gaussian analysis / 4.6.1：
Wiener processes as geometric rough paths / 4.6.2：
Comments and notes on Chapter 4 / 4.7：
Path integration along rough paths / 5：
Lipschitz one-forms / 5.1：
Integration theory: degree two / 5.2：
Lipschitz continuity of integration / 5.3：
Ito's formula and stochastic integration / 5.4：
Ito's formula / 5.4.1：
Stochastic integration / 5.4.2：
Integration against geometric rough paths / 5.5：
Appendix of Chapter 5 / 5.6：
Banach tensor products / 5.6.1：
Differentiation, Taylor's theorem / 5.6.2：
Comments and notes on Chapter 5 / 5.7：
Universal limit theorem / 6：
Ito maps: rough paths with 2 [less than or equal] p [less than sign] 3 / 6.1：
The Picard iteration / 6.2.1：
Basic estimates / 6.2.2：
Lipschitz continuity / 6.2.3：
Continuity theorem / 6.2.4：
Flows of diffeomorphisms / 6.2.6：
The Ito map: geometric rough paths / 6.3：
Comments and notes on Chapter 6 / 6.4：
Vector fields and flow equations / 7：
Smoothness of Ito maps / 7.1：
Ito's vector fields / 7.2：
Flows of Ito vector fields / 7.3：
Appendix: Driver's flow equation / 7.4：
Comments and notes on Chapter 7 / 7.5：
Bibliography
Index
Introduction / 1：
Background and general description / 1.1：
Controlled systems / 1.1.1：
30.

図書
図書
30. A primer of multivariate statistics
[by] Richard J. Harris
出版情報: New York : Academic Press, c1975  xiv, 332 p. ; 24 cm
所蔵情報: loading…
目次情報: 続きを見る
The Forest before the Trees / 1：
Why Statistics? / 1.0：
Statistics as a Form of Social Control / 1.01：
Objections to Null Hypothesis Significance Testing / 1.02：
Should Significance Tests be Banned? / 1.03：
Math Modeling's the Ultimate Answer / 1.04：
Some Recent Developments in Univariate Statistics / 1.05：
Why Multivariate Statistics? / 1.1：
Bonferroni Adjustment: An Alternative to Multivariate Statistics / 1.1.1：
Why Isn't Bonferroni Adjustment Enough? / 1.1.2：
A Heuristic Survey of Statistical Techniques / 1.2：
Student's t test / 1.2.1：
One-Way Analysis of Variance / 1.2.2：
Hotelling's T[superscript 2] / 1.2.3：
One-Way Multivariate Analysis of Variance / 1.2.4：
Higher Order Analysis of Variance / 1.2.5：
Higher Order Manova / 1.2.6：
Pearson r and Bivariate Regression / 1.2.7：
Multiple Correlation and Regression / 1.2.8：
Path Analysis / 1.2.9：
Canonical Correlation / 1.2.10：
Analysis of Covariance / 1.2.11：
Principal Component Analysis / 1.2.12：
Factor Analysis / 1.2.13：
Structural Equation Modeling / 1.2.14：
Learning to Use Multivariate Statistics / 1.3：
A Taxonomy of Linear Combinatons / 1.3.1：
Why the Rest of the Book? / 1.3.2：
Quiz 1 See How Much You Know after Reading Just One Chapter!
Sample Answers to Quiz 1
Multiple Regression: Predicting One Variable from Many / 2：
Data Set 1
The Model / 2.1：
Choosing Weights / 2.2：
Least Squares Criterion / 2.2.1：
Maximum Correlation Criterion / 2.2.2：
The Utility of Matrix Algebra / 2.2.3：
Independence of Irrelevant Parameters / 2.2.4：
Relating the Sample Equation to the Population Equation / 2.3：
R[subscript x] versus S[subscript x] versus x'x as the Basis for MRA / 2.3.1：
Specific Comparisons / 2.3.2：
Illustrating Significance Tests / 2.3.3：
Stepwise Multiple Regression Analysis / 2.3.4：
Computer Programs for Multiple Regression / 2.4：
Computer Logic and Organization / 2.4.1：
Sage Advice on Use of Computer Programs / 2.4.2：
Computerized Multiple Regression Analysis / 2.4.3：
Some General Properties of Covariance Matrices / 2.5：
Measuring the Importance of the Contribution of a Single Variable / 2.6：
Anova via MRA / 2.7：
Alternatives to the Least-Squares Criterion / 2.8：
Path analytic Terminology / 2.9：
Preconditions for Path Analysis / 2.9.2：
Estimating and Testing Path coefficients / 2.9.3：
Decomposition of Correlations into Components / 2.9.4：
Overall Test of Goodness of fit / 2.9.5：
Examples / 2.9.6：
Some Path-Analysis References / 2.9.7：
Demonstration Problem
Answers
Some Real Data and a Quiz Thereon
Path Analysis Problem
Answers to Path Analysis Problem
Hotelling's T[superscript 2]: Tests on One or Two Mean Vectors / 3：
Single-Sample t and T[superscript 2] / 3.1：
Linearly Related Outcome Variables / 3.2：
Two-Sample t and T[superscript 2] / 3.3：
Profile Analysis / 3.4：
Discriminant Analysis / 3.5：
Relationship between T[superscript 2] and MRA / 3.6：
Assumptions Underlying T[superscript 2] / 3.7：
The Assumption of Equal Covariance Matrices / 3.7.1：
Known Covariance Matrix / 3.7.2：
The Assumption of Multivariate Normality / 3.7.3：
Analyzing Repeated-Measures Designs via T[superscript 2] / 3.8：
Single-Symbol Expressions for Simple Cases / 3.9：
Computerized T[superscript 2] / 3.10：
Single-Sample and Two-Sample T[superscript 2] / 3.10.1：
Within-Subjects Anova / 3.10.2：
Demonstration Problems
Multivariate Analysis of Variance: Differences Among Several Groups on Several Measures / 4：
One-Way (Univariate) Analysis of Variance / 4.1：
The Overall Test / 4.1.1：
Multiple Profile Analysis / 4.1.2：
Multiple Discriminant Analysis / 4.4：
Greatest Characteristic Roots versus Multiple-Root Tests in Manova / 4.5：
"Protected" Univariate Tests / 4.5.1：
Simulataneous Test Procedures and Union Intersection / 4.5.2：
Invalidity of Partitioned-U Tests of Individual Roots / 4.5.3：
Simplified Coefficients as a Solution to the Robustness Problem / 4.5.4：
Finite-Intersection Tests / 4.5.5：
Simple Cases of Manova / 4.6：
Higher Order Anova: Interactions / 4.7：
Within-Subject Univariate Anova Versus Manova / 4.8：
Computerized Manova / 4.10：
Generic Setup for SPSS MANOVA / 4.10.1：
Supplementary Computations / 4.10.2：
Pointing and Clicking to a Manova on SPSS PC / 4.10.3：
Generic Setup for SAS PROC GLM / 4.10.4：
Canonical Correlation: Relationships Between Two Sets of Variables / 5：
Formulae for Computing Canonical Rs / 5.1：
Heuristic Justification of Canonical Formulae / 5.1.1：
Simple Cases of Canonical Correlations / 5.1.2：
Example of a Canonical Analysis / 5.1.3：
Relationships to Other Statistical Techniques / 5.2：
Likelihood-Ratio Tests of Relationships between Sets of Variables / 5.3：
Generalization and Specialization of Canonical Analysis / 5.4：
Testing the Independence of m Sets of Variables / 5.4.1：
Repeated-Battery Canona / 5.4.2：
Rotation of Canonical Variates / 5.4.3：
The Redundancy Coefficient / 5.4.4：
What's Missing from Canonical Analysis? / 5.4.5：
Computerized Canonical Correlation / 5.5：
Matrix-Manipulation Systems / 5.5.1：
SAS PROC CANCORR / 5.5.2：
Canona via SPSS MANOVA / 5.5.3.：
SPSS Canona From Correlation Matrix: Be Careful / 5.5.4：
Demonstration Problems and Some Real Data Employing Canonical Correlation
Principal Component Analysis: Relationships Within a Single Set of Variables / 6：
Definition of Principal Components / 6.1：
Terminology and Notation in PCA and FA / 6.1.1：
Scalar Formulae for Simple Cases of PCA / 6.1.2：
Computerized PCA / 6.1.3：
Additional Unique Properties (AUPs) of PCs / 6.1.4：
Interpretation of Principal Components / 6.2：
Uses of Principal Components / 6.3：
Uncorrelated Contributions / 6.3.1：
Computational Convenience / 6.3.2：
Principal Component Analysis as a Means of Handling Linear Dependence / 6.3.3：
Examples of PCA / 6.3.4：
Quantifying Goodness of Interpretation of Components / 6.3.5：
Significance Tests for Principal Components / 6.4：
Sampling Properties of Covariance-Based PCs / 6.4.1：
Sampling Properties of Correlation-Based PCs / 6.4.2：
Rotation of Principal Components / 6.5：
Basic Formulae for Rotation / 6.5.1：
Objective Criteria for Rotation / 6.5.2：
Examples of Rotated PCs / 6.5.3：
Individual Scores on Rotated PCs / 6.5.4：
Uncorrelated-Components Versus Orthogonal-Profiles Rotation / 6.5.5：
Factor Analysis: The Search for Structure / 7：
Communalities / 7.1：
Theoretical Solution / 7.2.1：
Empirical Approximations / 7.2.2：
Iterative Procedure / 7.2.3：
Is the Squared Multiple Correlation the True Communality? / 7.2.4：
Factor Analysis Procedures Requiring Communality Estimates / 7.3：
Principal Factor Analysis / 7.3.1：
Triangular (Choleski) Decomposition / 7.3.2：
Centroid Analysis / 7.3.3：
Methods Requiring Estimate of Number of Factors / 7.4：
Other Approaches to Factor Analysis / 7.5：
Factor Loadings versus Factor Scores / 7.6：
Factor Score Indeterminacy / 7.6.1：
Relative Validities of Loadings-Derived versus Scoring-Coefficient-Derived Factor Interpretations / 7.6.2：
Regression-Based Interpretation of Factors is Still a Hard Sell / 7.6.3：
Relative Merits of Principal Component Analysis versus Factor Analysis / 7.7：
Similarity of Factor Scoring Coefficients / 7.7.1：
Bias in Estimates of Factor Loadings / 7.7.2：
Computerized Exploratory Factor Analysis / 7.8：
Confirmatory Factor Analysis / 7.9：
Sas Proc Calis / 7.9.1：
The Forest Revisited / 8：
Scales of Measurement and Multivariate Statistics / 8.1：
Effects of Violations of Distributional Assumptions in Multivariate Analysis / 8.2：
Nonlinear Relationships in Multivariate Statistics / 8.3：
The Multivariate General Linear Hypothesis / 8.4：
General Approach and Examples / 8.5：
SEM Is Not a General Model for Multivariate Statistics / 8.5.2：
Other User-Friendly SEM Programs / 8.5.3：
Where to Go from Here / 8.6：
Summing Up / 8.7：
Finding Maxima and Minima of Polynomials / Digression 1：
Derivatives and Slopes / D1.1：
Optimization Subject to Constraints / D1.2：
Matrix Algebra / Digression 2：
Basic Notation / D2.1：
Linear Combinations of Matrices / D2.2：
Multiplication of Matrices / D2.3：
Permissible Manipulations / D2.4：
Inverses / D2.5：
Determinants / D2.6：
Some Handy Formulae for Inverses and Determinants in Simple Cases / D2.7：
Rank / D2.8：
Matrix Calculus / D2.9：
Partitioned Matrices / D2.10：
Characteristic Roots and Vectors / D2.11：
Solution of Homogeneous Systems of Equations / D2.12：
Solution of Cubic Equations / Digression 3：
Statistical Tables / Appendix A：
(Why omitted from this edition) / A.1 - A.4：
Greatest Characteristic Root Distribution / A.5：
Computer Programs Available from the Author / Appendix B：
cvinter: p values and Critical Values for Univariate Statistics / B.1：
gcrinter: Critical Values for the Greatest Characteristic Root (g.c.r.) Distribution / B.2：
Derivations / Appendix C：
Per-Experiment and Experimentwise Error Rates for Bonferroni-Adjusted Tests / Derivation 1.1：
Scalar Formulae for MRA with One, Two, and Three Predictors / Derivation 2.1：
Coefficients That Minimize Error Also Maximize Correlation / Derivation 2.2：
Maximizing r via Matrix Algebra / Derivation 2.3：
Variances of b[subscript j]s and of Linear Combinations Thereof / Derivation 2.4：
Drop in R[superscript 2] = b[superscript 2][subscript j](1 - [characters not reproducible]) / Derivation 2.6：
MRA on Group-Membership Variables Yields Same F As Anova / Derivation 2.7：
Unweighted Means and Least-Squares Anova Are Identical in the 2[superscript n] Design / Derivation 2.8：
T[superscript 2] and Associated Discriminant Function / Derivation 3.1：
Single-Sample T[superscript 2]
Two-Sample T[superscript 2]
Two-Sample t Versus Pearson r With Group-Membership Variables / Derivation 3.2：
Single-Sample t Test versus "Raw-Score" r[subscript xy]
T[superscript 2] Versus MRA
Maximizing F(a) in Manova / Derivation 4.1：
Canonical Correlation and Canonical Variates / Derivation 5.1：
Canonical Correlation as "Mutual Regression Analysis" / Derivation 5.2：
Relationship between Canonical Analysis and Manova / Derivation 5.3：
Principal Components / Derivation 6.1：
PC Coefficients Define Both Components in Terms of Xs and Xs in Terms of PCs / Derivation 6.2：
What Does Rotation of Loadings Do to Coefficients? / Derivation 6.3：
Near Equivalence of PCA and Equal-Communalities PFA / Derivation 7.1：
References
Index
The Forest before the Trees / 1：
Why Statistics? / 1.0：
Statistics as a Form of Social Control / 1.01：
31.

