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1.

図書
図書
1. Mental representation and processing of geographic knowledge : a computational approach
Thomas Barkowsky
出版情報: Berlin ; Tokyo : Springer, c2002  x, 174 p. ; 24 cm
シリーズ名: Lecture notes in computer science ; 2541 . Lecture notes in artificial intelligence
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Introduction / 1：
Mental Processing of Geographic Knowledge / 1.1：
Cognitive Maps / 1.1.1：
Mental Construction of Spatial Knowledge: An Example / 1.1.2：
Theses and Assumptions / 1.2：
Knowledge Construction and Human Memory / 1.2.1：
Characteristics of Geographic Knowledge / 1.2.2：
Spatial Knowledge Organization in Long-Term Memory / 1.2.3：
Visual Mental Images and Diagrammatic Reasoning / 1.2.4：
Research Questions and Goals / 1.3：
Research Questions / 1.3.1：
Goals / 1.3.2：
Approach: Experimental Computational Modeling / 1.4：
Computational Cognition / 1.4.1：
Building Computational Models / 1.4.2：
Modeling as Experimental Approach / 1.4.3：
Organization of this Thesis / 1.5：
State of the Art / 2：
Spatial Knowledge Conceptions: Cognitive Maps and Other Metaphors / 2.1：
Rubber Sheet Maps, Cognitive Atlases, Collages, and Geographic Information Systems / 2.1.1：
Spatial Mental Models / 2.1.3：
Other Conceptions / 2.1.4：
Human Memory / 2.2：
Working Memory / 2.2.1：
Long-Term Memory / 2.2.2：
Interacting Memory Systems in Mental Imagery / 2.2.3：
Mental Imagery / 2.3：
The Imagery Debate / 2.3.1：
Psychological and Neuroscientific Foundations / 2.3.2：
The Kosslyn Models / 2.3.3：
The 1980 Model / 2.3.3.1：
The 1994 Model / 2.3.3.2：
Spatial Reasoning / 2.4：
Topology / 2.4.1：
Orientation / 2.4.2：
Distance / 2.4.3：
Shape / 2.4.4：
Computational Geometry / 2.4.5：
Diagrammatic Reasoning / 2.5：
Propositional vs. Analogical Knowledge Representation / 2.5.1：
Types of Diagrammatic Reasoning Systems / 2.5.2：
Examples for Diagrammatic Reasoning Architectures / 2.5.3：
DEPIC-2D / 2.5.3.1：
WHISPER / 2.5.3.2：
Computational Imagery / 2.5.3.3：
Summary / 2.6：
MIRAGE - Developing the Model / 3：
Characteristics of the Model / 3.1：
Evaluating the Working Memory Representation / 3.1.1：
MIRAGE - Outline of the Model / 3.2：
Types of Entities and Spatial Relations in MIRAGE / 3.3：
Entities / 3.3.1：
Relations / 3.3.2：
Subsystems, Structures, and Processes / 3.4：
Long-Term Memory Activation / 3.4.1：
Spatial Knowledge Fragments / 3.4.1.1：
The Hierarchical Long-Term Memory Representation / 3.4.1.2：
The Access Process / 3.4.1.3：
The Activated Long-Term Memory Representation / 3.4.1.4：
The Construction Process / 3.4.1.5：
Visual Mental Image Construction / 3.4.2：
The Enriched Representation / 3.4.2.1：
The Conversion Process / 3.4.2.2：
The Visual Buffer / 3.4.2.3：
The Visualization Process / 3.4.2.4：
Image Inspection / 3.4.3：
The Inspection Result / 3.4.3.1：
The Inspection Process / 3.4.3.2：
Visual Mental Image Construction in Detail / 4：
A More Demanding Scenario / 4.1：
Diagrammatic Representations of Lean Knowledge / 4.2：
Consequences for Image Construction / 4.3：
Relaxation of Spatial Constraints / 4.3.1：
Completion of Qualitative Spatial Relations / 4.3.2：
Interpretation of Qualitative Spatial Relations / 4.3.3：
Image Revision Strategies in MIRAGE / 4.4：
Unstable Images / 4.4.1：
Omission of Facts / 4.4.2：
Revision of Relational Completion / 4.4.3：
Variation of Relational Completion / 4.4.3.1：
Relaxation of Relational Completion / 4.4.3.2：
Revision of Image Specification / 4.4.4：
Depicting Qualitative Spatial Relations / 4.4.4.1：
Depicting Unspecified Spatial Relations / 4.4.4.2：
MIRAGE Implementation / 4.5：
