close
1.

図書
図書
1. 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：
2.

図書
図書
2. 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：
3.

図書
図書
3. 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：
4.

図書
図書
4. 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：
5.

図書
図書
5. 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：
6.

図書
図書
6. An introduction to dynamical systems (: hard ; : pbk)
D.K. Arrowsmith, C.M. Place
出版情報: Cambridge [England] ; New York : Cambridge University Press, 1990  423 p. ; 26 cm
所蔵情報: loading…
目次情報: 続きを見る
Preface
Diffeomorphisms and flows / 1：
Introduction / 1.1：
Elementary dynamics of diffeomorphisms / 1.2：
Definitions / 1.2.1：
Diffeomorphisms of the circle / 1.2.2：
Flows and differential equations / 1.3：
Invariant sets / 1.4：
Conjugacy / 1.5：
Equivalence of flows / 1.6：
Poincare maps and suspensions / 1.7：
Periodic non-autonomous systems / 1.8：
Hamiltonian flows and Poincare maps / 1.9：
Exercises
Local properties of flows and diffeomorphisms / 2：
Hyperbolic linear diffeomorphisms and flows / 2.1：
Hyperbolic non-linear fixed points / 2.2：
Diffeomorphisms / 2.2.1：
Flows / 2.2.2：
Normal forms for vector fields / 2.3：
Non-hyperbolic singular points of vector fields / 2.4：
Normal forms for diffeomorphisms / 2.5：
Time-dependent normal forms / 2.6：
Centre manifolds / 2.7：
Blowing-up techniques on R[superscript 2] / 2.8：
Polar blowing-up / 2.8.1：
Directional blowing-up / 2.8.2：
Structural stability, hyperbolicity and homoclinic points / 3：
Structural stability of linear systems / 3.1：
Local structural stability / 3.2：
Flows on two-dimensional manifolds / 3.3：
Anosov diffeomorphisms / 3.4：
Horseshoe diffeomorphisms / 3.5：
The canonical example / 3.5.1：
Dynamics on symbol sequences / 3.5.2：
Symbolic dynamics for the horseshoe diffeomorphism / 3.5.3：
Hyperbolic structure and basic sets / 3.6：
Homoclinic points / 3.7：
The Melnikov function / 3.8：
Local bifurcations I: planar vector fields and diffeomorphisms on R / 4：
Saddle-node and Hopf bifurcations / 4.1：
Saddle-node bifurcation / 4.2.1：
Hopf bifurcation / 4.2.2：
Cusp and generalised Hopf bifurcations / 4.3：
Cusp bifurcation / 4.3.1：
Generalised Hopf bifurcations / 4.3.2：
Diffeomorphisms on R / 4.4：
D[subscript x]f(0) = +1: the fold bifurcation / 4.4.1：
D[subscript x]f(0) = -1: the flip bifurcation / 4.4.2：
The logistic map / 4.5：
Local bifurcations II: diffeomorphisms on R[superscript 2] / 5：
Arnold's circle map / 5.1：
Irrational rotations / 5.3：
Rational rotations and weak resonance / 5.4：
Vector field approximations / 5.5：
Irrational [beta] / 5.5.1：
Rational [beta] = p/q, q [greater than or equal] 3 / 5.5.2：
Rational [beta] = p/q, q = 1, 2 / 5.5.3：
Equivariant versal unfoldings for vector field approximations / 5.6：
q = 2 / 5.6.1：
q = 3 / 5.6.2：
q = 4 / 5.6.3：
q [greater than or equal] 5 / 5.6.4：
Unfoldings of rotations and shears / 5.7：
Area-preserving maps and their perturbations / 6：
Rational rotation numbers and Birkhoff periodic points / 6.1：
The Poincare-Birkhoff Theorem / 6.2.1：
Vector field approximations and island chains / 6.2.2：
Irrational rotation numbers and the KAM Theorem / 6.3：
The Aubry-Mather Theorem / 6.4：
Invariant Cantor sets for homeomorphisms on S[superscript 1] / 6.4.1：
Twist homeomorphisms and Mather sets / 6.4.2：
Generic elliptic points / 6.5：
Weakly dissipative systems and Birkhoff attractors / 6.6：
Birkhoff periodic orbits and Hopf bifurcations / 6.7：
Double invariant circle bifurcations in planar maps / 6.8：
Hints for exercises
References
Index
Preface
Diffeomorphisms and flows / 1：
Introduction / 1.1：
7.