図書
図書
31. Numerical bifurcation analysis for reaction-diffusion equations
Zhen Mei
出版情報: Berlin : Springer, c2000  xiv, 414 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; 28
所蔵情報: loading…
目次情報: 続きを見る
Reaction-Diffusion Equations / 1：
Introduction / 1.1：
Bifurcations and Pattern Formations / 1.2：
Boundary Conditions / 1.3：
Continuation Methods / 2：
Parameterization of Solution Curves / 2.1：
Natural parameterization / 2.1.1：
Parameterization with arclength / 2.1.2：
Parameterization with pseudo-arclength / 2.1.3：
Local Parameterization of Solution Manifolds / 2.2：
Predictor-Corrector Methods / 2.3：
Euler-Newton method / 2.3.1：
A continuation-Lanczos algorithm / 2.3.2：
A continuation-Arnoldi algorithm / 2.3.3：
Computation of Multi-Dimensional Solution Manifolds / 2.4：
Detecting and Computing Bifurcation Points / 3：
Generic Bifurcation Points / 3.1：
One-parameter problems / 3.1.1：
Two-parameter problems / 3.1.2：
Test Functions / 3.2：
Test functions for turning points / 3.2.1：
Test functions for simple bifurcation point / 3.2.2：
Test functions for Hopf bifurcations / 3.2.3：
Minimally extended systems / 3.2.4：
Computing Simple Bifurcation Points / 3.3：
Simple bifurcation points / 3.3.1：
Extended systems / 3.3.2：
Newton-like methods / 3.3.3：
Rank-1 corrections for sparse problems / 3.3.4：
A numerical example / 3.3.5：
Computing Hopf Bifurcation Points / 3.4：
Hopf points / 3.4.1：
Newton method for extended systems / 3.4.2：
Branch Switching at Simple Bifurcation Points / 4：
Structure of Bifurcating Solution Branches / 4.1：
Behavior of the Linearized Operator / 4.2：
Euler-Newton Continuation / 4.3：
Branch Switching via Regularized Systems / 4.4：
Other Branch Switching Techniques / 4.5：
Bifurcation Problems with Symmetry / 5：
Basic Group Concepts / 5.1：
Equivariant Bifurcation Problems / 5.2：
Equivariant Branching Lemma / 5.3：
A Semi-linear Elliptic PDE on the Unite Square / 5.4：
Liapunov-Schmidt Method / 6：
Liapunov-Schmidt Reduction / 6.1：
Equivariance of the Reduced Bifurcation Equations / 6.2：
Derivatives and Taylor Expansion / 6.3：
Equivalence, Determinacy and Stability / 6.4：
Simple Bifurcation Points / 6.5：
Truncated Liapunov-Schmidt Method / 6.6：
Branch Switching at Multiple Bifurcation Points / 6.7：
Branch switching with prescribed tangents / 6.7.1：
Branch switching with scaling techniques / 6.7.2：
Corank-2 Problems with Dm-symmetry / 6.8：
Semilinear elliptic PDEs on a square / 6.8.1：
A semilinear elliptic PDE on a hexagon / 6.8.2：
Center Manifold Theory / 7：
Center Manifolds and Their Properties / 7.1：
Approximation of Center Manifolds / 7.2：
Symmetry and Normal Form / 7.3：
Hopf bifurcations / 7.4.1：
Waves in Reaction-Diffusion Equations / 7.5：
Oscillating waves / 7.5.1：
Long waves / 7.5.2：
Long time and large spatial behavior / 7.5.3：
A Bifurcation Function for Homoclinic Orbits / 8：
A Bifurcation Function / 8.1：
Approximation of Homoclinic Orbits / 8.2：
Solving the Adjoint Variational Problem / 8.3：
Preserving the inner product / 8.3.1：
Systems with continuous symmetries / 8.3.2：
The Approximate Bifurcation Function / 8.4：
Examples / 8.5：
Freire et al.'s circuit / 8.5.1：
Kuramoto-Sivashinsky equation / 8.5.2：
One-Dimensional Reaction-Diffusion Equations / 9：
Linear Stability Analysis / 9.1：
The general system / 9.2.1：
The Brusselator equations / 9.2.2：
Solution Branches at Double Bifurcations / 9.3：
The reflection symmetry and its induced action / 9.3.1：
(k,m) = (odd, odd) or (odd, even) / 9.3.2：
(k,m) = (even, even) / 9.3.3：
Central Difference Approximations / 9.3.4：
General systems / 9.4.1：
Numerical Results for the Brusselator Equations / 9.4.2：
The length <$>\ell = 1<$>, diffusion rates d1 = 1, d2 = 2 / 9.5.1：
The length <$>\ell = 10<$>, diffusion rates d1 = 1, d2 = 2 / 9.5.2：
Reaction-Diffusion Equations on a Square / 10：
D4-Symmetry / 10.1：
Eigenpairs of the Laplacian / 10.2：
Bifurcation Points / 10.3：
Steady state bifurcation points / 10.4.1：
Hopf bifurcation points / 10.4.2：
Mode Interactions / 10.5：
Steady/steady state mode interactions / 10.5.1：
Hopf/steady state mode interactions / 10.5.2：
Hopf/Hopf mode interactions / 10.5.3：
Kernels of Du G0 and <$>(D_u G_0)^{\ast}<$> / 10.6：
Simple and Double Bifurcations / 10.7：
Simple bifurcations / 10.8.1：
Double bifurcations induced by the D4 symmetries / 10.8.2：
Normal Forms for Hopf Bifurcations / 11：
Domain Symmetries and Their Extensions / 11.1：
Actions of D4 on the Center Eigenspace / 11.3：
The Normal Form / 11.4：
Analysis of the Normal Form / 11.5：
Odd parity / 11.5.1：
Even parity / 11.5.2：
Brusselator Equations / 11.6：
Linear stability analysis / 11.6.1：
Bifurcation scenario / 11.6.2：
Nonlinear degeneracy / 11.6.3：
Steady/Steady State Mode Interactions / 12：
Induced Actions / 12.1：
Interaction of Two D4-Modes / 12.2：
Interaction of two even modes / 12.2.1：
Interaction of an even mode with an odd mode / 12.2.2：
Interaction of two odd modes / 12.2.3：
Mode Interactions of Three Modes / 12.3：
Induced actions / 12.3.1：
Interactions of the modes (m,n,k) =(even, odd, odd) / 12.3.2：
Interactions of the modes (m,n,k) =(even, odd, even) / 12.3.3：
Interactions of Four Modes / 12.4：
Interactions of the modes (m, n, k, l) = (even, odd, even, odd) / 12.4.1：
Interactions of the modes (m, n, k, l) = (even, even, even, odd) / 12.4.2：
Reactions with Z2-Symmetry / 12.5：
Hopf/Steady State Mode Interactions / 13：
Normal Forms / 13.1：
Bifurcation Scenario / 13.4：
Calculations of the Normal Form / 13.5：
Homotopy of Boundary Conditions / 14：
Homotopy of boundary conditions / 14.1：
Boundary conditions for different components / 14.1.2：
Mixed boundary conditions along the sides / 14.1.3：
Dynamical boundary conditions / 14.1.4：
A Brief Review of Sturm-Liouville Theory / 14.2：
Laplacian with Robin Boundary Conditions / 14.3：
Variational Form / 14.4：
Continuity of Solutions along the Homotopy / 14.5：
Neumann and Dirichlet Problems / 14.6：
Properties of Eigenvalues / 14.7：
One-dimensional problems / 14.7.1：
Two-dimensional problems / 14.7.2：
Bifurcations along a Homotopy of BCs / 15：
Stability and Symmetries / 15.1：
Variations of Bifurcations along the Homotopy / 15.3：
(κ1, κ2) = (odd, even) or (even, odd) / 15.4.1：
(κ1, κ2) = (odd, odd) / 15.4.2：
(κ1, κ2) = (even, even) / 15.4.3：
A Numerical Example / 15.5：
Discretization with finite difference methods / 15.5.1：
Homotopy of (κ1(μ), κ2(μ)) from (1,2) to (2,3) / 15.5.2：
Homotopy of (κl(μ), κ2(μ)) from (1,3) to (2,4) / 15.5.3：
Homotopy of (κ1(μ), κ2(μ)) from (2,4) to (3,5) / 15.5.4：
Forced Symmetry-Breaking in BCs / 15.6：
Bifurcation points / 15.6.1：
Bifurcation scenarios / 15.6.2：
A Mode Interaction on a Homotopy of BCs / 16：
Symmetries and Normal Forms / 16.1：
Generic Bifurcation Behavior / 16.3：
Solutions with the modes φ1, φ2 / 16.3.1：
Pure φ3-mode solutions / 16.3.2：
Interactions of three modes / 16.3.3：
Scales of Solution Branches / 16.4：
Secondary Bifurcations / 16.5：
Secondary Hopf bifurcations / 16.5.1：
Truncated Bifurcation Equations / 16.6：
Derivatives with respect to homotopy parameter / 16.6.1：
Reduced Stability / 16.7：
Stability of solution branches at (0, λ1(μ),μ) / 16.7.1：
Stability of solution branches at (0, λ2(μ), μ) / 16.7.2：
Stability of solution branches at mode interaction / 16.7.3：
Solution branches along (0; λ1(μ),μ) / 16.8：
Solution branches along (0, λ2(μ),μ) / 16.8.2：
Mode interaction / 16.8.3：
Switching and continuation of solution branches / 16.8.4：
List of Figures
List of Tables
Bibliography
Index
Reaction-Diffusion Equations / 1：
Introduction / 1.1：
Bifurcations and Pattern Formations / 1.2：
32.

図書
図書
32. Financial and actuarial statistics : an introduction
Dale S. Borowiak
出版情報: New York : M. Dekker, c2003  xi, 330 p. ; 24 cm
シリーズ名: Statistics : textbooks and monographs ; v. 167
所蔵情報: loading…
目次情報: 続きを見る
Preface
Statistical Concepts / 1：
Probability / 1.1：
Random Variables / 1.2：
Discrete Random Variables / 1.2.1：
Continuous Random Variables / 1.2.2：
Mixed Random Variables / 1.2.3：
Expectations / 1.3：
Moment Generating Function / 1.4：
Survival Functions / 1.5：
Conditional Distributions / 1.6：
Joint Distributions / 1.7：
Sampling Distributions and Estimation / 1.8：
Point Estimation / 1.8.1：
Percentiles and Prediction Intervals / 1.8.2：
Parameter Interval Estimation / 1.8.3：
Aggregate Sums of Independent Random Variables / 1.9：
Order Statistics / 1.10：
Approximating Aggregate Sums / 1.11：
Central Limit Theorem / 1.11.1：
Haldane Type A Approximation / 1.11.2：
Saddlepoint Approximation / 1.11.3：
Compound Random Variables / 1.12：
Expectations of Compound Variables / 1.12.1：
Limiting Distributions for Compound Variables / 1.12.2：
Regression Modeling / 1.13：
Least Squares Estimation / 1.13.1：
Regression Model Based Inference / 1.13.2：
Autoregressive Systems / 1.14：
Problems
Financial Computational Models / 2：
Fixed Financial Rate Models / 2.1：
Financial Rate Based Calculations / 2.1.1：
General Period Discrete Rate Models / 2.1.2：
Continuous Rate Models / 2.1.3：
Fixed Rate Annuities / 2.2：
Discrete Annuity Models / 2.2.1：
Continuous Annuity Models / 2.2.2：
Stochastic Rate Models / 2.3：
Discrete Stochastic Rate Model / 2.3.1：
Continuous Stochastic Rate Models / 2.3.2：
Discrete Stochastic Annuity Models / 2.3.3：
Continuous Stochastic Annuity Models / 2.3.4：
Deterministic Status Models / 3：
Basic Loss Model / 3.1：
Deterministic Loss Models / 3.1.1：
Stochastic Loss Criterion / 3.1.2：
Risk Criteria / 3.2.1：
Percentile Criteria / 3.2.2：
Single Risk Models / 3.3：
Insurance Pricing / 3.3.1：
Investment Pricing / 3.3.2：
Options Pricing / 3.3.3：
Short Time Period Collective Aggregate Models / 3.4：
Fixed Number of Variables / 3.4.1：
Stochastic Number of Variables / 3.4.2：
Aggregate Stop - Loss Insurance and Dividends / 3.4.3：
Stochastic Surplus Model / 3.5：
Future Lifetime Random Variable / 4：
Continuous Future Lifetime / 4.1：
Discrete Future Lifetime / 4.2：
Force of Mortality / 4.3：
Fractional Ages / 4.4：
Multiple Future Lifetimes / 4.5：
Joint Life Status / 4.5.1：
Last Survivor Status / 4.5.2：
General Contingent Status / 4.5.3：
Select Future Lifetimes / 4.6：
Multiple Decrement Lifetimes / 4.7：
Continuous Multiple Decrements / 4.7.1：
Forces of Mortality / 4.7.2：
Discrete Multiple Decrements / 4.7.3：
Single Decrement Probabilities / 4.7.4：
Uniformly Distributed Single Decrement Rates / 4.7.5：
Single Decrement Probability Bounds / 4.7.6：
Future Lifetime Models and Tables / 5：
Survivorship Groups / 5.1：
Life Models and Tables / 5.2：
Estimated Life Models and Tables / 5.3：
Life Models and Life Table Parameters / 5.4：
Population Parameters / 5.4.1：
Aggregate Parameters / 5.4.2：
Fractional Age Adjustments / 5.4.3：
Multiple Life Tables and Parameters / 5.5：
Select and Ultimate Life Tables / 5.6：
Multiple Decrement Tables / 5.7：
Multiple Decrement Life Tables / 5.7.1：
Single Decrement Life Tables / 5.7.2：
Stochastic Status Models / 6：
Stochastic Present Value Functions / 6.1：
Risk Evaluations / 6.2：
Continuous Risk Calculations / 6.2.1：
Discrete Risk Calculations / 6.2.2：
Mixed Risk Calculations / 6.2.3：
Percentile Evaluations / 6.3：
Life Insurance / 6.4：
Types of Unit Benefit Life Insurance / 6.4.1：
Life Annuities / 6.5：
Types of Unit Payment Life Annuities / 6.5.1：
Apportionable Annuities / 6.5.2：
Relating Risk Calculations / 6.6：
Relations Among Insurance Expectations / 6.6.1：
Relations Among Insurance and Annuity Expectations / 6.6.2：
Relations Among Annuity Expectations / 6.6.3：
Life Table Applications / 6.7：
Insurance Premiums / 6.8：
Unit Benefit Premium Notation / 6.8.1：
Reserves / 6.9：
Unit Benefit Reserves Notations / 6.9.1：
Relations Among Reserves Calculations / 6.9.2：
Survivorship Group Approach to Reserve Calculations / 6.9.3：
General Time Period Models / 6.10：
General Period Expectations / 6.10.1：
Relations Among General Period Expectations / 6.10.2：
Multiple Decrement Computations / 6.11：
Pension Plans / 6.12：
Multiple Decrement Benefits / 6.12.1：
Pension Contributions / 6.12.2：
Future Salary Based Benefits and Contributions / 6.12.3：
Yearly Based Retirement Benefits / 6.12.4：
Models Including Expenses / 6.13：
Scenario and Simulation Testing / 7：
Fixed Rate Deterministic Status Models / 7.1：
Simulation Methods / 7.2：
Bootstrap Resampling / 7.2.1：
Simulation Sampling / 7.2.2：
Simulation Inference on Deterministic Status Models / 7.3：
Simulation Inference on Collective Aggregate Models / 7.4：
Simulation Inference on Stochastic Status Models / 7.5：
Investment Pricing Models / 7.5.1：
Stochastic Surplus Models / 7.5.2：
Further Directions in Resampling / 7.6：
Further Statistical Considerations / 8：
Statistical Investigations / 8.1：
Mortality Adjustment Factors / 8.2：
Linear Acceleration Factors / 8.2.1：
Mean Acceleration Factors / 8.2.2：
Survival Acceleration Factors / 8.2.3：
Mortality Trend Modeling / 8.3：
Standard Normal Tables / Appendix：
References
Index
Preface
Statistical Concepts / 1：
Probability / 1.1：
33.