Computational Tools for Modeling: SIMSIS / 5.1：
The Idea of SIMSIS / 5.1.1：
The Aspect Map Model / 5.1.1.1：
Modeling Aspect Maps in SIMSIS / 5.1.1.2：
Depictions, Scenarios, and Interpretations / 5.1.2：
SIMSIS Pictures / 5.1.2.1：
SIMSIS Facts and Scenarios / 5.1.2.2：
SIMSIS Interpretations and Meaning Systems / 5.1.2.3：
Realization of the Model / 5.2：
MIRAGE Structures / 5.2.1：
Entities, Relations, and Spatial Knowledge Fragments / 5.2.1.1：
The Long-Term Memory Representations / 5.2.1.2：
MIRAGE Processes / 5.2.1.3：
The Long-Term Memory Activation Processes / 5.2.2.1：
The Image Construction Processes / 5.2.2.2：
Operation and Behavior of MIRAGE / 5.2.2.3：
Conclusion and Outlook / 6：
Results and Discussion / 6.1：
Reflecting the Theses / 6.2.1：
Spatial Knowledge Construction / 6.2.1.1：
Underdeterminacy in Long-Term Memory / 6.2.1.2：
Fragmentation and Hierarchical Organization / 6.2.1.3：
Visual Mental Imagery / 6.2.1.4：
The Parameters of the Model / 6.2.2：
Explicit Parameters / 6.2.2.1：
Implicit Parameters / 6.2.2.2：
Conclusions / 6.2.3：
Future Work / 6.3：
Extending MIRAGE / 6.3.1：
Geographic Entities and Spatial Relations / 6.3.1.1：
Partially Aggregated Knowledge Structures / 6.3.1.2：
Mental Imagery Functionality / 6.3.1.3：
Parameters of MIRAGE / 6.3.1.4：
Empirical Investigations / 6.3.2：
Use of Default Knowledge / 6.3.2.1：
Control of Image Construction / 6.3.2.2：
Processing Capacity for Mental Images / 6.3.2.3：
Use of Chunking Facilities / 6.3.2.4：
Combination of Propositional and Image-Based Reasoning / 6.3.2.5：
Application Perspectives / 6.3.3：
Adequate Presentation of Visual Information / 6.3.3.1：
External Support of Reasoning in Mental Images / 6.3.3.2：
Bibliography
Index
Introduction / 1：
Mental Processing of Geographic Knowledge / 1.1：
Cognitive Maps / 1.1.1：
2.

図書
図書
2. 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
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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：
3.

図書
図書
3. Fundamentals and applications of microfluidics
Nam-Trung Nguyen, Steven T. Wereley
出版情報: Boston : Artech House, c2002  xiii, 471 p. ; 24 cm
シリーズ名: MEMS--Microelectromechanical systems series
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Preface
Acknowledgments
Introduction / Chapter 1：
Microfluidics--The Emerging Technology / 1.1：
What Is Microfluidics? / 1.1.1：
Commercial Aspects / 1.1.2：
Scientific Aspects / 1.1.3：
Milestones of Microfluidics / 1.2：
Device Development / 1.2.1：
Technology Development / 1.2.2：
Organization of the Book / 1.3：
References
Fluid Mechanics Theory / Chapter 2：
Intermolecular Forces / 2.1：
The Three States of Matter / 2.1.2：
Continuum Assumption / 2.1.3：
Continuum Fluid Mechanics at Small Scales / 2.2：
Gas Flows / 2.2.1：
Liquid Flows / 2.2.2：
Boundary Conditions / 2.2.3：
Parallel Flows / 2.2.4：
Low Reynolds Number Flows / 2.2.5：
Entrance Effects / 2.2.6：
Surface Tension / 2.2.7：
Molecular Approaches / 2.3：
MD / 2.3.1：
DSMC Technique / 2.3.2：
Electrokinetics / 2.4：
Electro-Osmosis / 2.4.1：
Electrophoresis / 2.4.2：
Dielectrophoresis / 2.4.3：
Conclusion / 2.5：
Problems
Fabrication Techniques for Microfluidics / Chapter 3：
Basic Microtechniques / 3.1：
Photolithography / 3.1.1：
Additive Techniques / 3.1.2：
Subtractive Techniques / 3.1.3：
Pattern Transfer Techniques / 3.1.4：
Silicon-Based Micromachining Techniques / 3.2：
Silicon Bulk Micromachining / 3.2.1：
Silicon Surface Micromachining / 3.2.2：
Polymer-Based Micromachining Techniques / 3.3：
Thick Resist Lithography / 3.3.1：
Polymeric Surface Micromachining / 3.3.2：
Soft Lithography / 3.3.3：
Microstereo Lithography / 3.3.4：