図書
図書
7. Supersymmetry and equivariant de Rham theory
Victor W. Guillemin, Shlomo Sternberg
出版情報: Berlin : Springer, 1999  xxiii, 228 p. ; 25 cm
所蔵情報: loading…
目次情報: 続きを見る
Introduction
Equivariant Cohomology in Topology / 1：
Equivariant Cohomology via Classifying Bundles / 1.1：
Existence of Classifying Spaces / 1.2：
Bibliographical Notes for Chapter 1 / 1.3：
G* Modules / 2：
Differential-Geometric Identities / 2.1：
The Language of Superalgebra / 2.2：
From Geometry to Algebra / 2.3：
Cohomology / 2.3.1：
Acyclicity / 2.3.2：
Chain Homotopies / 2.3.3：
Free Actions and the Condition (C) / 2.3.4：
The Basic Subcomplex / 2.3.5：
Equivariant Cohomology of G* Algebras / 2.4：
The Equivariant de Rham Theorem / 2.5：
Bibliographical Notes for Chapter 2 / 2.6：
The Weil Algebra / 3：
The Koszul Complex / 3.1：
Classifying Maps / 3.2：
W* Modules / 3.4：
Bibliographical Notes for Chapter 3 / 3.5：
The Weil Model and the Cartan Model / 4：
The Mathai-Quillen Isomorphism / 4.1：
The Cartan Model / 4.2：
Equivariant Cohomology of W* Modules / 4.3：
H ((A ⊗ E)bas) does not depend on E / 4.4：
The Characteristic Homomorphism / 4.5：
Commuting Actions / 4.6：
The Equivariant Cohomology of Homogeneous Spaces / 4.7：
Exact Sequences / 4.8：
Bibliographical Notes for Chapter 4 / 4.9：
Cartan's Formula / 5：
The Cartan Model for W* Modules / 5.1：
Bibliographical Notes for Chapter 5 / 5.2：
Spectral Sequences / 6：
Spectral Sequences of Double Complexes / 6.1：
The First Term / 6.2：
The Long Exact Sequence / 6.3：
Useful Facts for Doing Computations / 6.4：
Functorial Behavior / 6.4.1：
Gaps / 6.4.2：
Switching Rows and Columns / 6.4.3：
The Cartan Model as a Double Complex
HG(A) as an S(g*)G-Module
Morphisms of G* Modules
Restricting the Group
Bibliographical Notes for Chapter 6 / 6.5：
Fermionic Integration / 7：
Definition and Elementary Properties / 7.1：
Integration by Parts / 7.1.1：
Change of Variables / 7.1.2：
Gaussian Integrals / 7.1.3：
Iterated Integrals / 7.1.4：
The Fourier Transform / 7.1.5：
The Mathai-Quillen Construction
The Fourier Transform of the Koszul Complex / 7.2：
Bibliographical Notes for Chapter 7 / 7.3：
Characteristic Classes / 8：
Vector Bundles / 8.1：
The Invariants / 8.2：
G = U(n) / 8.2.1：
G = O(n) / 8.2.2：
G = SO(2n) / 8.2.3：
Relations Between the Invariants / 8.3：
