The Bellman Continuum

The following sections are included:

• PREFACE

• CONTENTS

It is unusual to start the collected works of a famous person with anecdotes by his family. We are doing it because, despite the enormous productivity of Richard Bellman, one thing most people who knew him, remember is that he didn't act like the stereotype of an academician. He was a Renaissance man amid narrow specialists. He played tennis and chess, loved classical music and jazz, and was educated in the arts and literature of several nations. He knew many languages, including Sanskrit, Latin and Greek. He loved stories, jokes and puns. With wit and intelligence, he was rarely bombastic, but almost always dominating in presence…

The following sections are included:

• Introductory Comments

• ON THE THEORY OF DYNAMIC PROGRAMMING

• SOME APPLICATIONS OF THE THEORY OF DYNAMIC PROGRAMMING–A REVIEW

• THE THEORY OF DYNAMIC PROGRAMMING

• DYNAMIC PROGRAMMING AND LAGRANGE MULTIPLIERS

• ON A CLASS OF VARIATIONAL PROBLEMS

• DYNAMIC PROGRAMMING AND THE NUMERICAL SOLUTION OF VARIATIONAL PROBLEMS

The following sections are included:

• Introductory Comments

• ON THE EXISTENCE AND BOUNDEDNESS OF SOLUTIONS OF NON-LINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS

• ASYMPTOTIC SERIES FOR THE SOLUTIONS OF LINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS

• ON THE LIMIT OF SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATIONS AS THE RETARDATION APPROACHES ZERO

• ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF DIFFERENTIAL DIFFERENCE EQUATIONS

• STABILITY THEORY AND ADJOINT OPERATORS FOR LINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS

• Mathematical Experimentation in Time-Lag˜ Modulation

The following sections are included:

• Introductory Comments

• ON THE PRINCIPLE OF INVARIANT IMBEDDING AND PROPAGATION THROUGH INHOMOGENEOUS MEDIA

• ON THE PRINCIPLE OF INVARIANT IMBEDDING AND ONE-DIMENSIONAL NEUTRON MULTIPLICATION

• On the Principle of Invariant Imbedding and Neutron Transport Theory – I – One-Dimensional Case

• Invariant imbedding and Neutron Transport Theory II—Functional Equations

• INVARIANT IMBEDDING, WAVE PROPAGATION, AND THE WKB APPROXIMATION

• Invariant Imbedding and Neutron Transport Theory V — Diffusion as a Limiting Case

• INVARIANT IMBEDDING AND THE REDUCTION OF TWO-POINT BOUNDARY VALUE PROBLEMS TO INITIAL VALUE PROBLEMS

• Invariant Imbedding and Mathematical Physics. I. Particle Processes

• INVARIANT IMBEDDING AND RANDOM WALK

• Invariant Imbedding and the Computation of Internal Fields for Transport Processes

The following sections are included:

• Introductory Comments

• Inverse Problems in Radiative Transfer: Layered Media

• Estimation of Internal Source Distributions Using External Field Measurements in Radiative Transfer

• INVARIANT IMBEDDING AND A REFORMULATION OF THE INTERNAL INTENSITY PROBLEM IN RADIATIVE TRANSFER THEORY

• NUMERICAL RESULTS FOR THE AUXILIARY EQUATION OF RADIATIVE TRANSFER

• NUMERICAL RESULTS FOR CHANDRASEKHAR'S X AND Y FUNCTIONS OF RADIATIVE TRANSFER

The following sections are included:

• Introductory Comments

• SOME MATHEMATICAL ASPECTS OF CHEMOTHERAPY: I. ONE-ORGAN MODELS

• SOME MATHEMATICAL ASPECTS OF CHEMOTHERAPY—II: THE DISTRIBUTION OF A DRUG IN THE BODY

• A Mathematical Model of Drug Distribution in the Body: Implications for Cancer Chemotherapy