Micromolding / 3.3.5：
Other Micromachining Techniques / 3.4：
Assembly and Packaging of Microfluidic Devices / 3.4.1：
Wafer Level Assembly and Packaging / 3.5.1：
Device Level Packaging / 3.5.2：
Biocompatibility / 3.6：
Material Response / 3.6.1：
Tissue and Cellular Response / 3.6.2：
Biocompatibility Tests / 3.6.3：
Experimental Flow Characterization / Chapter 4：
Pointwise Methods / 4.1：
Full-Field Methods / 4.1.2：
Overview of Micro-PIV / 4.2：
Fundamental Physics Considerations of Micro-PIV / 4.2.1：
Special Processing Methods for Micro-PIV Recordings / 4.2.2：
Advanced Processing Methods Suitable for Both Micro/Macro-PIV Recordings / 4.2.3：
Micro-PIV Examples / 4.3：
Flow in a Microchannel / 4.3.1：
Flow in a Micronozzle / 4.3.2：
Flow Around a Blood Cell / 4.3.3：
Flow in Microfluidic Biochip / 4.3.4：
Conclusions / 4.3.5：
Extensions of the Micro-PIV technique / 4.4：
Microfluidic Nanoscope / 4.4.1：
Microparticle Image Thermometry / 4.4.2：
Infrared Micro-PIV / 4.4.3：
Particle Tracking Velocimetry / 4.4.4：
Microfluidics for External Flow Control / Chapter 5：
Velocity and Turbulence Measurement / 5.1：
Velocity Sensors / 5.1.1：
Shear Stress Sensors / 5.1.2：
Turbulence Control / 5.2：
Microflaps / 5.2.1：
Microballoon / 5.2.2：
Microsynthetic Jet / 5.2.3：
Microair Vehicles / 5.3：
Fixed-Wing MAV / 5.3.1：
Flapping-Wing MAV / 5.3.2：
Microrotorcraft / 5.3.3：
Microrockets / 5.3.4：
Microfluidics for Internal Flow Control: Microvalves / Chapter 6：
Design Considerations / 6.1：
Actuators / 6.1.1：
Valve Spring / 6.1.2：
Valve Seat / 6.1.3：
Pressure Compensation Design / 6.1.4：
Pneumatic Valves / 6.2：
Pneumatic Actuators / 6.2.1：
Design Examples / 6.2.2：
Thermopneumatic Valves / 6.3：
Thermopneumatic Actuators / 6.3.1：
Thermomechanical Valves / 6.3.2：
Solid-Expansion Valves / 6.4.1：
Bimetallic Valves / 6.4.2：
Shape-Memory Alloy Valves / 6.4.3：
Piezoelectric Valves / 6.5：
Piezoelectric Actuators / 6.5.1：
Electrostatic Valves / 6.5.2：
Electrostatic Actuators / 6.6.1：
Electromagnetic Valves / 6.6.2：
Electromagnetic Actuators / 6.7.1：
Electrochemical Valves / 6.7.2：
Capillary-Force Valves / 6.9：
Capillary-Force Actuators / 6.9.1：
Microfluidics for Internal Flow Control: Micropumps / 6.9.2：
Mechanical Pumps / 7.1：
Check-Valve Pumps / 7.1.1：
Peristaltic Pumps / 7.1.3：
Valveless Rectification Pumps / 7.1.4：
Rotary Pumps / 7.1.5：
Centrifugal Pumps / 7.1.6：
Ultrasonic Pumps / 7.1.7：
Nonmechanical Pumps / 7.2：
Electrical Pumps / 7.2.1：
Surface Tension Driven Pumps / 7.2.2：
Chemical Pumps / 7.2.3：
Magnetic Pumps / 7.2.4：
Scaling Law for Micropumps / 7.3：
Microfluidics for Internal Flow Control: Microflow Sensors / Chapter 8：
Nonthermal Flow Sensors / 8.1：
Differential Pressure Flow Sensors / 8.1.1：
Drag Force Flow Sensors / 8.1.2：
Lift Force Flow Sensors / 8.1.3：
Coriolis Flow Sensors / 8.1.4：
Electrohydrodynamic Flow Sensors / 8.1.5：
Thermal Flow Sensors / 8.2：
Thermoresistive Flow Sensors / 8.2.1：
Thermocapacitive Flow Sensors / 8.2.3：
Thermoelectric Flow Sensors / 8.2.4：
Thermoelectronic Flow Sensors / 8.2.5：
Pyroelectric Flow Sensors / 8.2.6：
Frequency Analog Sensors / 8.2.7：
Microfluidics for Life Sciences and Chemistry / Chapter 9：
Microfilters / 9.1：
Microneedles / 9.1.1：
Micromixers / 9.2.1：
Microreactors / 9.3.1：
Microdispensers / 9.4.1：
Microseparators / 9.5.1：
Gas Chromatography / 9.6.1：
Liquid Chromatography / 9.6.3：
List of Symbols / 9.6.4：
Resources for Microfluidics Research / Appendix B：
Abbreviations of Different Plastics / Appendix C：
Linear Elastic Deflection Models / Appendix D：
About the Authors
Index
Preface
Acknowledgments
Introduction / Chapter 1：
4.