Restriction from U(n) to O(n) / 8.3.1：
Restriction from SO(2n) to U(n) / 8.3.2：
Restriction from U(n) to U(k) × U(ℓ) / 8.3.3：
Symplectic Vector Bundles / 8.4：
Consistent Complex Structures / 8.4.1：
Characteristic Classes of Symplectic Vector Bundles / 8.4.2：
Equivariant Characteristic Classes / 8.5：
Equivariant Chern classes / 8.5.1：
Equivariant Characteristic Classes of a Vector Bundle Over a Point / 8.5.2：
Equivariant Characteristic Classes as Fixed Point Data / 8.5.3：
The Splitting Principle in Topology
Bibliographical Notes for Chapter 8
Equivariant Symplectic Forms / 9：
Equivariantly Closed Two-Forms / 9.1：
The Case M = G / 9.2：
Equivariantly Closed Two-Forms on Homogeneous Spaces / 9.3：
The Compact Case / 9.4：
Minimal Coupling / 9.5：
Symplectic Reduction / 9.6：
The Duistermaat-Heckman Theorem / 9.7：
The Cohomology Ring of Reduced Spaces / 9.8：
Flag Manifolds / 9.8.1：
Delzant Spaces / 9.8.2：
Reduction: The Linear Case / 9.8.3：
Equivariant Duistermaat-Heckman
Group Valued Moment Maps
The Canonical Equivariant Closed Three-Form on G / 9.10.1：
The Exponential Map / 9.10.2：
G-Valued Moment Maps on Hamiltonian G-Manifolds / 9.10.3：
Conjugacy Classes / 9.10.4：
Bibliographical Notes for Chapter 9 / 9.11：
The Thom Class and Localization / 10：
Fiber Integration of Equivariant Forms / 10.1：
The Equivariant Normal Bundle / 10.2：
Modifying ν / 10.3：
Verifying that τ is a Thom Form / 10.4：
The Thom Class and the Euler Class / 10.5：
The Fiber Integral on Cohomology / 10.6：
Push-Forward in General / 10.7：
Localization / 10.8：
The Localization for Torus Actions / 10.9：
Bibliographical Notes for Chapter 10 / 10.10：
The Abstract Localization Theorem / 11：
Relative Equivariant de Rham Theory / 11.1：
Mayer-Vietoris / 11.2：
S(g*) Modules / 11.3：
The Chang-Skjelbred Theorem / 11.4：
Some Consequences of Equivariant Formality / 11.6：
Two Dimensional G-Manifolds / 11.7：
A Theorem of Goresky-Kottwitz-Mac Pherson / 11.8：
Bibliographical Notes for Chapter 11 / 11.9：
Appendix
Notions d'algèbre différentielle; application aux groupes de Lie et aux variétés où opère un groupe de Lie / Henri Cartan
La transgression dans un groupe de Lie et dans un espace fibré principal
Bibliography
Index
Introduction
Equivariant Cohomology in Topology / 1：
Equivariant Cohomology via Classifying Bundles / 1.1：
8.