図書
図書
33. Special functions : a unified theory based on singularities (: hbk)
Sergei Yu. Slavyanov and Wolfgang Lay ; with a foreword by Alfred Seeger
出版情報: Oxford ; New York : Oxford University Press, 2000  xvi, 293 p. ; 25 cm
シリーズ名: Oxford mathematical monographs
Oxford science publications
所蔵情報: loading…
目次情報: 続きを見る
Linear second-order ODEs with polynomial coefficients / 1：
Regular singularities and Fuchsian equations / 1.1：
Regular and Fuchsian singularities / 1.1.1：
Fuchsian equations and their transformations / 1.1.2：
Characteristic exponents / 1.1.3：
Frobenius solutions / 1.1.4：
Irregular singularities and confluent equations / 1.2：
The s-rank of a singularity / 1.2.1：
Confluent and reduced confluent equations / 1.2.2：
The s-homotopic transformation / 1.2.3：
Asymptotic solutions at irregular singularities / 1.2.4：
Canonical forms / 1.2.5：
A generalization of Fuchs's theorem / 1.2.6：
Confluence and reduction processes / 1.3：
Strong and weak confluence. A confluence theorem / 1.3.1：
A confluence principle / 1.3.2：
Reduction of an equation / 1.3.3：
Classes and types of equations / 1.3.4：
Standard forms of equations / 1.3.5：
Invariants of s-homotopic transformations / 1.3.6：
Types of solutions / 1.4：
Eigenfunctions of singular Sturm--Liouville problems / 1.4.1：
Central and lateral connection problems / 1.4.2：
Stokes lines at singularities. Stokes matrices / 1.4.3：
Generalized Riemann scheme / 1.5：
Introduction / 1.5.1：
Applications / 1.5.2：
Central two-point connection problems (CTCPs) / 1.6：
Two regular singularities as relevant endpoints / 1.6.1：
One regular singularity and one irregular singularity as the endpoints / 1.6.3：
A proof / 1.6.4：
Two irregular singularities / 1.6.5：
The hypergeometric class of equations / 2：
Classification scheme / 2.1：
General presentation / 2.1.1：
Hypergeometric equation / 2.1.2：
Confluent equations / 2.1.3：
Reduced confluent equations / 2.1.4：
Difference equations / 2.2：
General consideration / 2.2.1：
Difference equations for hypergeometric functions / 2.2.2：
Confluent hypergeometric functions / 2.2.3：
Integral representations and integral relations / 2.3：
Preliminary lemmas / 2.3.1：
Integral representations / 2.3.2：
Integral relations / 2.3.3：
Central two-point connection problems / 2.4：
Standard sets of solutions for the hypergeometric equation / 2.4.1：
Connection relations for solutions of confluent hypergeometric equations / 2.4.2：
Polynomial solutions / 2.5：
Polynomial solutions of the hypergeometric equation / 2.5.1：
Jacobi polynomials / 2.5.3：
Specializations of Jacobi polynomials / 2.5.4：
Laguerre polynomials / 2.5.5：
Hermite polynomials / 2.5.6：
The Heun class of equations / 3：
A classification scheme / 3.1：
The Heun equation / 3.1.1：
Confluent Heun equations / 3.1.2：
Reduced confluent Heun equations / 3.1.3：
Solutions of the Heun equation / 3.2：
Confluent cases of the Heun equation / 3.2.2：
Integral equations and integral relations / 3.3：
Integral equations / 3.3.1：
An example of a proof / 3.3.3：
Basic asymptotic formulae for small t / 3.3.4：
Heun equation with nearby singularities / 3.4.1：
Large values of the scaling parameter / 3.5：
Avoided crossings for the triconfluent equation / 3.5.1：
Biconfluent Heun equation / 3.5.3：
The confluent Heun equation / 3.5.4：
Discussion / 3.5.5：
Differential equations in canonical form / 3.6：
Difference equations and Birkhoff sets / 3.6.3：
The eigenvalue conditions / 3.6.4：
Numerical aspects / 3.6.5：
Application to physical sciences / 4：
Problems in atomic and molecular physics / 4.1：
The hydrogen atom / 4.1.1：
The Stark effect on hydrogen / 4.1.2：
The hydrogen-molecule ion / 4.1.3：
Teukolsky equations in astrophysics / 4.2：
Rotating gravitational singularities / 4.2.1：
Dislocation movement in crystalline materials / 4.3：
The line-tension model / 4.3.1：
Differential equations / 4.3.2：
Static solutions / 4.3.3：
Explicit calculations / 4.3.4：
The discrete spectrum / 4.3.5：
The continuous spectrum / 4.3.6：
Quantum diffusion of kinks along dislocations / 4.3.7：
Tunneling in double-well potentials / 4.4：
Hill-type equations / 4.5：
The lunar perigee and node / 4.5.1：
Hill's solution / 4.5.2：
Floquet solutions and lateral connection problems / 4.5.3：
An ideal tunneling barrier / 4.6：
Forms of equations / 4.6.1：
Asymptotic study / 4.6.3：
Numerical algorithm / 4.6.4：
Results / 4.6.5：
Conclusion / 4.6.6：
Irradiation-amplified diffusion in crystals / 4.7：
The Painleve class of equations / 5：
The Painleve property / 5.1：
Fixed and movable singular points of a nonlinear ODE / 5.1.1：
The Painleve property and Painleve equations / 5.1.2：
Proof that movable singularities are poles in the case of P[superscript II] / 5.1.3：
The Hamiltonian structure / 5.2：
Heun-class equations and Painleve equations / 5.2.1：
Alternative classification of Painleve equations / 5.2.2：
Linearization of Painleve equations / 5.2.3：
Monodromy preserving deformations / 5.3：
The gamma function and related functions / Appendix A：
The gamma function / A.1：
The beta function / A.2：
The Pochhammer symbol / A.3：
CTCPs for Heun equations in general form / Appendix B：
Heun's equation and confluent cases / B.1：
Asymptotic factors and Jaffe transformations / B.2：
Jaffe expansions and difference equations / B.3：
Characteristic equations and Birkhoff sets / B.4：
Multipole matrix elements / Appendix C：
Auxiliary differential equations / C.1：
The integral transform / C.3：
The harmonic oscillator / C.4：
The anharmonic oscillator / C.5：
SFTools-Database of the special functions / Appendix D：
Stand-alone version of the program / D.6：
Internet version / D.8：
Possible future development / D.9：
How to order SFTools / D.20：
Bibliography
Index
Linear second-order ODEs with polynomial coefficients / 1：
Regular singularities and Fuchsian equations / 1.1：
Regular and Fuchsian singularities / 1.1.1：
34.

図書
図書
34. Prandtl's essentials of fluid mechanics. 2nd ed
Herbert Oertel, editor ; with contributions by M. Böhle ... [et al.] ; translated by Katherine Mayes
出版情報: New York ; Tokyo : Springer, c2004  xii, 723 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v.158
所蔵情報: loading…
目次情報: 続きを見る
Preface
Introduction / 1：
Properties of Liquids and Gases / 2：
Properties of Liquids / 2.1：
State of Stress / 2.2：
Liquid Pressure / 2.3：
Properties of Gases / 2.4：
Gas Pressure / 2.5：
Interaction Between Gas Pressure and Liquid Pressure / 2.6：
Equilibrium in Other Force Fields / 2.7：
Surface Stress (Capillarity) / 2.8：
Problems / 2.9：
Kinematics of Fluid Flow / 3：
Methods of Representation / 3.1：
Acceleration of a Flow / 3.2：
Topology of a Flow / 3.3：
Dynamics of Fluid Flow / 3.4：
Dynamics of Inviscid Liquids / 4.1：
Continuity and the Bernoulli Equation / 4.1.1：
Consequences of the Bernoulli Equation / 4.1.2：
Pressure Measurement / 4.1.3：
Interfaces and Formation of Vortices / 4.1.4：
Potential Flow / 4.1.5：
Wing Lift and the Magnus Effect / 4.1.6：
Balance of Momentum for Steady Flows / 4.1.7：
Waves on a Free Liquid Surface / 4.1.8：
Dynamics of Viscous Liquids / 4.1.9：
Viscosity (Inner Friction), the Navier-Stokes Equation / 4.2.1：
Mechanical Similarity, Reynolds Number / 4.2.2：
Laminar Boundary Layers / 4.2.3：
Onset of Turbulence / 4.2.4：
Fully Developed Turbulence / 4.2.5：
Flow Separation and Vortex Formation / 4.2.6：
Secondary Flows / 4.2.7：
Flows with Prevailing Viscosity / 4.2.8：
Flows Through Pipes and Channels / 4.2.9：
Drag of Bodies in Liquids / 4.2.10：
Flows in Non-Newtonian Media / 4.2.11：
Dynamics of Gases / 4.2.12：
Pressure Propagation, Velocity of Sound / 4.3.1：
Steady Compressible Flows / 4.3.2：
Conservation of Energy / 4.3.3：
Theory of Normal Shock Waves / 4.3.4：
Flows past Corners, Free Jets / 4.3.5：
Flows with Small Perturbations / 4.3.6：
Flows past Airfoils / 4.3.7：
Fundamental Equations of Fluid Mechanics / 4.3.8：
Continuity Equation / 5.1：
Navier-Stokes Equations / 5.2：
Laminar Flows / 5.2.1：
Reynolds Equations for Turbulent Flows / 5.2.2：
Energy Equation / 5.3：
Turbulent Flows / 5.3.1：
Fundamental Equations as Conservation Laws / 5.4：
Hierarchy of Fundamental Equations / 5.4.1：
Derived Model Equations / 5.4.2：
Multiphase Flows / 5.4.4：
Reactive Flows / 5.4.6：
Differential Equations of Perturbations / 5.5：
Aerodynamics / 5.6：
Fundamentals of Aerodynamics / 6.1：
Bird Flight and Technical Imitations / 6.1.1：
Airfoils and Wings / 6.1.2：
Airfoil and Wing Theory / 6.1.3：
Aerodynamic Facilities / 6.1.4：
Transonic Aerodynamics / 6.2：
Swept Wings / 6.2.1：
Shock-Boundary-Layer Interaction / 6.2.2：
Flow Separation / 6.2.3：
Supersonic Aerodynamics / 6.3：
Delta Wings / 6.3.1：
Fundamentals of Turbulent Flows / 6.4：
Linear Stability / 7.2：
Nonlinear Stability / 7.2.2：
Nonnormal Stability / 7.2.3：
Developed Turbulence / 7.3：
The Notion of a Mixing Length / 7.3.1：
Turbulent Mixing / 7.3.2：
Energy Relations in Turbulent Flows / 7.3.3：
Classes of Turbulent Flows / 7.4：
Free Turbulence / 7.4.1：
Flow Along a Boundary / 7.4.2：
Rotating and Strati.ed Flows, Flows with Curvature Effects / 7.4.3：
Turbulence in Tunnels / 7.4.4：
Two-Dimensional Turbulence / 7.4.5：
New Developments in Turbulence / 7.5：
Lagrangian Investigations of Turbulence / 7.5.1：
Field-Theoretic Methods / 7.5.2：
Outlook / 7.5.3：
Fluid-Mechanical Instabilities / 8：
Fundamentals of Fluid-Mechanical Instabilities / 8.1：
Examples of Fluid-Mechanical Instabilities / 8.1.1：
De.nition of Stability / 8.1.2：
Local Perturbations / 8.1.3：
Stratification Instabilities / 8.2：
Rayleigh-Benard Convection / 8.2.1：
Marangoni Convection / 8.2.2：
Diffusion Convection / 8.2.3：
Hydrodynamic Instabilities / 8.3：
Taylor Instability / 8.3.1：
Gortler Instability / 8.3.2：
Shear-Flow Instabilities / 8.4：
Boundary-Layer Flows / 8.4.1：
Tollmien-Schlichting and Cross-Flow Instabilities / 8.4.2：
Kelvin-Helmholtz Instability / 8.4.3：
Wake Flows / 8.4.4：
Convective Heat and Mass Transfer / 9：
Fundamentals of Heat and Mass Transfer / 9.1：
Free and Forced Convection / 9.1.1：
Heat Conduction and Convection / 9.1.2：
Diffusion and Convection / 9.1.3：
Free Convection / 9.2：
Convection at a Vertical Plate / 9.2.1：
Convection at a Horizontal Cylinder / 9.2.2：
Forced Convection / 9.3：
Pipe Flows / 9.3.1：
Bodies in Flows / 9.3.2：
Heat and Mass Exchange / 9.4：
Mass Exchange at the Flat Plate / 9.4.1：
Multiphase / 10：
Preface
Introduction / 1：
Properties of Liquids and Gases / 2：
35.

図書
図書
35. Classical microlocal analysis in the space of hyperfunctions
Seiichiro Wakabayashi
出版情報: Berlin : Springer, c2000  viii, 367 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1737
所蔵情報: loading…
目次情報: 続きを見る
Hyperfunctions / 1：
Function spaces? / 1.1：
Supports / 1.2：
Localization / 1.3：
Further applications of the Runge approximation theorem / 1.4：
Basic calculus of Fourier integral operators and pseudo-diferential operators / 2：
Preliminary lemmas / 2.1：
Symbol classes / 2.2：
Definition of Fouier integral operators / 2.3：
Product formula of Fourier integral operators I / 2.4：
Product formula of Fourier integral operators II / 2.5：
Pseudolocal properties / 2.6：
Pseudodifferential operators in ß / 2.7：
Parametrices of elliptic operators / 2.8：
Analytic wave ront sets and micro functions / 3：
Analytic wave front sets / 3.1：
Action of Fourier integral operators on wave front sets / 3.2：
The boundary values of analytic functions / 3.3：
Operations on hyperfunctions / 3.4：
Hyperfunctions supported by a half-space / 3.5：
Microfunctions / 3.6：
Formal analytic symbols / 3.7：
Microlocal uniqueness / 4：
General results / 4.1：
Microhyperbolic operators / 4.3：
Canonical transformation / 4.4：
Hypoellipticity / 4.5：
Local solvability / 5：
Preliminaries / 5.1：
Necessary conditions on local solvability and hypoellipticity 268 / 5.2：
Sufficient conditions on local solvability / 5.3：
Some examples / 5.4：
A Proofs of product formulae
Proof of Theorem 2.4.4 / A.l：
Proof of Corollary 2.4.5 / A.2：
Proof of Theorem 2.4.6 / A.3：
Proof of Corollary 2.4.7 / A.4：
Proof of Theorem 2.5.3 / A.5：
A priori estimates / B：
Grusin operators / B.1：
A class of operators with double characteristics / B.2：
Hyperfunctions / 1：
Function spaces? / 1.1：
Supports / 1.2：
36.