図書
図書
4. Polymer solutions : an introduction to physical properties
Iwao Teraoka
出版情報: New York : Wiley, c2002  xv, 338 p ; 25 cm
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Preface
Models of Polymer Chains / 1：
Introduction / 1.1：
Chain Architecture / 1.1.1：
Models of a Linear Polymer Chain / 1.1.2：
Real Chains and Ideal Chains / 1.1.3：
Ideal Chains / 1.2：
Random Walk in One Dimension / 1.2.1：
Random Walks in Two and Three Dimensions / 1.2.2：
Dimensions of Random-Walk Chains / 1.2.3：
Problems / 1.2.4：
Gaussian Chain / 1.3：
What is a Gaussian Chain? / 1.3.1：
Dimension of a Gaussian Chain / 1.3.2：
Entropy Elasticity / 1.3.3：
Real Chains / 1.3.4：
Excluded Volume / 1.4.1：
Dimension of a Real Chain / 1.4.2：
Self-Avoiding Walk / 1.4.3：
Semirigid Chains / 1.4.4：
Examples of Semirigid Chains / 1.5.1：
Wormlike Chain / 1.5.2：
Branched Chains / 1.5.3：
Architecture of Branched Chains / 1.6.1：
Dimension of Branched Chains / 1.6.2：
Molecular Weight Distribution / 1.6.3：
Average Molecular Weights / 1.7.1：
Typical Distributions / 1.7.2：
Concentration Regimes / 1.7.3：
Concentration Regimes for Linear Flexible Polymers / 1.8.1：
Concentration Regimes for Rodlike Molecules / 1.8.2：
Thermodynamics of Dilute Polymer Solutions / 1.8.3：
Polymer Solutions and Thermodynamics / 2.1：
Flory-Huggins Mean-Field Theory / 2.2：
Model / 2.2.1：
Free Energy, Chemical Potentials, and Osmotic Pressure / 2.2.2：
Dilute Solutions / 2.2.3：
Coexistence Curve and Stability / 2.2.4：
Polydisperse Polymer / 2.2.5：
Phase Diagram and Theta Solutions / 2.2.6：
Phase Diagram / 2.3.1：
Theta Solutions / 2.3.2：
Coil-Globule Transition / 2.3.3：
Solubility Parameter / 2.3.4：
Static Light Scattering / 2.3.5：
Sample Geometry in Light-Scattering Measurements / 2.4.1：
Scattering by a Small Particle / 2.4.2：
Scattering by a Polymer Chain / 2.4.3：
Scattering by Many Polymer Chains / 2.4.4：
Correlation Function and Structure Factor / 2.4.5：
Structure Factor of a Polymer Chain / 2.4.6：
Light Scattering of a Polymer Solution / 2.4.7：
Other Scattering Techniques / 2.4.8：
Size Exclusion Chromatography and Confinement / 2.4.9：
Separation System / 2.5.1：
Plate Theory / 2.5.2：
Partitioning of Polymer with a Pore / 2.5.3：
Calibration of SEC / 2.5.4：
SEC With an On-Line Light-Scattering Detector / 2.5.5：
Appendixes / 2.5.6：
Review of Thermodynamics for Colligative Properties in Nonideal Solutions / 2.A：
Osmotic Pressure / 2.A.1：
Vapor Pressure Osmometry / 2.A.2：
Another Approach to Thermodynamics of Polymer Solutions / 2.B：
Correlation Function of a Gaussian Chain / 2.C：
Dynamics of Dilute Polymer Solutions / 3：
Dynamics of Polymer Solutions / 3.1：
Dynamic Light Scattering and Diffusion of Polymers / 3.2：
Measurement System and Autocorrelation Function / 3.2.1：
Autocorrelation Function / 3.2.2：
Dynamic Structure Factor of Suspended Particles / 3.2.3：
Diffusion of Particles / 3.2.4：
Diffusion and DLS / 3.2.5：
Dynamic Structure Factor of a Polymer Solution / 3.2.6：
Hydrodynamic Radius / 3.2.7：
Particle Sizing / 3.2.8：
Diffusion From Equation of Motion / 3.2.9：
Diffusion as Kinetics / 3.2.10：
Concentration Effect on Diffusion / 3.2.11：
Diffusion in a Nonuniform System / 3.2.12：
Viscosity / 3.2.13：
Viscosity of Solutions / 3.3.1：
Measurement of Viscosity / 3.3.2：
Intrinsic Viscosity / 3.3.3：
Flow Field / 3.3.4：
Normal Modes / 3.3.5：
Rouse Model / 3.4.1：
Normal Coordinates / 3.4.2：
Equation of Motion for the Normal Coordinates in the Rouse Model / 3.4.3：
Results of the Normal-Coordinates / 3.4.4：
Results for the Rouse Model / 3.4.5：
Zimm Model / 3.4.6：
Dynamic Structure Factor / 3.4.7：
Motion of Monomers / 3.4.9：
Dynamics of Rodlike Molecules / 3.4.10：
Diffusion Coefficients / 3.5.1：
Rotational Diffusion / 3.5.2：
Dynamics of Wormlike Chains / 3.5.3：
Appendices / 3.5.6：
Evaluation of [left angle bracket]q[subscript i superscript 2 right angle bracket subscript eq] / 3.A：
Evaluation of [left angle bracket]exp[ik [middle dot] (Aq - Bp) right angle bracket] / 3.B：
Initial Slope of S[subscript 1](k,t) / 3.C：
Thermodynamics and Dynamics of Semidilute Solutions / 4：
Semidilute Polymer Solutions / 4.1：
Thermodynamics of Semidilute Polymer Solutions / 4.2：
Blob Model / 4.2.1：
Scaling Theory and Semidilute Solutions / 4.2.2：
Partitioning with a Pore / 4.2.3：
Dynamics of Semidilute Solutions / 4.2.4：
Cooperative Diffusion / 4.3.1：
Tube Model and Reptation Theory / 4.3.2：
References / 4.3.3：
Further Readings
Delta Function / A1：
Fourier Transform / A2：
Integrals / A3：
Series / A4：
Index
Preface
Models of Polymer Chains / 1：
Introduction / 1.1：
5.