• SIMULATED MYOCARDIAL INFARCTION WITH A MATHEMATICAL MODEL OF THE HEART CONTAINING DISTANCE AND BOUNDARY EFFECTS

• Quasilinearization and the Estimation of Chemical Rate Constants from Raw Kinetic Data

• Topics in Pharmacokinetics, II: Identification of Time-Lag Processes

• Invariant Imbedding and Radiation Dosimetry: Finite Order Scattering and Transmission Function

The following sections are included:

• Introductory Comments

• FUNCTIONAL EQUATIONS IN THE THEORY OF DYNAMIC PROGRAMMING. v. POSITIVITY AND QUASI-LINEARITY

• ON EXPLICIT SOLUTIONS OF SOME TRINOMIAL EQUATIONS IN TERMS OF THE MAXIMUM OPERATION

• ON MONOTONE CONVERGENCE TO SOLUTIONS OF u′ = g(u, T)

• On the Computational Solution of Differential-Difference Equations

• On the iterative solution of two-point boundary value problems

• Some Numerical Experiments Using Newton's Method for Nonlinear Parabolic and Elliptic Boundary-Value Problems

• Successive Approximations and Computer Storage Problems in Ordinary Differential Equations

• ORBIT DETERMINATION AS A MULTI-POINT BOUNDARY-VALUE PROBLEM AND QUASILINEARIZATION

• DYNAMIC PROGRAMMING, INVARIANT IMBEDDING AND QUASILINEARIZATION: COMPARISONS AND INTERCONNECTIONS

• Quasilinearization, Boundary-Value Problems and Linear Programming

• ON THE IDENTIFICATION OF SYSTEMS AND THE UNSCRAMBLING OF DATA, I. HIDDEN PERIODICITIES

The following sections are included:

• Introductory Comments

• ON AGE-DEPENDENT BINARY BRANCHING PROCESSES

• On the Role of Dynamic Programming in Statistical Communication Theory

• Dynamic Programming and Stochastic Control Processes

• MATHEMATICAL MODELS OF CHEMOTHERAPY

• ON THE FOUNDATIONS OF A THEORY OF STOCHASTIC VARIATIONAL PROCESSES

• New Classes of Stochastic Control Processes

• DECISION-MAKING IN A FUZZY ENVIRONMENT

• On Moment Behavior of a Class of Stochastic Difference Equations

The following sections are included:

• Introductory Comments

• ON THE IDENTIFICATION OF SYSTEMS AND THE UNSCRAMBLING OF DATA: SOME PROBLEMS SUGGESTED BY NEUROPHYSIOLOGY

• QUASILINEARIZATION, SYSTEM IDENTIFICATION AND PREDICTION

• Segmental Differential Approximation and the “Black Box” Problem

• ON THE CONSTRUCTION OF A MATHEMATICAL THEORY OF THE IDENTIFICATION OF SYSTEMS

• A NOTE ON THE IDENTIFICATION OF LINEAR SYSTEMS

• Segmental Differential Approximation and Biological Systems: An Analysis of a Metabolic Process

• On the Identification of Systems and the Unscrambling of Data III: One-Dimensional Wave and Diffusion Processes

• A New Method for the Identification of Systems

• On Structural Identifiability

• Systems Identification with Partial Information

The following sections are included:

• Introductory Comments

• MAN, SOCIETY AND THE COMPUTER

• MYOPIA, CORNUCOPIA AND UTOPIA

• RESEARCH FOR SURVIVAL

• Communication, Ambiguity and Understanding

• SYSTEMS OF SOCIETY

• Mathematics in the Field of History

• MATHEMATICAL MODELING AND IDENTIFICATION

The following sections are included:

• APPENDIX 1 LIST OF PUBLISHED BOOKS

• BIODATA

• APPENDIX 2 LIST OF PUBLISHED PAPERS

• APPENDIX 3 SUBJECT INDEX

• APPENDIX 4 AUTHOR INDEX