図書
図書
8. Elements of Bayesian statistics
Jean Pierre Florens, Michel Mouchart, Jean-Marie Rolin
出版情報: New York : M. Dekker, c1990  xxxi, 499 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 134
所蔵情報: loading…
目次情報: 続きを見る
Preface
Notation
Basic Tools and Notation from Probability Theory / 0.：
Introduction / 0.1.：
Measurable Spaces / 0.2.：
[sigma]-Fields / 0.2.1.：
Measurable Functions / 0.2.2.：
Product of Measurable Spaces / 0.2.3.：
Monotone Class Theorems / 0.2.4.：
Probability Spaces / 0.3.：
Measures and Integrals / 0.3.1.：
Probabilities. Expectations. Null Sets / 0.3.2.：
Transition and Product Probability / 0.3.3.：
Conditional Expectation / 0.3.4.：
Densities / 0.3.5.：
Bayesian Experiments / 1.：
The Basic Concepts of Bayesian Experiments / 1.1.：
General Definitions / 1.2.1.：
Dominated Experiments / 1.2.2.：
Three Remarks on Regular and Dominated Experiments / 1.2.3.：
A Remark Regarding the Interpretation of Bayesian Experiments / 1.2.4.：
A Remark on Sampling Theory and Bayesian Methods / 1.2.5.：
A Remark Regarding So-called "Improper" Prior Distributions / 1.2.6.：
Families of Bayesian Experiments / 1.2.7.：
Some Examples of Bayesian Experiments / 1.3.：
Reduction of Bayesian Experiments / 1.4.：
Marginal Experiments / 1.4.1.：
Conditional Experiment / 1.4.3.：
Complementary Reductions / 1.4.4.：
Dominance in Reduced Experiments / 1.4.5.：
Admissible Reductions: Sufficiency and Ancillarity / 2.：
Conditional Independence / 2.1.：
Definition of Conditional Independence / 2.2.1.：
Null Sets and Completion / 2.2.3.：
Basic Properties of Conditional Independence / 2.2.4.：
Conditional Independence and Densities / 2.2.5.：
Conditional Independence as Point Properties / 2.2.6.：
Admissible Reductions of an Unreduced Experiment / 2.3.：
Admissible Reductions on the Sample Space / 2.3.1.：
Admissible Reductions on the Parameter Space / 2.3.3.：
Some Comments on the Definitions / 2.3.4.：
Elementary Properties of Sufficiency and Ancillarity / 2.3.5.：
Sufficiency and Ancillarity in a Dominated Experiment / 2.3.6.：
Sampling Theory and Bayesian Methods / 2.3.7.：
A First Result on the Relations between Sufficiency and Ancillarity / 2.3.8.：
Admissible Reductions in Reduced Experiments / 3.：
Admissible Reduction in Marginal Experiments / 3.1.：
Basic Concepts / 3.2.1.：
Sufficiency and Ancillarity in Unreduced and in Marginal Experiments / 3.2.3.：
A Remark on "Partial" Sufficiency / 3.2.4.：
Admissible Reductions in Conditional Experiments / 3.3.：
Reductions in the Sample Space / 3.3.1.：
Reductions in the Parameter Space / 3.3.3.：
Elementary Properties / 3.3.4.：
Relationships between Sufficiency and Ancillarity / 3.3.5.：
Sufficiency and Ancillarity in a Dominated Reduced Experiment / 3.3.6.：
Jointly Admissible Reductions / 3.4.：
Mutual Sufficiency / 3.4.1.：
Mutual Exogeneity / 3.4.2.：
Bayesian Cut / 3.4.3.：
Joint Reductions in a Dominated Experiment / 3.4.4.：
Joint Reductions in a Conditional Experiment / 3.4.5.：
Some Examples / 3.4.6.：
Comparison of Experiments / 3.5.：
Comparison on the Sample Space: Sufficiency / 3.5.1.：
Comparison on the Parameter Space: Encompassing / 3.5.2.：
Optimal Reductions: Maximal Ancillarity and Minimal Sufficiency / 4.：
Maximal Ancillarity / 4.1.：
Projections of [sigma]-Fields / 4.3.：
Definition and Elementary Properties / 4.3.1.：
Projections and Conditional Independence / 4.3.3.：
Minimal Sufficiency / 4.4.：
Minimal Sufficiency in Unreduced and in Marginal Experiments / 4.4.1.：
Elementary Properties of Minimal Sufficiency / 4.4.2.：
Minimal Sufficiency in a Dominated Experiment / 4.4.3.：
Minimal Sufficiency in Conditional Experiment / 4.4.4.：