図書
図書
5. 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
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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：
6.

図書
図書
6. Computational contact and impact mechanics : fundamentals of modeling interfacial phenomena in nonlinear finite element analysis
Tod A. Laursen
出版情報: Berlin ; Tokyo : Springer, c2002  xv, 454 p. ; 24 cm
シリーズ名: Engineering online library
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目次情報: 続きを見る
Preface
Introduction / 1：
Scope of this Monograph / 1.1：
Useful Background for this Presentation / 1.2：
Overview / 1.3：
Finite Element Formulations in Nonlinear Solid Mechanics / 2：
Initial/Boundary Value Problems in the Kinematically Lin-ear Regime / 2.1：
Strong Form of the EBVP / 2.1.1：
Weak Form of the IBVP / 2.1.2：
The IBVP in the Finite Strain Case / 2.2：
Notation and Problem Formulation / 2.2.1：
Finite Strain Kinematics / 2.2.2：
Stress Definitions Appropriate for Large Deformations / 2.2.3：
Frame Indifference / 2.2.4：
The Strong Form in Finite Strains / 2.2.5：
The Weak Form in Finite Strains / 2.2.6：
Finite Element Discretization / 2.3：
Discretized Weak Form; Generation of Discrete Non-linear Equations / 2.3.1：
Discrete Nonlinear Equations for the Kinematically Linear Case / 2.3.2：
Solution Strategies for Spatially Discrete Systems / 2.4：
Quasistatics and Incremental Load Methods / 2.4.1：
Dynamics and Global Time Stepping Procedures / 2.4.2：
Local (Constitutive) Time Stepping Procedures / 2.4.3：
Nonlinear Equation Solving / 2.4.4：
Consistent Algorithmic Linearization of Material Re-sponse / 2.4.5：
The Kinematically Linear Contact Problem / 3：
Strong Forms in Linearized Frictionless Contact / 3.1：
The Signorini Problem: Contact with a Rigid Obstacle / 3.1.1：
The Two Body Contact Problem / 3.1.2：
Weak Statements of the Contact Problem / 3.2：
Variational Inequalities / 3.2.1：
The Quasistatic Elastic Case: Contact as a Problem of Constrained Optimization / 3.2.2：
Methods of Constraint Enforcement / 3.3：
Classical Lagrange Multiplier Methods / 3.3.1：
Penalty Methods / 3.3.2：
Augmented Lagrangian Methods / 3.3.3：
Inclusion of Friction into the Problem Description / 3.4：
Friction Kinematics and Traction Measures / 3.4.1：
Unregularized Coulomb Friction Laws / 3.4.2：
Regularization of Friction / 3.4.3：
Variational Statements Including Friction / 3.4.4：
Nonlocal Frictional Descriptions / 3.4.5：
Continuum Mechanics of Large Deformation Contact / 4：
Two Body Contact Problem Definition / 4.1：
Local Momentum Balances / 4.1.1：
Initial and Boundary Conditions / 4.1.2：
Contact Constraints in Large Deformations / 4.2：
The Gap Function as Defined by Closest Point Projection / 4.2.1：
Frictional Kinematics on Interfaces / 4.2.2：
Frame Indifference of Contact Rate Variables / 4.2.3：
Coulomb Friction in Large Sliding / 4.2.4：
Summary: Strong Form of the Large Deformation Contact Problem / 4.3：
Virtual Work Expressions Incorporating Contact / 4.4：
Contact Virtual Work: The Contact Integral / 4.4.1：
Linearization of Contact Virtual Work / 4.4.2：
Summary: Weak Form of the Large Deformation Con-tact Problem / 4.4.3：
Finite Element Implementation of Contact Interaction / 5：
Finite Dimensional Representation of Contact Interaction / 5.1：
Contact Surface Discretization / 5.1.1：
