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《Constraint Theory: Multidimensional Mathematical Model Management》第二版
约束理论：多维数学模型管理
作者：
George J. Friedman
Phan Phan
Viterbi School of Engineering
University of Southern California
出版社：Springer
出版时间：2017年
《Constraint Theory: Multidimensional Mathematical Model Management》第二版
《Constraint Theory: Multidimensional Mathematical Model Management》第二版
《Constraint Theory: Multidimensional Mathematical Model Management》第二版
《Constraint Theory: Multidimensional Mathematical Model Management》第二版
目录
CHAPTER 1 – MOTIVATIONS 1
WHAT IS CONSTRAINT THEORY AND WHY IS IT IMPORTANT?
1.1 TRENDS AND PROBLEMS IN SYSTEM TECHNOLOGIES
1.2 AN EXAMPLE OF LOW DIMENSION
1.3 THE MANAGER AND ANALYST CONTINUE THEIR DIALOGUE
1.4 PRELIMINARY CONCLUSIONS
1.5 A LITTLE WINDOW INTO FUTURE CHAPTERS
1.6 PROBLEMS FOR THE CURIOUS READER
CHAPTER 2: THE FOUR-FOLD WAY 25
HOW TO PERCEIVE COMPLEX MATHEMATICAL MODELS AND
WELL-POSED PROBLEMS
2.1 PROLOGUE: THE MANAGER AND ANALYST DISCUSS THE
ORIGINS OF MULTIDIMENSIONAL MODELS AND WELLPOSEDNESS
2.2 THE FIRST VIEW: SET THEORETIC
2.3 THE SECOND VIEW: FAMILY OF SUBMODELS
2.4 THE THIRD VIEW: THE BIPARTITE GRAPH
2.5 THE FOURTH VIEW: THE CONSTRAINT MATRIX
2.6 MODEL CONSISTENCY AND COMPUTATIONAL ALLOWABILITY
2.7 THE MANAGER AND ANALYST CONTINUE THEIR DIALOGUE
2.8 CHAPTER SUMMARY
2.9 PROBLEMS FOR THE INTERESTED STUDENT
Constraint theory
CHAPTER 3: GENERAL RESULTS 49
FROM PROTOMATH TO MATH TO METAMATH
3.1 LANGUAGE AND MATHEMATICS
3.2 MOST GENERAL TRUSTWORTHY RESULTS
3.3 CLASSES OF RELATIONS
3.4 MANAGER AND ANALYST REVISITED
3.5 CHAPTER SUMMARY
3.6 PROBLEMS FOR THE GENERAL STUDENT
CHAPTER 4: REGULAR RELATIONS 6 1
SEARCHING FOR THE KERNELS OF CONSTRAINT
4.1 COGNITIVE BARRIERS TO CIRCUITS
4.2 NODE, KNOT AND BASIC NODAL SQUARE SANCTIFICATION
4.3 USEFUL PROPERTIES OF B GRAPHS
4.4 CORNERING THE CULPRIT KERNELS; TEN EASY PIECES
4.5 CONTINUING THE PURSUIT INSIDE THE CIRCUIT CLUSTERS (CC)
4.6 LOCATING BNSS ITHIN ODEL
4.7 QUERIES FOR THE REGULAR STUDENT
CHAPTER 5: MODEL CONSISTENCY AND COMPUTATIONAL 10 1
ALLOWABILITY
5.1 ZERO CONSTRAINT ALL ALONG THE COMPUTATIONAL PATH
5.2 RECAPITULATION OF COMPUTATIONAL FLOW
5.3 GENERAL PROCEDURE FOR ETERMINING
5.4 DETECTION OF OVERLAPPING BNS
5.5 RELIEF OF OVER-CONSTRAINT
5.6 EXPANSION OF RESULTANT CONSTRAINT DOMAINS
5.7 PROCESSING OF COMPUTATIONAL REQUESTS
5.8 SUMMARY OF CHAPTER AND CONSTRAINT THEORY TOOLKIT
5.9 QUERIES FOR THE REGULAR STUDENT
CHAPTER 6: DISCRETE AND INTERVAL RELATIONS 137
THE DIMINISHED UTILITY OF METAMODELS
6.1 METAMODEL ISSUES AND PERSPECTIVES
6.2 THE GENERAL TAXONOMY AND PRIMARY PROPERTY OF
DISCRETE RELATIONS
6.3 BOOLEAN RELATIONS
6.4 TOPOLOGICAL IMPLICATIONS
6.5 ALLOWABILITY OF DISCRETE COMPUTATIONS
6.6 INEQUALITY RELATIONS
IPARTITE
W A M GRAPH
AND ALLOWABILITY IN A ODEL OF
D CONSISTENCY
M REGULAR R ELATIONS
CHAPTER 7: THE LOGICAL STRUCTURE OF CONSTRAINT THEORY 155
A COMPACT SUMMARY
7.1 OVERVIEW
7.2 POSTULATES AND PHILOSOPHICAL ASSUMPTIONS
7.3 DEFINITIONS
7.4 THEOREMS
7.5 GRAPHS OF THE LOGICAL STRUCTURE OF CONSTRAINT THEORY
7.6 COMPLETENESS
CHAPTER 8: EXAMPLES OF CONSTRAINT THEORY APPLIED TO REALWORLD
PROBLEMS 163
8.1 APOLOGIES NOT REQUIRED
8.2 COST AS AN INDEPENDENT VARIABLE (CAIV)
8.3 THE KINEMATICS OF FREE-FALL WEAPONS
8.4 THE DEFLECTION OF AN EARTH-THREATENING ASTEROID
EMPLOYING MASS DRIVERS
CHAPTER 9: MANAGER AND ANALYST MEET AGAIN 183
GISTS AND SCHIZOPHRENIA
APPENDIX A: COMPUTATIONAL REQUEST DISAPPOINTMENTS; 189
RESULTS OF THE USC ALLOWABILITY PROJECT
APPENDIX B: GRAPH THEORY OVERVIEW 197
APPENDIX C: THE LOGIC OF “IF” AND “IF AND ONLY IF” 20 1
APPENDIX D: 203
REFERENCES 211
INDEX 215
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