Optimal Mutual Sufficiency / 4.4.6.：
Identification Among [sigma]-Fields / 4.5.：
Identification in Bayesian Experiments / 4.6.：
Identification in a Reduced Experiment / 4.6.1.：
Exact and Totally Informative Experiments / 4.6.2.：
Punctual Exact Estimability / 4.8.：
Optimal Reductions: Further Results / 5.：
Measurable Separability / 5.1.：
Measurable Separability in Bayesian Experiments / 5.3.：
Measurably Separated Bayesian Experiment / 5.3.1.：
Basu Second Theorem / 5.3.2.：
Strong Identification of [sigma]-Fields / 5.3.3.：
Definition and General Properties / 5.4.1.：
Strong Identification and Conditional Independence / 5.4.2.：
Minimal Splitting / 5.4.3.：
Completeness in Bayesian Experiments / 5.5.：
Completeness and Sufficiency / 5.5.1.：
Completeness and Ancillarity / 5.5.2.：
Successive Reductions of a Bayesian Experiment / 5.5.3.：
Identifiability of Mixtures / 5.5.4.：
Sequential Experiments / 6.：
Sequences of Conditional Independences / 6.1.：
Definition of Sequential Experiments / 6.3.：
Admissible Reductions in Sequential Experiments / 6.3.2.：
Transitivity / 6.4.：
Basic Theory / 6.4.1.：
Markovian Property and Transitivity / 6.4.2.：
Relations Among Admissible Reductions / 6.5.：
Admissible Reductions in Joint Reductions / 6.5.1.：
The Role of Transitivity: Further Results / 6.6.：
Weakening of Transitivity Conditions / 6.6.1.：
Necessity of Transitivity Conditions / 6.6.2.：
Asymptotic Experiments / 7.：
Limit of Sequences of Conditional Independences / 7.1.：
Asymptotically Admissible Reductions / 7.3.：
Asymptotic Properties of Sequential Experiments / 7.3.1.：
Asymptotic Sufficiency / 7.3.2.：
Asymptotic Admissibility of Joint Reductions / 7.3.3.：
Asymptotically Admissible Reductions in Conditional Experiments / 7.3.4.：
Asymptotic Exact Estimability / 7.4.：
Exact Estimability and Bayesian Consistency / 7.4.1.：
Estimability of Discrete [sigma]-Fields / 7.4.2.：
Mutual Conditional Independence and Conditional 0-1 Laws / 7.6.：
Mutual Conditional Independence / 7.6.1.：
Sifted Sequences of [sigma]-Fields / 7.6.2.：
Tail-Sufficient and Independent Bayesian Experiments / 7.7.：
Bayesian Tail-Sufficiency / 7.7.1.：
Bayesian Independence / 7.7.2.：
Independent Tail-Sufficient Bayesian Experiments / 7.7.3.：
An Example / 7.8.：
Global and Sequential Analysis / 7.8.1.：
Asymptotic Analysis / 7.8.2.：
The Case [beta] = [infinity] / 7.8.3.：
The Case [beta less than sign infinity] / 7.8.4.：
Invariant Experiments / 8.：
Invariance, Ergodicity and Mixing / 8.1.：
Invariant Sets and Functions / 8.2.1.：
Invariance as Point Properties / 8.2.2.：
Invariance and Conditional Invariance of [sigma]-Fields / 8.2.3.：
Ergodicity and Mixing / 8.2.4.：
Existence of Invariant Measure / 8.2.5.：
Randomization of the Set of Transformations / 8.2.6.：
Construction and Definition of an Invariant Bayesian Experiment / 8.3.：
Invariance and Reduction / 8.3.2.：
Invariance and Exact Estimability / 8.3.3.：
Invariance in Stochastic Processes / 9.：
Bayesian Stochastic Processes and Representations / 9.1.：
Representation of Experiments / 9.2.1.：
Bayesian Stochastic Processes / 9.2.3.：
Shift and Permutations / 9.2.4.：
Standard Bayesian Stochastic Processes / 9.3.：
Stationary Processes / 9.3.1.：
Exchangeable and i.i.d. Processes / 9.3.2.：
Moving Average Processes / 9.3.3.：
Markovian Stationary Processes / 9.3.4.：
Autoregressive Moving Average Processes / 9.3.5.：
Conditional Stochastic Processes / 9.3.6.：
Shift in Conditional Stochastic Processes / 9.4.1.：
Conditional Shift-Invariance / 9.4.3.：
Bibliography
Author Index
Subject Index
Preface
Notation
Basic Tools and Notation from Probability Theory / 0.：
9.