Numerical Integration of the Contact Integral / 5.1.2：
Contact Detection (Searching) / 5.1.3：
Time Discretization / 5.2：
Global time integration schemes / 5.2.1：
Temporally Discrete Frictional Laws for the Penalty Regularized Case / 5.2.2：
Contact Stiffness and Residual: Penalty Regularized Case / 5.3：
Three dimensional matrix expressions / 5.3.1：
Two dimensional matrix expressions / 5.3.2：
Augmented Lagrangian Constraint Enforcement Algorithms / 5.4：
Uzawa's Method (Method of Multipliers) / 5.4.1：
Algorithmic Symmetrization Using Augmented La-grangians / 5.4.2：
Augmented Lagrangian Discrete Force and Stiffness Expressions / 5.4.3：
Numerical Examples / 5.5：
General Demonstrations of the Computational Frame-work / 5.5.1：
Demonstrations of Augmented Lagrangian Algorith-mic Performance / 5.5.2：
Tribological Complexity in Interface Constitutive Models / 6：
Rate and State Dependent Friction / 6.1：
Motivation / 6.1.1：
One Dimensional Model Development / 6.1.2：
Model Incorporation into Convective Slip Advected Frame / 6.1.3：
Local Time Stepping Algorithm / 6.1.4：
Contact Force Vector and Stiffness Matrix / 6.1.5：
Thermomechanically Coupled Friction on Interfaces / 6.1.6：
Thermally Coupled Problem Definition / 6.2.1：
A Thermodynamically Consistent Friction Model / 6.2.3：
Variational Principle and Finite Element Implemen-tation / 6.2.4：
Thermodynamical Algorithmic Consistency / 6.2.5：
Constitutive Framework for Bulk Continua / 6.3.1：
Thermomechanical Interface Model Framework / 6.3.2：
A Priori Stability Estimates for Dynamic Frictional Contact / 6.3.3：
A New Partitioned Scheme for Thermomechanical Contact / 6.3.4：
Algorithmic Treatment of Contact Conditions According to the Adiabatic Split / 6.3.5：
Energy-Momentum Approaches to Impact Mechanics / 7：
Energy Stability of Traditional Schemes / 7.1：
A Model System / 7.1.1：
The Concept of Energy Stability / 7.1.2：
Influence of Contact Constraints on System Energy / 7.1.3：
Energy-Momentum Methods for Elastodynamics / 7.2：
Conservation Laws / 7.2.1：
Conservative Discretization Schemes / 7.2.2：
Energy-Momentum Algorithmic Treatment of Prictionless Impact / 7.3：
Discrete Contact Constraints / 7.3.1：
Spatial Discretization and Implementation / 7.3.2：
Introduction of Frictional and Bulk Dissipation: Energy Con-sistency / 7.3.3：
Coulomb Friction Model Formulation / 7.4.1：
Local Split of the Coulomb Model / 7.4.2：
Algorithmic Formulation / 7.4.3：
Energy Consistent Treatment of Bulk Inelasticity / 7.4.4：
Numerical Examples With Friction and Inelasticity / 7.4.5：
EM Algorithms Involving a Discontinuous Velocity Update / 7.5：
Temporally Discontinuous Velocity Update / 7.5.1：
Reexamination of Conservation Conditions / 7.5.2：
Contact Constraints / 7.5.3：
Summary of the Algorithm / 7.5.4：
Emerging Paradigms for Contact Surface Discretization / 7.5.5：
Contact Smoothing / 8.1：
An Alternative Variational Framework / 8.1.1：
Smoothing Strategies in Two Dimensions / 8.1.2：
Smoothing Strategies in Three Dimensions / 8.1.3：
Mortar-Finite Element Methods for Contact Description / 8.1.4：
Tied Contact and the Role of Mortar Formulations in Convergence / 8.2.1：
A Mortar-Finite Element Formulation of Frictional Contact / 8.2.2：
Numerical Examples of Mortar Treatment of Frictional Contact / 8.2.3：
References
Index
Preface
Introduction / 1：
Scope of this Monograph / 1.1：
7.