図書
図書
36. Borcherds products on O(2,l) and Chern classes of Heegner divisors
Jan H. Bruinier
出版情報: Berlin : Springer, c2002  viii, 152 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1780
所蔵情報: loading…
目次情報: 続きを見る
Introduction
Vector valued modular forms for the metaplectic group / 1：
The Weil representation / 1.1：
Poincaré series and Eisenstein series / 1.2：
Poincaré series / 1.2.1：
The Petersson scalar product / 1.2.2：
Eisenstein series / 1.2.3：
Non-holomorphic Poincare series of negative weight / 1.3：
The regularized theta lift / 2：
Siegel theta functions / 2.1：
The theta integral / 2.2：
The Fourier expansion of the theta lift / 2.3：
Lorentzian lattices / 3.1：
The hyperbolic Laplacian / 3.1.1：
Lattices of signature (2,l) / 3.2：
Modular forms on orthogonal groups / 3.3：
Borcherds products / 3.4：
Examples / 3.4.1：
Some Riemann geometry on O(2, l) / 4：
The invariant Laplacian / 4.1：
Modular forms with zeros and poles on Heegner divisors / 4.2：
Chern classes of Heegner divisors / 5：
A lifting into the cohomology / 5.1：
Comparison with the classical theta lift / 5.1.1：
Modular forms with zeros and poles on Heegner divisors II / 5.2：
References
Notation
Index
Introduction
Vector valued modular forms for the metaplectic group / 1：
The Weil representation / 1.1：
37.

図書
図書
37. Topics in symbolic dynamics and applications (: pbk)
edited by F. Blanchard, A. Maass, A. Nogueira
出版情報: Cambridge : Cambridge University Press, 2000  xvi, 245 p. ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 279
所蔵情報: loading…
目次情報: 続きを見る
Sequences of Low Complexity: Automatic and Sturmian Sequences / 1：
Introduction / 1.1：
Complexity Function / 1.2：
Definition / 1.2.1：
Frequencies and Measure-Theoretic Entropy / 1.2.2：
Variational Principle / 1.2.3：
Symbolic Dynamical Systems / 1.3：
The Graph of Words / 1.4：
The Line Graph / 1.4.1：
Graph and Frequencies / 1.4.2：
Special factors / 1.5：
Sturmian sequences / 1.6：
A Particular Coding of Rotations / 1.6.1：
Frequencies of Factors of Sturmian Sequences / 1.6.2：
Automatic Sequences / 1.7：
Automata and Transcendence / 1.7.1：
Applications / 1.7.2：
The Multidimensional Case / 1.7.3：
Application to Diagonals / 1.7.4：
Transcendence of the Bracket Series / 1.7.5：
Complexity and Frequencies / 1.7.6：
Conclusion / 1.8：
Automaticity and Sturmian sequences / 1.8.1：
Sub-affine Complexity / 1.8.2：
Substitution Subshifts and Bratteli Diagrams / 2：
Subshifts / 2.1：
Notation: Words, Sequences, Morphisms / 2.1.1：
Minimal Systems / 2.1.2：
Substitutions / 2.2：
Substitution Subshifts / 2.2.1：
Fixed Points / 2.2.2：
Unique Ergodicity / 2.3：
Perron-Frobenius Theorem / 2.3.1：
Density of Letters / 2.3.2：
The Substitution [sigma subscript kappa] on the Words of Length [kappa] / 2.3.3：
Structure of Substitution Subshifts / 2.4：
Structure of Substitution Dynamical Systems / 2.4.1：
Substitutions and Bratteli Diagrams / 2.5：
Bratteli Diagram Associated to a Substitution / 2.5.1：
The Vershik Map / 2.5.2：
An Isomorphism / 2.5.3：
The General Case / 2.5.4：
Algebraic Aspects of Symbolic Dynamics / 3：
General Subshifts / 3.1：
Dynamical Systems / 3.2.1：
Full Shifts / 3.2.2：
Examples / 3.2.3：
Block Codes / 3.3：
Codes / 3.3.1：
Curtis-Hedlund-Lyndon / 3.3.2：
Higher Block Presentations / 3.3.4：
One-Block Codes / 3.3.5：
Shifts of Finite Type / 3.4：
Vertex Shifts / 3.4.1：
Edge Shifts / 3.4.2：
Matrices / 3.4.3：
Markov Characterization / 3.4.4：
SFT-like Subshifts / 3.4.5：
Sofic Shifts / 3.5.1：
Specification / 3.5.2：
Synchronized Systems / 3.5.3：
Coded Systems / 3.5.4：
The Progression / 3.5.5：
Minimal Subshifts / 3.6：
Matrix Invariants for SFTS / 3.7：
Nonnegative Matrices / 3.7.1：
Transitivity / 3.7.2：
Mixing / 3.7.3：
Entropy / 3.7.4：
Periodic Points / 3.7.5：
Zeta Function / 3.7.6：
Isomorphism / 3.7.7：
Eventual Isomorphism / 3.7.8：
Flow Equivalence / 3.7.9：
Relations / 3.7.10：
Dimension Groups and Shift Equivalence / 3.8：
Dimension Groups / 3.8.1：
Dimension Modules / 3.8.2：
Shift Equivalence / 3.8.3：
Further Developments / 3.8.4：
Automorphisms and Classification of SFTS / 3.9：
Automorphisms / 3.9.1：
Representations / 3.9.2：
The KRW Factorization Theorem / 3.10：
Statement of the Theorem / 3.10.1：
Nonsurjectivity of [rho] / 3.10.2：
A Long Story / 3.10.3：
Classification / 3.11：
SE does not imply SSE: the Reducible Case / 3.11.1：
SE does not imply SSE: the Irreducible Case / 3.11.2：
Dynamics of Z[superscript d] Actions on Markov Subgroups / 4：
One-Dimensional Markov Subgroups / 4.1：
Decidability in One and Two-Dimensions / 4.3：
Markov Subgroups of (Z/2Z)[superscript Z superscript 2] / 4.4：
Markov Subgroups Polynomial Rings / 4.5：
Conjugacy and Isomorphism in (Z/2Z)[superscript Z superscript 2] / 4.6：
General Z[superscript d] Actions / 4.7：
Asymptotic Laws for Symbolic Dynamical Systems / 5：
Preliminaries / 5.1：
Bernoulli Trials / 5.2.1：
Occurrence and Waiting Times / 5.2.2：
General Setup and Motivation / 5.3：
Return Maps and Expected Return Times / 5.3.1：
Asymptotically Rare Events / 5.3.2：
Known Results and Motivation / 5.3.3：
Shifts of Finite Type and Equilibrium States / 5.4：
Holder Potentials / 5.4.1：
Entropy and Pressure / 5.4.2：
Ruelle-Perron-Frobenius Operator / 5.4.3：
The Central Limit Theorem / 5.4.4：
Pianigiani-Yorke Measure / 5.4.5：
Point Processes and Convergence in Law / 5.5：
Convergence of Point Processes / 5.5.1：
Entrance Times and Visiting Times / 5.5.2：
Final Remarks / 5.5.3：
Some Questions / 5.5.4：
Ergodic Theory and Diophantine Problems / 6：
Some Diophantine Problems Related to Polynomials and their Connections with Combinatorics and Dynamics / 6.1：
Ramsey Theory and Topological Dynamics / 6.3：
Density Ramsey Theory and Ergodic Theory of Multiple Recurrence / 6.4：
Polynomial Ergodic Theorems and Ramsey Theory / 6.5：
Appendix / 6.6：
Number Representation and Finite Automata / 7：
Words and Finite Automata / 7.1：
Standard Representations of Numbers / 7.3：
Representation of Integers / 7.3.1：
Representation of Real Numbers / 7.3.2：
b-Recognizable Sets of Integers / 7.3.3：
Beta-Expansions / 7.4：
Definitions / 7.4.1：
The [beta]-Shift / 7.4.2：
Classes of Numbers / 7.4.3：
Normalization in Base [beta] / 7.4.4：
U-Representations / 7.5：
The Set L(U) / 7.5.1：
Normalization in the Linear Numeration System U / 7.5.3：
U-Recognizable Sets of Integers / 7.5.4：
A Note on the Topological Classification of Lorenz Maps on the Interval / 8：
Statements of the Results / 8.1：
Proof of the Results / 8.3：
Sequences of Low Complexity: Automatic and Sturmian Sequences / 1：
Introduction / 1.1：
Complexity Function / 1.2：
38.

図書
図書
38. Geometric, control and numerical aspects of nonholonomic systems
Jorge Cortés Monforte
出版情報: Berlin ; Tokyo : Springer, c2002  xiv, 219 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1793
所蔵情報: loading…
目次情報: 続きを見る
Preface
Introduction / 1：
Literature review / 1.1：
Contents / 1.2：
Basic geometric tools / 2：
Manifolds and tensor calculus / 2.1：
Generalized distributions and codistributions / 2.2：
Lie groups and group actions / 2.3：
Principal connections / 2.4：
Riemannian geometry / 2.5：
Metric connections / 2.5.1：
Symplectic manifolds / 2.6：
Symplectic and Hamiltonian actions / 2.7：
Almost-Poisson manifolds / 2.8：
Almost-Poisson reduction / 2.8.1：
The geometry of the tangent bundle / 2.9：
Nonholonomic systems / 3：
Variational principles in Mechanics / 3.1：
HamiltonÆs principle / 3.1.1：
Symplectic formulation / 3.1.2：
Introducing constraints / 3.2：
The rolling disk / 3.2.1：
A homogeneous ball on a rotating table / 3.2.2：
The Snakeboard / 3.2.3：
A variation of BenentiÆs example / 3.2.4：
The Lagrange-d'Alembert principle / 3.3：
Geometric formalizations / 3.4：
Symplectic approach / 3.4.1：
Affine connection approach / 3.4.2：
Symmetries of nonholonomic systems / 4：
Nonholonomic systems with symmetry / 4.1：
The purely kinematic case / 4.2：
Reduction / 4.2.1：
Reconstruction / 4.2.2：
The case of horizontal symmetries / 4.3：
The general case / 4.3.1：
A special subcase: kinematic plus horizontal / 4.4.1：
The nonholonomic free particle modified / 4.5.1：
Chaplygin systems / 5：
Generalized Chaplygin systems / 5.1：
Reduction in the affine connection formalism / 5.1.1：
Two motivating examples / 5.1.2：
Mobile robot with fixed orientation / 5.2.1：
Two-wheeled planar mobile robot / 5.2.2：
Relation between both approaches / 5.3：
Invariant measure / 5.4：
KoillerÆs question / 5.4.1：
A counter example / 5.4.2：
A class of hybrid nonholonomic systems / 6：
Mechanical systems subject to constraints of variable rank / 6.1：
Impulsive forces / 6.2：
Generalized constraints / 6.3：
Momentum jumps / 6.3.1：
The holonomic case / 6.3.2：
Examples / 6.4：
The rolling sphere / 6.4.1：
Particle with constraint / 6.4.2：
Nonholonomic integrators / 7：
Symplectic integration / 7.1：
Variational integrators / 7.2：
Discrete Lagrange-d'Alembert principle / 7.3：
Construction of integrators / 7.4：
Geometric invariance properties / 7.5：
The symplectic form / 7.5.1：
The momentum / 7.5.2：
Numerical examples / 7.5.3：
Nonholonomic particle / 7.6.1：
Mobile robot with fixed orientation with a potential / 7.6.2：
Control of mechanical systems / 8：
Simple mechanical control systems / 8.1：
Homogeneity and Lie algebraic structure / 8.1.1：
Controllability notions / 8.1.2：
Existing results / 8.2：
On controllability / 8.2.1：
Series expansions / 8.2.2：
The one-input case / 8.3：
Systems underactuated by one control / 8.4：
The planar rigid body / 8.5：
A simple example / 8.5.2：
Mechanical systems with isotropic damping / 8.6：
Local accessibility and controllability / 8.6.1：
Kinematic controllability / 8.6.2：
Series expansion / 8.6.3：
References / 8.6.4：
Index
Preface
Introduction / 1：
Literature review / 1.1：
39.