図書
図書
9. Differential equations with Mathematica
Martha L. Abell, James P. Braselton
出版情報: Boston : Academic Press, c1993  viii, 631 p. ; 24 cm
所蔵情報: loading…
目次情報: 続きを見る
Preface
Introduction to Differential Equations / 1：
Definitions and Concepts / 1.1：
Solutions of Differential Equations / 1.2：
Initial and Boundary-Value Problems / 1.3：
Direction Fields / 1.4：
First-Order Ordinary Differential Equations / 2：
Theory of First-Order Equations: A Brief Discussion / 2.1：
Separation of Variables / 2.2：
Application: Kidney Dialysis
Homogeneous Equations / 2.3：
Application: Models of Pursuit
Exact Equations / 2.4：
Linear Equations / 2.5：
Integrating Factor Approach / 2.5.1：
Variation of Parameters and the Method of Undetermined Coefficients / 2.5.2：
Application: Antibiotic Production
Numerical Approximations of Solutions to First-Order Equations / 2.6：
Built-In Methods / 2.6.1：
Application: Modeling the Spread of a Disease
Other Numerical Methods / 2.6.2：
Applications of First-Order Ordinary Differential Equations / 3：
Orthogonal Trajectories / 3.1：
Application: Oblique Trajectories
Population Growth and Decay / 3.2：
The Malthus Model / 3.2.1：
The Logistic Equation / 3.2.2：
Application: Harvesting
Application: The Logistic Difference Equation
Newton's Law of Cooling / 3.3：
Free-Falling Bodies / 3.4：
Higher-Order Differential Equations / 4：
Preliminary Definitions and Notation / 4.1：
Introduction / 4.1.1：
The nth-Order Ordinary Linear Differential Equation / 4.1.2：
Fundamental Set of Solutions / 4.1.3：
Existence of a Fundamental Set of Solutions / 4.1.4：
Reduction of Order / 4.1.5：
Solving Homogeneous Equations with Constant Coefficients / 4.2：
Second-Order Equations / 4.2.1：
Higher-Order Equations / 4.2.2：
Application: Testing for Diabetes
Introduction to Solving Nonhomogeneous Equations with Constant Coefficients / 4.3：
Nonhomogeneous Equations with Constant Coefficients: The Method of Undetermined Coefficients / 4.4：
Nonhomogeneous Equations with Constant Coefficients: Variation of Parameters / 4.4.1：
Higher-Order Nonhomogeneous Equations / 4.5.1：
Cauchy-Euler Equations / 4.6：
Second-Order Cauchy-Euler Equations / 4.6.1：
Higher-Order Cauchy-Euler Equations / 4.6.2：
Variation of Parameters / 4.6.3：
Series Solutions / 4.7：
Power Series Solutions about Ordinary Points / 4.7.1：
Series Solutions about Regular Singular Points / 4.7.2：
Method of Frobenius / 4.7.3：
Application: Zeros of the Bessel Functions of the First Kind
Application: The Wave Equation on a Circular Plate
Nonlinear Equations / 4.8：
Applications of Higher-Order Differential Equations / 5：
Harmonic Motion / 5.1：
Simple Harmonic Motion / 5.1.1：
Damped Motion / 5.1.2：
Forced Motion / 5.1.3：
Soft Springs / 5.1.4：
Hard Springs / 5.1.5：
Aging Springs / 5.1.6：
Application: Hearing Beats and Resonance
The Pendulum Problem / 5.2：
Other Applications / 5.3：
L-R-C Circuits / 5.3.1：
Deflection of a Beam / 5.3.2：
Bode Plots / 5.3.3：
The Catenary / 5.3.4：
Systems of Ordinary Differential Equations / 6：
Review of Matrix Algebra and Calculus / 6.1：
Defining Nested Lists, Matrices, and Vectors / 6.1.1：