図書
図書
7. Modular specification and verification of object-oriented programs
Peter Müller
出版情報: Berlin : Springer, c2002  xiv, 292 p. ; 24 cm
シリーズ名: Lecture notes in computer science ; 2262
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Introduction / 1：
Motivation / 1.1：
Specification and Verification Technique / 1.2：
The Problem / 1.3：
Modular Correctness / 1.3.1：
The Frame Problem / 1.3.2：
Modular Verification of Type Invariants / 1.3.3：
The Extended State Problem / 1.3.4：
Alias Control / 1.3.5：
Modularity Aspects of Programs, Specifications, and Proofs / 1.4：
Modularity of Programs / 1.4.1：
Modularity of Universal Specifications / 1.4.2：
Modularity of Interface Specifications / 1.4.3：
Modularity of Correctness Proofs / 1.4.4：
Approach, Outline, and Contributions / 1.5：
Approach / 1.5.1：
Outline / 1.5.2：
Contributions / 1.5.3：
Related Work / 1.6：
Specification Techniques / 1.6.1：
Verification and Analysis Techniques / 1.6.2：
Mojave and the Universe Type System / 2：
Mojave: The Language / 2.1：
The Language Core / 2.1.1：
Modularity / 2.1.2：
Universes: A Type System for Flexible Alias Control / 2.2：
The Ownership Model / 2.2.1：
The Universe Programming Model / 2.2.2：
Programming with Universes / 2.2.3：
Examples / 2.2.4：
Formalization of the Universe Type System / 2.2.5：
Discussion / 2.2.6：
The Semantics of Mojave / 2.3：
Programming Logic / 3.1：
Formal Data and State Model / 3.1.1：
Axiomatic Semantics / 3.1.2：
Language Properties / 3.1.3：
Type Safety / 3.2.1：
Liveness Properties / 3.2.2：
Properties of Readonly Methods / 3.2.3：
Correctness / 3.3：
Correctness of Closed Programs / 3.3.1：
Correctness of Open Programs: Modular Correctness / 3.3.2：
Modular Soundness / 3.3.3：
Composition of Modular Correct Open Programs / 3.3.4：
Modular Specification and Verification of Functional Behavior / 3.4：
Foundations of Interface Specifications / 4.1：
Specification of Functional Behavior / 4.2：
Abstract Fields / 4.2.1：
Pre-post-specifications / 4.2.2：
Verification of Functional Behavior / 4.3：
Verification of Method Bodies / 4.3.1：
Proofs for Virtual Methods / 4.3.2：
Example / 4.3.3：
Modular Specification and Verification of Frame Properties / 4.4：
Meaning of Modifies-Clauses / 5.1：
Explicit Dependencies / 5.1.2：
Modularity Rules / 5.1.3：
Formalization of Explicit Dependencies / 5.2：
Declaration of Dependencies / 5.2.1：
Axiomatization of the Depends-Relation / 5.2.2：
Consistency with Representation / 5.2.3：
Formalization of the Modularity Rules / 5.2.4：
Axiomatization of the Notdepends-Relation / 5.2.5：
Formalization of Modifies-Clauses / 5.2.6：
Verification of Frame Properties / 5.4：
Local Update Property / 5.4.1：
Accessibility Properties / 5.4.3：
Modularity Theorem for Frame Properties / 5.4.4：
Leino's and Nelson's Work on Dependencies / 5.4.5：
Other Work on the Frame Problem / 5.5.2：
Modular Specification and Verification of Type Invariants / 6：
Motivation and Approach / 6.1：
Invariant Semantics for Nonmodular Programs / 6.1.1：
Problems for Modular Verification of Invariants / 6.1.2：
Specification of Type Invariants / 6.1.3：
Declaration of Type Invariants / 6.2.1：
Formal Meaning of Invariants / 6.2.2：
Verification of Type Invariants / 6.3：
Verification Methodology / 6.3.1：
Module Invariants / 6.3.2：
History Constraints / 6.4.2：
Conclusion / 6.5：
Summary and Contributions / 7.1：
The Lopex Project / 7.2：
Tool Support / 7.3：
Directions for Future Work / 7.4：
Formal Background and Notations / A：
Formal Background / A.1：
Notations / A.2：
Predefined Type Declarations / B：
Doubly Linked List / C：
Property Editor / C.2：
Auxiliary Lemmas, Proofs, and Models / D：
Auxiliary Lemmas and Proofs from Chapter 3 / D.1：
Auxiliary Lemmas and Proofs from Chapter 5 / D.2：
Auxiliary Lemmas and Proofs from Chapter 6 / D.3：
A Model for the Axiomatization of the Depends-Relation / D.4：
Bibliography
List of Figures
Index
Introduction / 1：
Motivation / 1.1：
Specification and Verification Technique / 1.2：
8.