図書
図書
39. Partial difference equations
Sui Sun Cheng
出版情報: London : Taylor & Francis, 2003  xii, 267 p. ; 24 cm
シリーズ名: Advances in Discrete Mathematics and Applications ; 3
所蔵情報: loading…
目次情報: 続きを見る
Series Editors' Preface
Preface
Modelling / 1：
Introduction / 1.1：
Examples / 1.2：
Discrete Heat Equations / 1.2.1：
Two-Level Equations / 1.2.2：
Multi-Level Equations / 1.2.3：
Implicit Reaction Diffusion Equations / 1.2.4：
Discrete Time Independent Equations / 1.2.5：
Auxiliary Conditions / 1.3：
Notes and Remarks / 1.4：
Basic Tools / 2：
Subsets of the Lattice Plane / 2.1：
Classifications of Partial Difference Equations / 2.2：
Finite Differences / 2.3：
Summable Infinite Sequences / 2.4：
Convolution of Doubly Infinite Sequences / 2.5：
Frequency Measures / 2.6：
Useful Results For Matrices / 2.7：
Discrete Gronwall Inequalities / 2.8：
Miscellaneous / 2.9：
Symbolic Calculus / 2.10：
Semi-Infinite Univariate Sequences / 3.1：
Ring of Sequences / 3.2.1：
Operators / 3.2.2：
Summation Operators / 3.2.3：
Translation or Shift Operators / 3.2.4：
Rational Operators / 3.2.5：
Attenuation Operators / 3.2.6：
Sequences and Series of Operators / 3.2.7：
Algebraic Derivatives / 3.2.8：
Algebraic Integrals / 3.2.9：
Ordinary Difference Equations / 3.2.10：
Semi-Infinite Bivariate Sequences / 3.3：
Ring of Double Sequences / 3.3.1：
Separable Double Sequences / 3.3.2：
Basic Relations Between Operators / 3.3.4：
Monotonicity and Convexity / 3.3.5：
Univariate Maximum Principles / 4.1：
Bivariate Maximum Principles / 4.3：
Univariate Wirtinger's Inequalities / 4.4：
Bivariate Wirtinger's Inequalities / 4.5：
Explicit Solutions / 4.6：
Formal Methods / 5.1：
The Method of Translation / 5.3：
The Method of Operators / 5.4：
The Method of Separable Solutions / 5.5：
The Method of Convolution / 5.6：
Two-Level Equations over the Upper Half Lattice Plane / 5.6.1：
Three-Level Equations over the Upper Half Lattice Plane / 5.6.2：
Method of Linear Systems / 5.7：
Stability / 5.8：
Stability Concepts / 6.1：
Equations Over Cylinders / 6.2：
Method of General Solutions / 6.2.1：
Method of Maximum Principles / 6.2.2：
Method of Energies / 6.2.3：
Method of Functional Inequalities / 6.2.4：
Spectral Methods / 6.2.5：
Method of Separable Solutions / 6.2.6：
Equations Over Half Planes / 6.3：
Method of Exact Solutions for Two-Level Equations / 6.3.1：
Method of Exact Solutions for Three-Level Equations / 6.3.2：
Method of Induction for Three-Level Equations / 6.3.3：
Equations Over Quadrants / 6.4：
Method of Exact Solutions for a Two-Level Equation / 6.4.1：
Method of Induction for a Two-Level Nonhomogeneous Equation / 6.4.2：
Method of Induction for a Four-Point Equation / 6.4.3：
Method of Induction for a Four-Point Delay Equation / 6.4.4：
Method of Induction for a Five-Point Delay Equation / 6.4.5：
Equations Over Finite Domains / 6.5：
Existence / 6.6：
Traveling Waves / 7.1：
Positive and Bounded Solutions / 7.3：
Monotone Method for a Finite Laplace Equation / 7.4：
Contraction Method for a Finite Laplace Equation / 7.5：
Monotone Method for Evolutionary Equations / 7.6：
Eigenvalue Method for a Boundary Problem / 7.7：
Contraction Method for a Boundary Problem / 7.8：
Monotone Method for Boundary Problems / 7.9：
Nonexistence / 7.10：
Equations Over The Plane / 8.1：
Three-Point Equations with Two Constant Coefficients / 8.3：
Four-Point Equations with Three Constant Coefficients / 8.3.2：
Characteristic Initial Value Problems / 8.3.3：
Delay Partial Difference Equations / 8.3.4：
Frequently Positive Solutions / 8.3.5：
Linear Discrete Heat Equation With Constant Coefficients / 8.4：
Parabolic Type Equations with Variable Coefficients / 8.4.2：
Discrete Elliptic Equations / 8.4.3：
Initial Boundary Value Problems / 8.4.4：
Linear Hybrid Five-Point Equations / 8.4.5：
Bibliography / 8.5：
Index
Series Editors' Preface
Preface
Modelling / 1：
40.

図書
図書
40. Wave Motion (: hard ; : pbk.)
J. Billingham, A. C. King
出版情報: Cambridge : Cambridge University Press, 2000  ix, 468 p. ; 23 cm
シリーズ名: Cambridge texts in applied mathematics
所蔵情報: loading…
目次情報: 続きを見る
Introduction
Linear Waves / Part 1：
Basic Ideas / 1：
Exercises
Waves on a Stretched String / 2：
Derivation of the Governing Equation / 2.1：
Standing Waves on Strings of Finite Length / 2.2：
D'Alembert's Solution for Strings of Infinite Length / 2.3：
Reflection and Transmission of Waves by Discontinuities in Density / 2.4：
A Single Discontinuity / 2.4.1：
Two Discontinuities: Impedance Matching / 2.4.2：
Sound Waves / 3：
Plane Waves / 3.1：
Acoustic Energy Transmission / 3.3：
Plane Waves In Tubes / 3.4：
Acoustic Waveguides / 3.5：
Reflection of a Plane Acoustic Wave by a Rigid Wall / 3.5.1：
A Planar Waveguide / 3.5.2：
A Circular Waveguide / 3.5.3：
Acoustic Sources / 3.6：
The Acoustic Source / 3.6.1：
Energy Radiated by Sources and Plane Waves / 3.6.2：
Radiation from Sources in a Plane Wall / 3.7：
Linear Water Waves / 4：
Derivation of the Governing Equations / 4.1：
Linear Gravity Waves / 4.2：
Progressive Gravity Waves / 4.2.1：
Standing Gravity Waves / 4.2.2：
The Wavemaker / 4.2.3：
The Extraction of Energy from Water Waves / 4.2.4：
The Effect of Surface Tension: Capillary--Gravity Waves / 4.3：
Edge Waves / 4.4：
Ship Waves / 4.5：
The Solution of Initial Value Problems / 4.6：
Shallow Water Waves: Linear Theory / 4.7：
The Reflection of Sea Swell by a Step / 4.7.1：
Wave Amplification at a Gently Sloping Beach / 4.7.2：
Wave Refraction / 4.8：
The Kinematics of Slowly Varying Waves / 4.8.1：
Wave Refraction at a Gently Sloping Beach / 4.8.2：
The Effect of Viscosity / 4.9：
Waves in Elastic Solids / 5：
Waves in an Infinite Elastic Body / 5.1：
One-Dimensional Dilatation Waves / 5.2.1：
One-Dimensional Rotational Waves / 5.2.2：
Plane Waves with General Orientation / 5.2.3：
Two-Dimensional Waves in Semi-infinite Elastic Bodies / 5.3：
Normally Loaded Surface / 5.3.1：
Stress-Free Surface / 5.3.2：
Waves in Finite Elastic Bodies / 5.4：
Flexural Waves in Plates / 5.4.1：
Waves in Elastic Rods / 5.4.2：
Torsional Waves / 5.4.3：
Longitudinal Waves / 5.4.4：
The Excitation and Propagation of Elastic Wavefronts / 5.5：
Wavefronts Caused by an Internal Line Force in an Unbounded Elastic Body / 5.5.1：
Wavefronts Caused by a Point Force on the Free Surface of a Semi-infinite Elastic Body / 5.5.2：
Electromagnetic Waves / 6：
Electric and Magnetic Forces and Fields / 6.1：
Electrostatics: Gauss's Law / 6.2：
Magnetostatics: Ampere's Law and the Displacement Current / 6.3：
Electromagnetic Induction: Farady's Law / 6.4：
Plane Electromagnetic Waves / 6.5：
Conductors and Insulators / 6.6：
Reflection and Transmission at Interfaces / 6.7：
Boundary Conditions at Interfaces / 6.7.1：
Reflection by a Perfect Conductor / 6.7.2：
Reflection and Refraction by Insulators / 6.7.3：
Waveguides / 6.8：
Metal Waveguides / 6.8.1：
Weakly Guiding Optical Fibres / 6.8.2：
Radiation / 6.9：
Scalar and Vector Potentials / 6.9.1：
The Electric Dipole / 6.9.2：
The Far Field of a Localised Current Distribution / 6.9.3：
The Centre Fed Linear Antenna / 6.9.4：
Nonlinear Waves / Part 2：
The Formation and Propagation of Shock Waves / 7：
Traffic Waves / 7.1：
Small Amplitude Disturbances of a Uniform State / 7.1.1：
The Nonlinear Initial Value Problem / 7.1.3：
The Speed of the Shock / 7.1.4：
Compressible Gas Dynamics / 7.2：
Some Essential Thermodynamics / 7.2.1：
Equations of Motion / 7.2.2：
Construction of the Characteristic Curves / 7.2.3：
The Rankine--Hugoniot Relations / 7.2.4：
Detonations / 7.2.5：
Nonlinear Water Waves / 8：
Nonlinear Shallow Water Waves / 8.1：
The Dam Break Problem / 8.1.1：
A Shallow Water Bore / 8.1.2：
The Effect of Nonlinearity on Deep Water Gravity Waves: Stokes' Expansion / 8.2：
The Korteweg-de Vries Equation for Shallow Water Waves: the Interaction of Nonlinear Steepening and Linear Dispersion / 8.3：
Derivation of the Korteweg-de Vries Equation / 8.3.1：
Travelling Wave Solutions of the KdV Equation / 8.3.2：
Nonlinear Capillary Waves / 8.4：
Chemical and Electrochemical Waves / 9：
The Law of Mass Action / 9.1：
Molecular Diffusion / 9.2：
Reaction-Diffusion Systems / 9.3：
Autocatalytic Chemical Waves with Unequal Diffusion Coefficients* / 9.4：
Existence of Travelling Wave Solutions / 9.4.1：
Asymptotic Solution for [delta] [[ 1 / 9.4.2：
The Transmission of Nerve Impulses: the Fitzhugh-Nagumo Equations / 9.5：
The Fitzhugh-Nagumo Model / 9.5.1：
The Existence of a Threshold / 9.5.2：
Travelling Waves / 9.5.3：
Advanced Topics / Part 3：
Burgers' Equation: Competition between Wave Steepening and Wave Spreading / 10：
Burgers' Equation for Traffic Flow / 10.1：
The Effect of Dissipation on Weak Shock Waves in an Ideal Gas / 10.2：
Simple Solutions of Burgers' Equation / 10.3：
Asymptotic Solutions for v [[ 1 / 10.3.1：
Diffraction and Scattering / 11：
Diffraction of Acoustic Waves by a Semi-infinite Barrier / 11.1：
Preliminary Estimates of the Potential / 11.1.1：
Pre-transform Considerations / 11.1.2：
The Fourier Transform Solution / 11.1.3：
The Diffraction of Waves by an Aperture / 11.2：
Scalar Diffraction: Acoustic Waves / 11.2.1：
Vector Diffraction: Electromagnetic Waves / 11.2.2：
Scattering of Linear, Deep Water Waves by a Surface Piercing Cylinder / 11.3：
Solitons and the Inverse Scattering Transform / 12：
The Korteweg-de Vries Equation / 12.1：
The Scattering Problem / 12.1.1：
The Inverse Scattering Problem / 12.1.2：
Scattering Data for KdV Potentials / 12.1.3：
Examples: Solutions of the KdV Equation / 12.1.4：
The Nonlinear Schrodinger Equation / 12.2：
Derivation of the Nonlinear Schrodinger Equation for Plane Electromagnetic Waves / 12.2.1：
Solitary Wave Solutions of the Nonlinear Schrodinger Equation / 12.2.2：
The Inverse Scattering Transform for the Nonlinear Schrodinger Equation / 12.2.3：
Useful Mathematical Formulas and Physical Data / Appendix 1：
Cartesian Coordinates / A1.1：
Cylindrical Polar Coordinates / A1.2：
Spherical Polar Coordinates / A1.3：
Some Vector Calculus Identities and Useful Results for Smooth Vector Fields / A1.4：
Physical constants / A1.5：
Bibliography
Index
Introduction
Linear Waves / Part 1：
Basic Ideas / 1：
41.