Extracting Elements of Matrices / 6.1.2：
Basic Computations with Matrices / 6.1.3：
Eigenvalues and Eigenvectors / 6.1.4：
Matrix Calculus / 6.1.5：
Systems of Equations: Preliminary Definitions and Theory / 6.2：
Preliminary Theory / 6.2.1：
Linear Systems / 6.2.2：
Homogeneous Linear Systems with Constant Coefficients / 6.3：
Distinct Real Eigenvalues / 6.3.1：
Complex Conjugate Eigenvalues / 6.3.2：
Alternate Method for Solving Initial-Value Problems / 6.3.3：
Repeated Eigenvalues / 6.3.4：
Nonhomogeneous First-Order Systems: Undetermined Coefficients, Variation of Parameters, and the Matrix Exponential / 6.4：
Undetermined Coefficients / 6.4.1：
The Matrix Exponential / 6.4.2：
Numerical Methods / 6.5：
Application: Controlling the Spread of a Disease / 6.5.1：
Euler's Method / 6.5.2：
Runge-Kutta Method / 6.5.3：
Nonlinear Systems, Linearization, and Classification of Equilibrium Points / 6.6：
Real Distinct Eigenvalues / 6.6.1：
Nonlinear Systems / 6.6.2：
Applications of Systems of Ordinary Differential Equations / 7：
Mechanical and Electrical Problems with First-Order Linear Systems / 7.1：
L-R-C Circuits with Loops / 7.1.1：
L-R-C Circuit with One Loop / 7.1.2：
L-R-C Circuit with Two Loops / 7.1.3：
Spring-Mass Systems / 7.1.4：
Diffusion and Population Problems with First-Order Linear Systems / 7.2：
Diffusion through a Membrane / 7.2.1：
Diffusion through a Double-Walled Membrane / 7.2.2：
Population Problems / 7.2.3：
Applications that Lead to Nonlinear Systems / 7.3：
Biological Systems: Predator-Prey Interactions, The Lotka-Volterra System, and Food Chains in the Chemostat / 7.3.1：
Physical Systems: Variable Damping / 7.3.2：
Differential Geometry: Curvature / 7.3.3：
Laplace Transform Methods / 8：
The Laplace Transform / 8.1：
Definition of the Laplace Transform / 8.1.1：
Exponential Order / 8.1.2：
Properties of the Laplace Transform / 8.1.3：
The Inverse Laplace Transform / 8.2：
Definition of the Inverse Laplace Transform / 8.2.1：
Laplace Transform of an Integral / 8.2.2：
Solving Initial-Value Problems with the Laplace Transform / 8.3：
Laplace Transforms of Step and Periodic Functions / 8.4：
Piecewise-Defined Functions: The Unit Step Function / 8.4.1：
Solving Initial-Value Problems / 8.4.2：
Periodic Functions / 8.4.3：
Impulse Functions: The Delta Function / 8.4.4：
The Convolution Theorem / 8.5：
Integral and Integrodifferential Equations / 8.5.1：
Applications of Laplace Transforms, Part I / 8.6：
Spring-Mass Systems Revisited / 8.6.1：
L-R-C Circuits Revisited / 8.6.2：
Population Problems Revisited / 8.6.3：
Application: The Tautochrone
Laplace Transform Methods for Systems / 8.7：
Applications of Laplace Transforms, Part II / 8.8：
Coupled Spring-Mass Systems / 8.8.1：
The Double Pendulum / 8.8.2：
Application: Free Vibration of a Three-Story Building
Eigenvalue Problems and Fourier Series / 9：
Boundary-Value Problems, Eigenvalue Problems, Sturm-Liouville Problems / 9.1：
Boundary-Value Problems / 9.1.1：
Eigenvalue Problems / 9.1.2：
Sturm-Liouville Problems / 9.1.3：
Fourier Sine Series and Cosine Series / 9.2：
Fourier Sine Series / 9.2.1：
Fourier Cosine Series / 9.2.2：