図書
図書
8. Number theory for computing. 2nd ed.
Song Y. Yan ; foreword by Martin E. Hellman
出版情報: Berlin : Springer-Verlag, c2002  xxii, 435 p. ; 24 cm
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目次情報: 続きを見る
Elementary Number Theory / 1：
Introduction / 1.1：
What is Number Theory? / 1.1.1：
Algebraic Preliminaries / 1.1.2：
Theory of Divisibility / 1.2：
Basic Properties of Divisibility / 1.2.1：
Fundamental Theorem of Arithmetic / 1.2.2：
Mersenne Primes and Fermat Numbers / 1.2.3：
Euclid's Algorithm / 1.2.4：
Continued Fractions / 1.2.5：
Diophantine Equations / 1.3：
Basic Concepts of Diophantine Equations / 1.3.1：
Linear Diophantine Equations / 1.3.2：
Pell's Equations / 1.3.3：
Arithmetic Functions / 1.4：
Multiplicative Functions / 1.4.1：
Functions ?(n), ?(n) and s(n) / 1.4.2：
Perfect, Amicable and Sociable Numbers / 1.4.3：
Functions ?(n), ?(n) and ?(n) / 1.4.4：
Distribution of Prime Numbers / 1.5：
Prime Distribution Function ?(x) / 1.5.1：
Approximations of ?(x) by x/ ln x / 1.5.2：
Approximations of ?(x) by Li(x) / 1.5.3：
The Riemann ?-Function ?(s) / 1.5.4：
The nth Prime / 1.5.5：
Distribution of Twin Primes / 1.5.6：
The Arithmetic Progression of Primes / 1.5.7：
Theory of Congruences / 1.6：
Basic Properties of Congruences / 1.6.1：
Modular Arithmetic / 1.6.2：
Linear Congruences / 1.6.3：
The Chinese Remainder Theorem / 1.6.4：
High-Order Congruences / 1.6.5：
Legendre and Jacobi Symbols / 1.6.6：
Orders and Primitive Roots / 1.6.7：
Indices and kth Power Residues / 1.6.8：
Arithmetic of Elliptic Curves / 1.7：
Basic Concepts of Elliptic Curves / 1.7.1：
Geometric Composition Laws of Elliptic Curves / 1.7.2：
Algebraic Computation Laws for Elliptic Curves / 1.7.3：
Group Laws on Elliptic Curves / 1.7.4：
Number of Points on Elliptic Curves / 1.7.5：
Bibliographic Notes and Further Reading / 1.8：
Algorithmic Number Theory / 2：
What is Algorithmic Number Theory? / 2.1：
E ective Computability / 2.1.2：
Computational Complexity / 2.1.3：
Complexity of Number-Theoretic Algorithms / 2.1.4：
Fast Modular Exponentiations / 2.1.5：
Fast Group Operations on Elliptic Curves / 2.1.6：
Algorithms for Primality Testing / 2.2：
Deterministic and Rigorous Primality Tests / 2.2.1：
Fermat's Pseudoprimality Test / 2.2.2：
Strong Pseudoprimality Test / 2.2.3：
Lucas Pseudoprimality Test / 2.2.4：
Elliptic Curve Test / 2.2.5：
Historical Notes on Primality Testing / 2.2.6：
Algorithms for Integer Factorization / 2.3：
Complexity of Integer Factorization / 2.3.1：
Trial Division and Fermat Method / 2.3.2：
Legendre's Congruence / 2.3.3：
Continued FRACtion Method (CFRAC) / 2.3.4：
Quadratic and Number Field Sieves (QS/NFS) / 2.3.5：
Polland's "rho" and "p - 1" Methods / 2.3.6：
Lenstra's Elliptic Curve Method (ECM) / 2.3.7：
Algorithms for Discrete Logarithms / 2.4：
Shanks' Baby-Step Giant-Step Algorithm / 2.4.1：
Silver{Pohlig{Hellman Algorithm / 2.4.2：
Subexponential Algorithms / 2.4.3：
Algorithm for the Root Finding Problem / 2.4.4：
Quantum Number-Theoretic Algorithms / 2.5：
Quantum Information and Computation / 2.5.1：
Quantum Computability and Complexity / 2.5.2：
Quantum Algorithm for Integer Factorization / 2.5.3：
Quantum Algorithms for Discrete Logarithms / 2.5.4：
Miscellaneous Algorithms in Number Theory / 2.6：
Algorithms for Computing ?(x) / 2.6.1：
Algorithms for Generating Amicable Pairs / 2.6.2：
Algorithms for Verifying Goldbach's Conjecture / 2.6.3：
Algorithm for Finding Odd Perfect Numbers / 2.6.4：
Applied Number Theory / 2.7：
Why Applied Number Theory? / 3.1：
Computer Systems Design / 3.2：
Representing Numbers in Residue Number Systems / 3.2.1：
Fast Computations in Residue Number Systems / 3.2.2：
Residue Computers / 3.2.3：
Complementary Arithmetic / 3.2.4：
Hashing Functions / 3.2.5：
Error Detection and Correction Methods / 3.2.6：
Random Number Generation / 3.2.7：
Cryptography and Information Security / 3.3：
Secret-Key Cryptography / 3.3.1：
Data/Advanced Encryption Standard (DES/AES) / 3.3.3：
Public-Key Cryptography / 3.3.4：
Discrete Logarithm Based Cryptosystems / 3.3.5：
RSA Public-Key Cryptosystem / 3.3.6：
Quadratic Residuosity Cryptosystems / 3.3.7：
Elliptic Curve Public-Key Cryptosystems / 3.3.8：
Digital Signatures / 3.3.9：
Digital Signature Algorithm/Standard (DSA/DSS) / 3.3.10：
Database Security / 3.3.11：
Secret Sharing / 3.3.12：
Internet/Web Security and Electronic Commerce / 3.3.13：
Steganography / 3.3.14：
Quantum Cryptography / 3.3.15：
Bibliography / 3.4：
Index
Elementary Number Theory / 1：
Introduction / 1.1：
What is Number Theory? / 1.1.1：
9.

図書
図書
9. 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
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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：
10.

図書
図書
10. 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：
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