図書
図書
41. Statistical computing
William J. Kennedy, Jr., James E. Gentle
出版情報: New York : M. Dekker, c1980  xi, 591 p. ; 24 cm
シリーズ名: Statistics : textbooks and monographs ; v. 33
所蔵情報: loading…
目次情報: 続きを見る
Preface
Introduction / 1：
Orientation / 1.1：
Purpose / 1.2：
Prerequisites / 1.3：
Presentation of Algorithms / 1.4：
Computer Organization / 2：
Components of the Digital Computer System / 2.1：
Representation of Numeric Values / 2.3：
Integer Mode Representation / 2.3.1：
Representation in Floating-Point Mode / 2.3.2：
Floating- and Fixed-Point Arithmetic / 2.4：
Floating-Point Arithmetic Operations / 2.4.1：
Fixed-Point Arithmetic Operations / 2.4.2：
Exercises
References
Error in Floating-Point Computation / 3：
Types of Error / 3.1：
Error Due to Approximation Imposed by the Computer / 3.3：
Analyzing Error in a Finite Process / 3.4：
Rounding Error in Floating-Point Computations / 3.5：
Rounding Error in Two Common Floating-Point Calculations / 3.6：
Condition and Numerical Stability / 3.7：
Other Methods of Assessing Error in Computation / 3.8：
Summary / 3.9：
Programming and Statistical Software / 4：
Programming Languages: Introduction / 4.1：
Components of Programming Languages / 4.2：
Data Types / 4.2.1：
Data Structures / 4.2.2：
Syntax / 4.2.3：
Control Structures / 4.2.4：
Program Development / 4.3：
Statistical Software / 4.4：
References and Further Readings
Approximating Probabilities and Percentage Points in Selected Probability Distributions / 5：
Notation and General Considerations / 5.1：
Probability Distributions / 5.1.1：
Accuracy Considerations / 5.1.2：
General Methods in Approximation / 5.2：
Approximate Transformation of Random Variables / 5.2.1：
Closed Form Approximations / 5.2.2：
General Series Expansion / 5.2.3：
Exact Relationship Between Distributions / 5.2.4：
Numerical Root Finding / 5.2.5：
Continued Fractions / 5.2.6：
Gaussian Quadrature / 5.2.7：
Newton-Cotes Quadrature / 5.2.8：
The Normal Distribution / 5.3：
Normal Probabilities / 5.3.1：
Normal Percentage Points / 5.3.2：
Student's t Distribution / 5.4：
t Probabilities / 5.4.1：
t-Percentage Points / 5.4.2：
The Beta Distribution / 5.5：
Evaluating the Incomplete Beta Function / 5.5.1：
Inverting the Incomplete Beta Function / 5.5.2：
F Distribution / 5.6：
F Probabilities / 5.6.1：
F Percentage Points / 5.6.2：
Chi-Square Distribution / 5.7：
Chi-Square Probabilities / 5.7.1：
Chi-Square Percentage Points / 5.7.2：
Random Numbers: Generation, Tests and Applications / 6：
Generation of Uniform Random Numbers / 6.1：
Congruential Methods / 6.2.1：
Feedback Shift Register Methods / 6.2.2：
Coupled Generators / 6.2.3：
Portable Generators / 6.2.4：
Tests of Random Number Generators / 6.3：
Theoretical Tests / 6.3.1：
Empirical Tests / 6.3.2：
Selecting a Random Number Generator / 6.3.3：
General Techniques for Generation of Nonuniform Random Deviates / 6.4：
Use of the Cumulative Distribution Function / 6.4.1：
Use of Mixtures of Distributions / 6.4.2：
Rejection Methods / 6.4.3：
Table Sampling Methods for Discrete Distributions / 6.4.4：
The Alias Method for Discrete Distributions / 6.4.5：
Generation of Variates from Specific Distributions / 6.5：
The Gamma Distribution / 6.5.1：
The F, t, and Chi-Square Distributions / 6.5.3：
The Binomial Distribution / 6.5.5：
The Poisson Distribution / 6.5.6：
Distribution of Order Statistics / 6.5.7：
Some Other Univariate Distributions / 6.5.8：
The Multivariate Normal Distribution / 6.5.9：
Some Other Multivariate Distributions / 6.5.10：
Applications / 6.6：
The Monte Carlo Method / 6.6.1：
Sampling and Randomization / 6.6.2：
Selected Computational Methods in Linear Algebra / 7：
Methods Based on Orthogonal Transformations / 7.1：
Householder Transformations / 7.2.1：
Givens Transformations / 7.2.2：
The Modified Gram-Schmidt Method / 7.2.3：
Singular-value Decomposition / 7.2.4：
Gaussian Elimination and the Sweep Operator / 7.3：
Cholesky Decomposition and Rank-One Update / 7.4：
Computational Methods for Multiple Linear Regression Analysis / 8：
Basic Computational Methods / 8.1：
Methods Using Orthogonal Triangularization of X / 8.1.1：
Sweep Operations and Normal Equations / 8.1.2：
Checking Programs, Computed Results and Improving Solutions Iteratively / 8.1.3：
Regression Model Building / 8.2：
All Possible Regressions / 8.2.1：
Stepwise Regression / 8.2.2：
Other Methods / 8.2.3：
A Special Case--Polynomial Models / 8.2.4：
Multiple Regression Under Linear Restrictions / 8.3：
Linear Equality Restrictions / 8.3.1：
Linear Inequality Restrictions / 8.3.2：
Computational Methods for Classification Models / 9：
Fixed-effects Models / 9.1：
Restrictions on Models and Constraints on Solutions / 9.1.2：
Reductions in Sums of Squares / 9.1.3：
An Example / 9.1.4：
The Special Case of Balance and Completeness for Fixed-Effects Models / 9.2：
Basic Definitions and Considerations / 9.2.1：
Computer-related Considerations in the Special Case / 9.2.2：
Analysis of Covariance / 9.2.3：
The General Problem for Fixed-Effects Models / 9.3：
Estimable Functions / 9.3.1：
Selection Criterion / 9.3.2：
Selection Criterion 2 / 9.3.3：
Computing Expected Mean Squares and Estimates of Variance Components / 9.3.4：
Computing Expected Mean Squares / 9.4.1：
Variance Component Estimation / 9.4.2：
Unconstrained Optimization and Nonlinear Regression / 10：
Preliminaries / 10.1：
Iteration / 10.1.1：
Function Minima / 10.1.2：
Step Direction / 10.1.3：
Step Size / 10.1.4：
Convergence of the Iterative Methods / 10.1.5：
Termination of Iteration / 10.1.6：
Methods for Unconstrained Minimization / 10.2：
Method of Steepest Descent / 10.2.1：
Newton's Method and Some Modifications / 10.2.2：
Quasi-Newton Methods / 10.2.3：
Conjugate Gradient Method / 10.2.4：
Conjugate Direction Method / 10.2.5：
Other Derivative-Free Methods / 10.2.6：
Computational Methods in Nonlinear Regression / 10.3：
Newton's Method for the Nonlinear Regression Problem / 10.3.1：
The Modified Gauss-Newton Method / 10.3.2：
The Levenberg-Marquardt Modification of Gauss-Newton / 10.3.3：
Alternative Gradient Methods / 10.3.4：
Minimization Without Derivatives / 10.3.5：
Test Problems / 10.3.6：
Model Fitting Based on Criteria Other Than Least Squares / 11：
Minimum L[subscript p] Norm Estimators / 11.1：
L[subscript 1] Estimation / 11.2.1：
L[subscript infinity] Estimation / 11.2.2：
Other L[subscript p] Estimators / 11.2.3：
Other Robust Estimators / 11.3：
Biased Estimation / 11.4：
Robust Nonlinear Regression / 11.5：
Selected Multivariate Methods / 12：
Canonical Correlations / 12.1：
Principal Components / 12.3：
Factor Analysis / 12.4：
Multivariate Analysis of Variance / 12.5：
Index
Preface
Introduction / 1：
Orientation / 1.1：
42.

図書
図書
42. Bosonic strings : a mathematical treatment
Jürgen Jost
出版情報: Providence, RI : American Mathematical Society : International Press, c2001  xi, 95 p. ; 27 cm
シリーズ名: AMS/IP studies in advanced mathematics ; v. 21
所蔵情報: loading…
目次情報: 続きを見る
Preface
Point particles / 1：
Point particles and path integrals / 1.1：
Faddeev-Popov gauge fixing and BRST symmetry / 1.2：
BRST quantization of the point particle / 1.3：
The Bosonic string / 2：
The classical action for strings / 2.1：
Sobolev spaces / 2.2：
Boundary regularity / 2.3：
Spaces of mappings and metrics / 2.4：
The global structure of the spaces of metrics, complex structures, and diffeomorphisms on a surface / 2.5：
Infinitesimal decompositions of metrics / 2.6：
Complex analytic aspects / 2.7：
Teichmuller and moduli spaces of Riemann surfaces / 2.8：
Determinants / 2.9：
The partition function for the Bosonic string / 2.10：
Some physical aspects / 2.11：
Bibliography
Index
Preface
Point particles / 1：
Point particles and path integrals / 1.1：
43.

図書
図書
43. Data mining in finance : advances in relational and hybrid methods
by Boris Kovalerchuk and Evgenii Vityaev
出版情報: Boston : Kluwer Academic Publishers, c2000  xiv, 308 p. ; 24 cm
シリーズ名: The Kluwer international series in engineering and computer science ; SECS 547
所蔵情報: loading…
目次情報: 続きを見る
Foreword / Gregory Piatetsky-Shapiro
Preface
Acknowledgements
The Scope and Methods of the Study / 1.：
Introduction / 1.1：
Problem definition / 1.2：
Data mining methodologies / 1.3：
Parameters / 1.3.1：
Problem ID and profile / 1.3.2：
Comparison of intelligent decision support methods / 1.3.3：
Modern methodologies in financial knowledge discovery / 1.4：
Deterministic dynamic system approach / 1.4.1：
Efficient market theory / 1.4.2：
Fundamental and technical analyses / 1.4.3：
Data mining and database management / 1.5：
Data mining: definitions and practice / 1.6：
Learning paradigms for data mining / 1.7：
Intellectual challenges in data mining / 1.8：
Numerical Data Mining Models with Financial Applications / 2.：
Statistical, autoregression models / 2.1：
ARIMA models / 2.1.1.：
Steps in developing ARIMA model / 2.1.2.：
Seasonal ARIMA / 2.1.3.：
Exponential smoothing and trading day regression / 2.1.4.：
Comparison with other methods / 2.1.5.：
Financial applications of autoregression models / 2.2.：
Instance-based learning and financial applications / 2.3.：
Neural networks / 2.4.：
Steps / 2.4.1.：
Recurrent networks / 2.4.3.：
Dynamically modifying network structure / 2.4.4.：
Neural networks and hybrid systems in finance / 2.5.：
Recurrent neural networks in finance / 2.6.：
Modular networks and genetic algorithms / 2.7.：
Mixture of neural networks / 2.7.1.：
Genetic algorithms for modular neural networks / 2.7.2.：
Testing results and the complete round robin method / 2.8.：
Approach and method / 2.8.1.：
Multithreaded implementation / 2.8.3.：
Experiments with SP500 and neural networks / 2.8.4.：
Expert mining / 2.9.：
Interactive learning of monotone Boolean functions / 2.10.：
Basic definitions and results / 2.10.1.：
Algorithm for restoring a monotone Boolean function / 2.10.2.：
Construction of Hansel chains / 2.10.3.：
Rule-Based and Hybrid Financial Data Mining / 3.：
Decision tree and DNF learning / 3.1.：
Advantages / 3.1.1.：
Limitation: size of the tree / 3.1.2.：
Constructing decision trees / 3.1.3.：
Ensembles and hybrid methods for decision trees / 3.1.4.：
Discussion / 3.1.5.：
Decision tree and DNF learning in finance / 3.2.：
Decision-tree methods in finance / 3.2.1.：
Extracting decision tree and sets of rules for SP500 / 3.2.2.：
Sets of decision trees and DNF learning in finance / 3.2.3.：
Extracting decision trees from neural networks / 3.3.：
Approach / 3.3.1.：
Trepan algorithm / 3.3.2.：
Extracting decision trees from neural networks in finance / 3.4.：
Predicting the Dollar-Mark exchange rate / 3.4.1.：
Comparison of performance / 3.4.2.：
Probabilistic rules and knowledge-based stochastic modeling / 3.5.：
Probabilistic networks and probabilistic rules / 3.5.1.：
The naive Bayes classifier / 3.5.2.：
The mixture of experts / 3.5.3.：
The hidden Markov model / 3.5.4.：
Uncertainty of the structure of stochastic models / 3.5.5.：
Knowledge-based stochastic modeling in finance / 3.6.：
Markov chains in finance / 3.6.1.：
Hidden Markov models in finance / 3.6.2.：
Relational Data Mining (RDM) / 4.：
Examples / 4.1.：
Relational data mining paradigm / 4.3.：
Challenges and obstacles in relational data mining / 4.4：
Theory of RDM / 4.5：
Data types in relational data mining / 4.5.1：
Relational representation of examples / 4.5.2：
First-order logic and rules / 4.5.3：
Background knowledge / 4.6：
Arguments constraints and skipping useless hypotheses / 4.6.1：
Initial rules and improving search of hypotheses / 4.6.2：
Relational data mining and relational databases / 4.6.3：
Algorithms: FOIL and FOCL / 4.7：
FOIL / 4.7.1：
FOCL / 4.7.3：
Algorithm MMDR / 4.8：
MMDR algorithm and existence theorem / 4.8.1：
Fisher test / 4.8.3：
MMDR pseudocode / 4.8.4：
Comparison of FOIL and MMDR / 4.8.5：
Numerical relational data mining / 4.9：
Data types / 4.10：
Problem of data types / 4.10.1：
Numerical data type / 4.10.2：
Representative measurement theory / 4.10.3：
Critical analysis of data types in ABL / 4.10.4：
Empirical axiomatic theories: empirical contents of data / 4.11：
Definitions / 4.11.1：
Representation of data types in empirical axiomatic theories / 4.11.2：
Discovering empirical regularities as universal formulas / 4.11.3：
Financial Applications of Relational Data Mining / 5.：
Transforming numeric data into relations / 5.1.：
Hypotheses and probabilistic "laws" / 5.3.：
Markov chains as probabilistic "laws" in finance / 5.4.：
Learning / 5.5.：
Method of forecasting / 5.6.：
Experiment 1 / 5.7.：
Forecasting Performance for hypotheses H1-H4 / 5.7.1.：
Forecasting performance for a specific regularity / 5.7.2.：
Forecasting performance for Markovian expressions / 5.7.3.：
Experiment 2 / 5.8.：
Interval stock forecast for portfolio selection / 5.9.：
Predicate invention for financial applications: calendar effects / 5.10.：
Conclusion / 5.11.：
Comparison of Performance of RDM and other methods in financial applications / 6：
Forecasting methods / 6.1.：
Approach: measures of performance / 6.2.：
Experiment 1: simulated trading performance / 6.3.：
Experiment 1: comparison with ARIMA / 6.4.：
Experiment 2: forecast and simulated gain / 6.5.：
Experiment 2: analysis of performance / 6.6.：
Fuzzy logic approach and its financial applications / 6.7.：
Knowledge discovery and fuzzy logic / 7.1.：
"Human logic" and mathematical principles of uncertainty / 7.2.：
Difference between fuzzy logic and probability theory / 7.3.：
Basic concepts of fuzzy logic / 7.4.：
Inference problems and solutions / 7.5.：
Constructing coordinated contextual linguistic variables / 7.6.：
Context space / 7.6.1.：
Acquisition of fuzzy sets and membership function / 7.6.3.：
Obtaining linguistic variables / 7.6.4.：
Constructing coordinated fuzzy inference / 7.7.：
Example / 7.7.1.：
Advantages of "exact complete" context for fuzzy inference / 7.7.3.：
Fuzzy logic in finance / 7.8.：
Review of applications of fuzzy logic in finance / 7.8.1.：
Fuzzy logic and technical analysis / 7.8.2.：
References
Subject Index
Foreword / Gregory Piatetsky-Shapiro
Preface
Acknowledgements
44.