Fourier Series / 9.3：
Even, Odd, and Periodic Extensions / 9.3.1：
Differentiation and Integration of Fourier Series / 9.3.3：
Parseval's Equality / 9.3.4：
Generalized Fourier Series / 9.4：
Partial Differential Equations / 10：
Introduction to Partial Differential Equations and Separation of Variables / 10.1：
The One-Dimensional Heat Equation / 10.1.1：
The Heat Equation with Homogeneous Boundary Conditions / 10.2.1：
Nonhomogeneous Boundary Conditions / 10.2.2：
Insulated Boundary / 10.2.3：
The One-Dimensional Wave Equation / 10.3：
The Wave Equation / 10.3.1：
D'Alembert's Solution / 10.3.2：
Problems in Two Dimensions: Laplace's Equation / 10.4：
Laplace's Equation / 10.4.1：
Two-Dimensional Problems in a Circular Region / 10.5：
Laplace's Equation in a Circular Region / 10.5.1：
The Wave Equation in a Circular Region / 10.5.2：
Other Partial Differential Equations / 10.5.3：
Getting Started / Appendix：
Introduction to Mathematica
A Note Regarding Different Versions of Mathematica
Getting Started with Mathematica
Five Basic Rules of Mathematica Syntax
Loading Packages
A Word of Caution
Getting Help from Mathematica
Mathematica Help
The Mathematica Menu
Bibliography
Index
Preface
Introduction to Differential Equations / 1：
Definitions and Concepts / 1.1：
10.

図書
図書
10. Complex algebraic curves (: hard ; : pbk)
Frances Kirwan
出版情報: Cambridge : Cambridge University Press, 1992  viii, 264 p. ; 24 cm
シリーズ名: London Mathematical Society student texts ; 23
所蔵情報: loading…
目次情報: 続きを見る
Introduction and background / 1：
A brief history of algebraic curves / 1.1：
Relationship with other parts of mathematics / 1.2：
Number theory / 1.2.1：
Singularities and the theory of knots / 1.2.2：
Complex analysis / 1.2.3：
Abelian integrals / 1.2.4：
Real Algebraic Curves / 1.3：
Hilbert's Nullstellensatz / 1.3.1：
Techniques for drawing real algebraic curves / 1.3.2：
Real algebraic curves inside complex algebraic curves / 1.3.3：
Important examples of real algebraic curves / 1.3.4：
Foundations / 2：
Complex algebraic curves in C[superscript 2] / 2.1：
Complex projective spaces / 2.2：
Complex projective curves in P[subscript 2] / 2.3：
Affine and projective curves / 2.4：
Exercises / 2.5：
Algebraic properties / 3：
Bezout's theorem / 3.1：
Points of inflection and cubic curves / 3.2：
Topological properties / 3.3：
The degree-genus formula / 4.1：
The first method of proof / 4.1.1：
The second method of proof / 4.1.2：
Branched covers of P[subscript 1] / 4.2：
Proof of the degree-genus formula / 4.3：
Riemann surfaces / 4.4：
The Weierstrass [weierp]-function / 5.1：
Differentials on Riemann surfaces / 5.2：
Holomorphic differentials / 6.1：
Abel's theorem / 6.2：
The Riemann-Roch theorem / 6.3：
Singular curves / 6.4：
Resolution of singularities / 7.1：
Newton polygons and Puiseux expansions / 7.2：
The topology of singular curves / 7.3：
Algebra / 7.4：
Topology / B：
Covering projections / C.1：
The genus is a topological invariant / C.2：
Spheres with handles / C.3：
Introduction and background / 1：
A brief history of algebraic curves / 1.1：
Relationship with other parts of mathematics / 1.2：
文献の複写および貸借の依頼を行う
 文献複写・貸借依頼