図書
図書
44. The Casimir effect : physical manifestations of zero-point energy
K. A. Milton
出版情報: New Jersey : World Scientific, c2001  xv, 301 p. ; 23 cm
所蔵情報: loading…
目次情報: 続きを見る
Preface
Introduction to the Casimir Effect / Chapter 1：
Van der Waals Forces / 1.1：
Casimir Effect / 1.2：
Dimensional Dependence / 1.3：
Applications / 1.4：
Local Effects / 1.5：
Sonoluminescence / 1.6：
Radiative Corrections / 1.7：
Other Topics / 1.8：
Conclusion / 1.9：
General References / 1.10：
Casimir Force Between Parallel Plates / Chapter 2：
Introduction / 2.1：
Dimensional Regularization / 2.2：
Scalar Green's Function / 2.3：
Massive Scalar / 2.4：
Finite Temperature / 2.5：
Electromagnetic Casimir Force / 2.6：
Variations / 2.6.1：
Fermionic Casimir Force / 2.7：
Summing Modes / 2.7.1：
Green's Function Method / 2.7.2：
Casimir Force Between Parallel Dielectrics / Chapter 3：
The Lifshitz Theory / 3.1：
Temperature Dependence for Conducting Plates / 3.2：
Finite Conductivity / 3.2.2：
van der Waals Forces / 3.2.3：
Force between Polarizable Molecule and a Dielectric Plate / 3.2.4：
Experimental Verification of the Casimir Effect / 3.3：
Casimir Effect with Perfect Spherical Boundaries / Chapter 4：
Electromagnetic Casimir Self-Stress on a Spherical Shell / 4.1：
Temperature Dependence / 4.1.1：
Fermion Fluctuations / 4.2：
The Casimir Effect of a Dielectric Ball: The Equivalence of the Casimir Effect and van der Waals Forces / Chapter 5：
Green's Dyadic Formulation / 5.1：
Stress on the Sphere / 5.2：
Total Energy / 5.3：
Fresnel Drag / 5.4：
Electrostriction / 5.5：
Dilute Dielectric-Diamagnetic Sphere / 5.6：
Dilute Dielectric Ball / 5.6.1：
Conducting Ball / 5.7.1：
Van der Waals Self-Stress for a Dilute Dielectric Sphere / 5.9：
Discussion / 5.10：
Application to Hadronic Physics: Zero-Point Energy in the Bag Model / Chapter 6：
Zero-point Energy of Confined Gluons / 6.1：
Zero-point Energy of Confined Virtual Quarks / 6.2：
Numerical Evaluation / 6.2.1：
J = 1/2 Contribution / 6.2.1.1：
Sum Over All Modes / 6.2.1.2：
Asymptotic Evaluation of Lowest J Contributions / 6.2.1.3：
Discussion and Applications / 6.3：
Fits to Hadron Masses / 6.3.1：
Calculation of the Bag Constant / 6.4：
Recent Work / 6.5：
Casimir Effect in Cylindrical Geometries / Chapter 7：
Conducting Circular Cylinder / 7.1：
Related Work / 7.1.1：
Parallelepipeds / 7.1.2：
Wedge-Shaped Regions / 7.1.3：
Dielectric-Diamagnetic Cylinder--Uniform Speed of Light / 7.2：
Integral Representation for the Casimir Energy / 7.2.1：
Casimir Energy of an Infinite Cylinder when [epsilon subscript 1 mu subscript 1] = [epsilon subscript 2 mu subscript 2] / 7.2.2：
Dilute Compact Cylinder and Perfectly Conducting Cylindrical Shell / 7.2.3：
Van der Waals Energy of a Dielectric Cylinder / 7.3：
Casimir Effect in Two Dimensions: The Maxwell-Chern-Simons Casimir Effect / Chapter 8：
Casimir Effect in 2 + 1 Dimensions / 8.1：
Temperature Effect / 8.2.1：
Casimir Force between Chern-Simons Surfaces / 8.2.2：
Circular Boundary Conditions / 8.3：
Casimir Self-Stress on a Circle / 8.3.1：
Numerical Results at Zero Temperature / 8.3.2：
High-Temperature Limit / 8.3.3：
Scalar Casimir Effect on a Circle / 8.3.4：
Casimir Effect on a D-dimensional Sphere / Chapter 9：
Scalar or TE Modes / 9.1：
TM Modes / 9.2：
Energy Derivation / 9.2.1：
Numerical Evaluation of the Stress / 9.2.2：
Convergent Reformulation of (9.52) / 9.2.2.1：
Casimir Stress for Integer D [less than or equal] 1 / 9.2.3：
Numerical results / 9.2.4：
Toward a Finite D = 2 Casimir Effect / 9.3：
Cosmological Implications of the Casimir Effect / Chapter 10：
Scalar Casimir Energies in M[superscript 4] X S[superscript N] / 10.1：
N = 1 / 10.1.1：
The General Odd-N Case / 10.1.2：
The Even-N Case / 10.1.3：
A Simple [xi]-Function Technique / 10.1.4：
Other Work / 10.2：
The Cosmological Constant / 10.3：
Parallel Plates / Chapter 11：
Local Casimir Effect for Wedge Geometry / 11.2：
Quark and Gluon Condensates in the Bag Model / 11.3：
Surface Divergences / 11.5：
Sonoluminescence and the Dynamical Casimir Effect / Chapter 12：
The Adiabatic Approximation / 12.1：
Discussion of Form of Force on Surface / 12.3：
Bulk Energy / 12.4：
Dynamical Casimir Effect / 12.5：
Radiative Corrections to the Casimir Effect / Chapter 13：
Formalism for Computing Radiative Corrections / 13.1：
Radiative Corrections for Parallel Conducting Plates / 13.2：
Radiative Corrections for a Spherical Boundary / 13.2.1：
Conclusions / 13.4：
Conclusions and Outlook / Chapter 14：
Relation of Contour Integral Method to Green's Function Approach / Appendix A：
Casimir Effect for a Closed String / Appendix B：
Open Strings / B.1：
Bibliography
Index
Preface
Introduction to the Casimir Effect / Chapter 1：
Van der Waals Forces / 1.1：
45.

図書
図書
45. 岩波講座基礎数学 (総索引 ; 月報 ; 月報(第3次))
小平邦彦監修 ; 岩堀長慶 [ほか] 編
出版情報: 東京 : 岩波書店, 1976.5-  冊 ; 22cm
所蔵情報: loading…
46.

図書
図書
46. Strong coupling, Monte Carlo methods, conformal field theory, and random systems (: hbk)
Claude Itzykson, Jean-Michel Drouffe
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1989  xvi, 405-810 p. ; 24 cm
シリーズ名: Cambridge monographs on mathematical physics ; . Statistical field theory / Claude Itzykson, Jean-Michel Drouffe ; v. 2
所蔵情報: loading…
目次情報: 続きを見る
Contents of Volume 1
Preface
Diagrammatic methods / 7：
General Techniques / 7.1：
Definitions and notations / 7.1.1：
Connected graphs and cumulants / 7.1.2：
Irreducibility and Legendre transformation / 7.1.3：
Series expansions / 7.2：
High temperature expansion / 7.2.1：
The role of symmetries / 7.2.2：
Low temperature expansion--discrete case / 7.2.3：
Low temperature expansion--continuous case / 7.2.4：
Strong field expansions / 7.2.5：
Fermionic fields / 7.2.6：
Enumeration of graphs / 7.3：
Configuration numbers with exclusion constraint / 7.3.1：
Multiply connected graphs / 7.3.2：
Results and analysis / 7.4：
Series analysis / 7.4.1：
An example: the Ising series on a body centered cubic lattice / 7.4.2：
Notes
Numerical simulations / 8：
Algorithms / 8.1：
Generalities / 8.1.1：
The classical algorithms / 8.1.2：
Microcanonical simulations / 8.1.3：
Practical considerations / 8.1.4：
Extraction of results in a simulation / 8.2：
Determination of transitions / 8.2.1：
Finite size effects / 8.2.2：
Monte Carlo renormalization group / 8.2.3：
Dynamics and the Langevin equation / 8.2.4：
Simulating fermions / 8.3：
The quenched approximation / 8.3.1：
Dynamical fermions / 8.3.2：
Hadron mass calculation in lattice gauge theory / 8.3.3：
Conformal invariance / 9：
Energy-momentum tensor--Virasoro algebra / 9.1：
Energy-momentum tensor / 9.1.1：
Two-dimensional conformal transformations / 9.1.3：
Central charge / 9.1.4：
Virasoro algebra / 9.1.5：
The Kac determinant / 9.1.6：
Unitary and minimal representations / 9.1.7：
Characters of the Virasoro algebra / 9.1.8：
Examples / 9.2：
Gaussian model / 9.2.1：
Ising model / 9.2.2：
Three state Potts model / 9.2.3：
Finite size effects and modular invariance / 9.3：
Partition functions on a torus / 9.3.1：
Kronecker's limit formula / 9.3.2：
The A-D-E classification of minimal models / 9.3.3：
Frustrations and discrete symmetries / 9.3.5：
Nonminimal models / 9.3.6：
Correlations in a half plane / 9.3.7：
The vicinity of the critical point / 9.3.8：
Jacobian [theta]-series and products / 9.A：
Superconformal algebra / 9.B：
Current algebra / 9.C：
Simple Lie algebras / 9.C.1：
The Wess-Zumino-Witten model / 9.C.2：
Representations and characters of KacMoody algebras / 9.C.3：
Disordered systems and fermionic methods / 10：
One-dimensional models / 10.1：
Gaussian random potential / 10.1.1：
Fokker-Planck equation / 10.1.2：
The replica trick / 10.1.3：
Random one-dimensional lattice / 10.1.4：
Two-dimensional electron gas in a strong field / 10.2：
Landau levels - Quantum Hall effect / 10.2.1：
One particle spectrum in the presence of impurities / 10.2.2：
Random matrices / 10.3：
Semicircle law / 10.3.1：
The fermionic method / 10.3.2：
Level spacings / 10.3.3：
The planar approximation / 10.4：
Combinatorics / 10.4.1：
The planar approximation in quantum mechanics / 10.4.2：
Spin systems with random interactions / 10.5：
Random external field and dimensional transmutation / 10.5.1：
The two-dimensional Ising model with random bonds / 10.5.2：
The Hall conductance as a topological invariant / 10.A：
Random geometry / 11：
Random lattices / 11.1：
Poissonian lattices and cell statistics / 11.1.1：
Field equations / 11.1.2：
The spectrum of the Laplacian / 11.1.3：
Random surfaces / 11.2：
Piecewise linear surfaces / 11.2.1：
The conformal anomaly and the Liouville action / 11.2.2：
Sums over smooth surfaces / 11.2.3：
Discretized models / 11.2.4：
Index
Disordered systems and Fermionic methods / 1：
Contents of Volume 1
Preface
Diagrammatic methods / 7：
47.

図書
図書
47. Methods of noncommutative geometry for group C[*]-algebras (: pbk)
Do Ngoc Diep
出版情報: Boca Raton, FL. ; London : Chapman & Hall/CRC, c2000  351 p. ; 24 cm
シリーズ名: Research notes in mathematics ; 416
所蔵情報: loading…
目次情報: 続きを見る
Preface
Introduction / 1：
The Scope and an Example / 1.1：
The Problem / 1.1.1：
BDF K-Homology Functor / 1.1.2：
Topological Invariant Index / 1.1.3：
Multidimensional Orbit Methods / 1.2：
Multidimensional Quantization / 1.2.1：
Category O and Globalization of Harish-Chandra Modules / 1.2.2：
KK-theory Invariant Index C* (G) / 1.3：
About KK-Functors / 1.3.1：
Construction and Reduction of the K-theory Invariant Index C* (G) / 1.3.2：
Deformation Quantization and Cyclic Theories / 1.4：
Star-products and Star-representations / 1.4.1：
Periodic Cyclic Homology / 1.4.2：
Chern Characters / 1.4.3：
Bibliographical Remarks / 1.5：
Elementary Theory: An Overview Based on Examples / I：
Classification of MD-Groups / 2：
Definitions / 2.1：
MD-criteria / 2.2：
Classification Theorem / 2.3：
The Structure of C*-algebras of MD-groups / 2.4：
The C*-algebra of Aff R / 3.1：
Statement of Theorems / 3.1.1：
Proof of Theorem 3.1 / 3.1.2：
Proof of Theorem 3.2 / 3.1.3：
Proof of Theorem 3.3 / 3.1.4：
The Structure of C* (Aff C) / 3.2：
Classification of MD[subscript 4]-groups / 3.3：
Real Diamond Group and Semidirect Products R [times] H[subscript 3] / 4.1：
Description of the Coadjoint Orbits / 4.2：
Some Remarks about the Coadjoint Representation / 4.3.1：
Description of Coadjoint Orbits / 4.3.2：
Measurable MD4-foliations / 4.4：
Measurable Foliations after A. Connes / 4.4.1：
Measurable MD[subscript 4]-foliations / 4.4.2：
Topological Classification of MD[subscript 4]-foliations / 4.4.3：
The Structure of C*-algebras of MD[subscript 4]-foliations / 4.5：
C*-algebras of Measurable Foliations / 5.1：
Holonomy Group of Foliations / 5.1.1：
Half-density Bundle / 5.1.2：
Connes-Thom Isomorphism / 5.1.3：
The C*-algebras of Measureable MD[subscript 4]-foliations / 5.2：
C*-algebras of MD[subscript 4]-foliations and Bundle Type / 5.2.1：
C*-algebras of MD[subscript 4]-foliations of Crossed Product Type / 5.2.2：
Advanced Theory: Multidimensional Quantization and the Index of Group C*-algebras / 5.3：
Induced Representations. Mackey Method of Small Subgroups / 6：
Criterion of Inductibility / 6.1.1：
The Mackey Method of Small Subgroups / 6.1.2：
Projective Representations and Mackey Obstructions / 6.1.3：
Symplectic Manifolds with Flat Action of Lie Groups / 6.2：
Flat Action / 6.2.1：
Classification / 6.2.2：
Prequantization / 6.3：
Quantization Procedure / 6.3.1：
Application / 6.3.2：
Polarization / 6.4：
Some Ideas from Physics / 6.4.1：
(F, [sigma])-polarizations and Polarizations / 6.4.2：
Complex Polarizations / 6.4.3：
Weak Lagrangian Distributions / 6.4.4：
Duflo Data / 6.4.5：
Partially Invariant Holomorphically Induced Representations / 6.5：
Holomorphically Induced Representations Lie Derivative / 7.1：
Unitarization / 7.1.1：
Lie Derivation / 7.1.3：
Irreducible Representations of Nilpotent Lie Groups / 7.2：
Duflo Construction / 7.2.1：
Metaplectic Shale-Weil Representation / 7.2.2：
Irreducible Unitary Representations of Nilpotent Lie Groups / 7.2.3：
Irreducible Representations of Extensions of Nilpotent Lie Groups / 7.2.4：
Representations of Connected Reductive Groups / 7.3：
Harish-Chandra Construction of [pi]([Lambda], [lambda]) / 7.3.1：
(Possibly Nonconnected) Reductive Groups / 7.3.2：
The Induction Procedure for General (Separable) Lie Groups / 7.3.3：
Representations of Almost Algebraic Lie Groups / 7.4：
Coisotropic Subalgebras / 7.4.1：
Irreducible Representations / 7.4.2：
The Trace Formula and the Plancherel Formula / 7.5：
Trace Formula / 7.5.1：
Plancherel Formula for Unimodular Groups / 7.5.2：
Reduction, Modification, and Supervision / 7.6：
Reduction to the Semisimple or Reductive Cases / 8.1：
Coisotropic Tangent Distributions / 8.1.1：
([sigma], [chi]F)-polarizations / 8.1.2：
Induced Representations Obtained from the Solvable or Unipotent Polarizations / 8.1.3：
Unitary Representations Arising in the Reduction of the Multidimensional Quantization Procedure / 8.1.4：
Multidimensional Quantization and U(1)-covering / 8.2：
Positive Polarizations / 8.2.1：
Lifted Characters / 8.2.2：
Induced Representations / 8.2.3：
U(1)-covering of Radicals and Semisimple or Reductive Data / 8.2.4：
Induction from Semisimple Data / 8.2.6：
A Reduction of the Multidimensional Quantization Procedure on the U(1)-covering / 8.2.7：
Globalization over U(1)-coverings / 8.3：
Classical Constructions and Three Geometric Complexes / 8.3.1：
Isomorphisms of Cohomologies / 8.3.2：
Maximal Real Polarizations and Change of Polarizations / 8.3.3：
Quantization of Mechanical Systems with Supersymmetry / 8.4：
Hilbert Superbundles with Connection / 8.4.1：
Quantization Superoperators / 8.4.2：
Superpolarizations and Induced Representations / 8.4.3：
Index of Type I C*-algebras / 8.5：
Compact Type Ideals in Type I C*-algebras / 9.1：
Canonical Composition Series / 9.2：
Compactness Criteria for Group C*-algebras / 9.3：
Compactness Criteria / 9.4.1：
Application to Lie Group Representations / 9.5：
The Case of Solvable Lie Groups / 9.5.1：
Generic Representations of Reductive Lie Groups / 9.5.2：
Invariant Index of Group C*-algebras / 9.6：
The Structure of Group C*-algebras / 10.1：
Construction of Index C* (G) / 10.2：
Reduction of the Indices / 10.3：
General Remarks on Computation of Indices / 10.4：
References / 10.5：
Preface
Introduction / 1：
The Scope and an Example / 1.1：
48.

図書
図書
48. 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
所蔵情報: loading…
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.：
49.

図書
図書
49. Topological graph theory
Jonathan L. Gross, Thomas W. Tucker
出版情報: New York : Wiley, c1987  xv, 351 p. ; 24 cm
シリーズ名: Wiley interscience series in discrete mathematics and optimization
所蔵情報: loading…
目次情報: 続きを見る
Introduction / 1.：
Representation of graphs / 1.1.：
Drawings / 1.1.1.：
Incidence matrix / 1.1.2.：
Euler's theorem on valence sum / 1.1.3.：
Adjacency matrix / 1.1.4.：
Directions / 1.1.5.：
Graphs, maps, isomorphisms / 1.1.6.：
Automorphisms / 1.1.7.：
Exercises / 1.1.8.：
Some important classes of graphs / 1.2.：
Walks, paths, and cycles; connectedness / 1.2.1.：
Trees / 1.2.2.：
Complete graphs / 1.2.3.：
Cayley graphs / 1.2.4.：
Bipartite graphs / 1.2.5.：
Bouquets of circles / 1.2.6.：
New graphs from old / 1.2.7.：
Subgraphs / 1.3.1.：
Topological representations, subdivisions, graph homeomorphisms / 1.3.2.：
Cartesian products / 1.3.3.：
Edge-complements / 1.3.4.：
Suspensions / 1.3.5.：
Amalgamations / 1.3.6.：
Regular quotients / 1.3.7.：
Regular coverings / 1.3.8.：
Surfaces and imbeddings / 1.3.9.：
Orientable surfaces / 1.4.1.：
Nonorientable surfaces / 1.4.2.：
Imbeddings / 1.4.3.：
Euler's equation for the sphere / 1.4.4.：
Kuratowski's graphs / 1.4.5.：
Genus of surfaces and graphs / 1.4.6.：
The torus / 1.4.7.：
Duality / 1.4.8.：
More graph-theoretic background / 1.4.9.：
Traversability / 1.5.1.：
Factors / 1.5.2.：
Distance, neighborhoods / 1.5.3.：
Graphs colorings and map colorings / 1.5.4.：
Edge operations / 1.5.5.：
Algorithms / 1.5.6.：
Connectivity / 1.5.7.：
Planarity / 1.5.8.：
A nearly complete sketch of the proof / 1.6.1.：
Connectivity and region boundaries / 1.6.2.：
Edge contraction and connectivity / 1.6.3.：
Planarity theorems for 3-connected graphs / 1.6.4.：
Graphs that are not 3-connected / 1.6.5.：
Kuratowski graphs for higher genus / 1.6.6.：
Other planarity criteria / 1.6.8.：
Voltage Graphs and Covering Spaces / 1.6.9.：
Ordinary voltages / 2.1.：
Drawings of voltage graphs / 2.1.1.：
Fibers and the natural projection / 2.1.2.：
The net voltage on a walk / 2.1.3.：
Unique walk lifting / 2.1.4.：
Preimages of cycles / 2.1.5.：
Which graphs are derivable with ordinary voltages? / 2.1.6.：
The natural action of the voltage group / 2.2.1.：
Fixed-point free automorphisms / 2.2.2.：
Cayley graphs revisited / 2.2.3.：
Automorphism groups of graphs / 2.2.4.：
Irregular covering graphs / 2.2.5.：
Schreier graphs / 2.3.1.：
Relative voltages / 2.3.2.：
Combinatorial coverings / 2.3.3.：
Most regular graphs are Schreier graphs / 2.3.4.：
Permutation voltage graphs / 2.3.5.：
Constructing covering spaces with permutations / 2.4.1.：
Preimages of walks and cycles / 2.4.2.：
Which graphs are derivable by permutation voltages? / 2.4.3.：
Identifying relative voltages with permutation voltages / 2.4.4.：
Subgroups of the voltage group / 2.4.5.：
The fundamental semigroup of closed walks / 2.5.1.：
Counting components of ordinary derived graphs / 2.5.2.：
The fundamental group of a graph / 2.5.3.：
Contracting derived graphs onto Cayley graphs / 2.5.4.：
Surfaces and Graph Imbeddings / 2.5.5.：
Surfaces and simplicial complexes / 3.1.：
Geometric simplicial complexes / 3.1.1.：
Abstract simplicial complexes / 3.1.2.：
Triangulations / 3.1.3.：
Cellular imbeddings / 3.1.4.：
Representing surfaces by polygons / 3.1.5.：
Pseudosurfaces and block designs / 3.1.6.：
Orientations / 3.1.7.：
Stars, links, and local properties / 3.1.8.：
Band decompositions and graph imbeddings / 3.1.9.：
Band decomposition for surfaces / 3.2.1.：
Orientability / 3.2.2.：
Rotation systems / 3.2.3.：
Pure rotation systems and orientable surfaces / 3.2.4.：
Drawings of rotation systems / 3.2.5.：
Tracing faces / 3.2.6.：
Which 2-complexes are planar? / 3.2.7.：
The classification of surfaces / 3.2.9.：
Euler characteristic relative to an imbedded graph / 3.3.1.：
Invariance of Euler characteristic / 3.3.2.：
Edge-deletion surgery and edge sliding / 3.3.3.：
Completeness of the set of orientable models / 3.3.4.：
Completeness of the set of nonorientable models / 3.3.5.：
The imbedding distribution of a graph / 3.3.6.：
The absence of gaps in the genus range / 3.4.1.：
The absence of gaps in the crosscap range / 3.4.2.：
A genus-related upper bound on the crosscap number / 3.4.3.：
The genus and crosscap number of the complete graph K[subscript 7] / 3.4.4.：
Some graphs of crosscap number 1 but arbitarily large genus / 3.4.5.：
Maximum genus / 3.4.6.：
Distribution of genus and face sizes / 3.4.7.：
Algorithms and formulas for minimum imbeddings / 3.4.8.：
Rotation-system algorithms / 3.5.1.：
Genus of an amalgamation / 3.5.2.：
Crosscap number of an amalgamation / 3.5.3.：
The White-Pisanski imbedding of a cartesian product / 3.5.4.：
Genus and crosscap number of cartesian products / 3.5.5.：
Imbedded Voltage Graphs and Current Graphs / 3.5.6.：
The derived imbedding / 4.1.：
Lifting rotation systems / 4.1.1.：
Lifting faces / 4.1.2.：
The Kirchhoff Voltage Law / 4.1.3.：
Imbedded permutation voltage graphs / 4.1.4.：
An orientability test for derived surfaces / 4.1.5.：
Branched coverings of surfaces / 4.1.7.：
Riemann surfaces / 4.2.1.：
Extension of the natural covering projection / 4.2.2.：
Which branch coverings come from voltage graphs? / 4.2.3.：
The Riemann-Hurwitz equation / 4.2.4.：
Alexander's theorem / 4.2.5.：
Regular branched coverings and group actions / 4.2.6.：
Groups acting on surfaces / 4.3.1.：
Graph automorphisms and rotation systems / 4.3.2.：
Regular branched coverings and ordinary imbedded voltage graphs / 4.3.3.：
Which regular branched coverings come from voltage graphs? / 4.3.4.：
Applications to group actions on the surface S[subscript 2] / 4.3.5.：
Current graphs / 4.3.6.：
Ringel's generating rows for Heffter's schemes / 4.4.1.：
Gustin's combinatorial current graphs / 4.4.2.：
Orientable topological current graphs / 4.4.3.：
Faces of the derived graph / 4.4.4.：
Nonorientable current graphs / 4.4.5.：
Voltage-current duality / 4.4.6.：
Dual directions / 4.5.1.：
The voltage graph dual to a current graph / 4.5.2.：
The dual derived graph / 4.5.3.：
The genus of the complete bipartite graph K[subscript m, n] / 4.5.4.：
Map Colorings / 4.5.5.：
The Heawood upper bound / 5.1.：
Average valence / 5.1.1.：
Chromatically critical graphs / 5.1.2.：
The five-color theorem / 5.1.3.：
The complete-graph imbedding problem / 5.1.4.：
Triangulations of surfaces by complete graphs / 5.1.5.：
Quotients of complete-graph imbeddings and some variations / 5.1.6.：
A base imbedding for orientable case 7 / 5.2.1.：
Using a coil to assign voltages / 5.2.2.：
A current-graph perspective on case 7 / 5.2.3.：
Orientable case 4: doubling 1-factors / 5.2.4.：
About orientable cases 3 and 0 / 5.2.5.：
The regular nonorientable cases / 5.2.6.：
Some additional tactics / 5.3.1.：
Nonorientable cases 3 and 7 / 5.3.2.：
Nonorientable case 0 / 5.3.4.：
Nonorientable case 4 / 5.3.5.：
About nonorientable cases 1, 6, 9, and 10 / 5.3.6.：
Additional adjacencies for irregular cases / 5.3.7.：
Orientable case 5 / 5.4.1.：
Orientable case 10 / 5.4.2.：
About the other orientable cases / 5.4.3.：
Nonorientable case 5 / 5.4.4.：
About nonorientable cases 11, 8, and 2 / 5.4.5.：
The Genus of a Group / 5.4.6.：
The genus of abelian groups / 6.1.：
Recovering a Cayley graph from any of its quotients / 6.1.1.：
A lower bound for the genus of most abelian groups / 6.1.2.：
Constructing quadrilateral imbeddings for most abelian groups / 6.1.3.：
The symmetric genus / 6.1.4.：
Rotation systems and symmetry / 6.2.1.：
Reflections / 6.2.2.：
Quotient group actions on quotient surfaces / 6.2.3.：
Alternative Cayley graphs revisited / 6.2.4.：
Group actions and imbeddings / 6.2.5.：
Are genus and symmetric genus the same? / 6.2.6.：
Euclidean space groups and the torus / 6.2.7.：
Triangle groups / 6.2.8.：
Groups of small symmetric genus / 6.2.9.：
The Riemann-Hurwitz equation revisited / 6.3.1.：
Strong symmetric genus 0 / 6.3.2.：
Symmetric genus 1 / 6.3.3.：
The geometry and algebra of groups of symmetric genus 1 / 6.3.4.：
Hurwitz's theorem / 6.3.5.：
Groups of small genus / 6.3.6.：
An example / 6.4.1.：
A face-size inequality / 6.4.2.：
Statement of main theorem / 6.4.3.：
Proof of Theorem 6.4.2: valence d = 4 / 6.4.4.：
Proof of Theorem 6.4.2: valence d = 3 / 6.4.5.：
Remarks about Theorem 6.4.2 / 6.4.6.：
References / 6.4.7.：
Bibliography
Supplementary Bibliography
Table of Notations
Subject Index
Introduction / 1.：
Representation of graphs / 1.1.：
Drawings / 1.1.1.：
50.

図書
図書
50. Stochastic processes : lectures given at Aarhus University
Kiyosi Itô ; edited by Ole E. Barndorff-Nielsen, Ken-iti Sato
出版情報: Berlin ; Tokyo : Springer, c2004  xii, 234 p. ; 24 cm
所蔵情報: loading…
目次情報: 続きを見る
Preliminaries / 0：
Independence / 0.1：
Central Values and Dispersions / 0.2：
Centralized Sum of Independent Random Variables / 0.3：
Infinitely Divisible Distributions / 0.4：
Continuity and Discontinuity of Infinitely Divisible Distributions / 0.5：
Conditional Probability and Expectation / 0.6：
Martingales / 0.7：
Additive Processes (Processes with Independent Increments) / 1：
Definitions / 1.1：
Decomposition of Additive Processes / 1.2：
The Levy Modification of Additive Processes Continuous in Probability / 1.3：
Elementary Lévy Processes / 1.4：
Fundamental Lemma / 1.5：
Structure of Sample Functions of Lévy Processes (a) / 1.6：
Structure of Sample Functions of Lévy Processes (b) / 1.7：
Three Components of Lévy Processes / 1.8：
Random Point Measures / 1.9：
Homogeneous Additive Processes and Homogeneous Lévy Processes / 1.10：
Levy Processes with Increasing Paths / 1.11：
Stable Processes / 1.12：
Markov Processes / 2：
Transition Probabilities and Transition Operators on Compact Metrizable Spaces / 2.1：
Summary of the Hille-Yosida Theory of Semi-Groups / 2.2：
Transition Semi-Group / 2.3：
Probability Law of the Path / 2.4：
Markov Property / 2.5：
The s-Algebras B, Bt, and B(S) / 2.6：
Strong Markov Property / 2.7：
Superposition of Stopping Times / 2.8：
An Inequality of Kolmogorov Type and its Application / 2.9：
Hitting Times of Closed Sets / 2.10：
Dynkin's Formula / 2.11：
Markov Processes in Generalized Sense / 2.12：
Examples / 2.13：
Markov Processes with a Countable State Space / 2.14：
Fine Topology / 2.15：
Generator in Generalized Sense / 2.16：
The Kac Semi-Group and its Application to the Arcsine Law / 2.17：
Markov Processes and Potential Theory / 2.18：
Brownian Motion and the Dirichlet Problem / 2.19：
Exercises
Chapter 0 / E.0：
Chapter 1 / E.1：
Chapter 2 / E.2：
Appendix: Solutions of Exercises
Index / A.0：
Preliminaries / 0：
Independence / 0.1：
Central Values and Dispersions / 0.2：
文献の複写および貸借の依頼を行う
 文献複写・貸借依頼