Friedman Constraint Theory

Multidimensional Mathematical Model Management
1. Auflage 2006
ISBN: 978-0-387-27650-2
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 188 Seiten

At first glance, this might appear to be a book on mathematics, but it is really intended for the practical engineer who wishes to gain greater control of the multidimensional mathematical models which are increasingly an important part of his environment. Another feature of the book is that it attempts to balance left- and right-brain perceptions; the author has noticed that many graph theory books are disturbingly light on actual topological pictures of their material. One thing that this book is not is a depiction of the Theory of Constraints, as defined by Eliyahu Goldratt in the 1980's. Constraint Theory was originally defined by the author in his PhD dissertation in 1967 and subsequent papers written over the following decade. It strives to employ more of a mathematical foundation to complexity than the Theory of Constraints. This merely attempts to differentiate this book from Goldratt's work, not demean his efforts. After all, the main body of work in the field of 1 Systems Engineering is still largely qualitative .

Autoren/Hrsg.

Friedman, George

Inhaltsverzeichnis

1;Fronticepiece;7
2;Preface;8
3;Acknowledgments;9
4;Introduction;10
5;A Warmup Problem in Complexity;14
6;About the Author;16
7;Contents;17
8;Chapter 1 MOTIVATIONS;20
8.1;What is Constraint Theory and why is it important?;20
8.2;1.1 TRENDS AND PROBLEMS IN SYSTEM TECHNOLOGIES;20
8.3;1.2 AN EXAMPLE OF LOW DIMENSION;23
8.4;1.3 THE MANAGER AND ANALYST CONTINUE THEIR DIALOGUE;35
8.5;1.4 PRELIMINARY CONCLUSIONS;39
8.6;1.5 A LITTLE WINDOW INTO FUTURE CHAPTERS;41
8.7;1.6 PROBLEMS FOR THE CURIOUS READER;42
9;Chapter 2 THE FOUR-FOLD WAY;43
9.1;How to Perceive Complex Mathematical Models and Well-Posed Problems;43
9.2;2.1 PROLOGUE: THE MANAGER AND ANALYST DISCUSS THE ORIGINS OF MULTIDIMENSIONAL MODELS AND WELL-POSEDNESS;43
9.3;2.2 THE FIRST VIEW: SET THEORETIC;46
9.4;2.3 THE SECOND VIEW: FAMILY OF SUBMODELS;53
9.5;2.4 THE THIRD VIEW: THE BIPARTITE GRAPH;56
9.6;2.5 THE FOURTH VIEW: THE CONSTRAINT MATRIX;57
9.7;2.6 MODEL CONSISTENCY AND COMPUTATIONAL ALLOWABILITY;58
9.8;2.7 THE MANAGER AND ANALYST CONTINUE THEIR DIALOGUE;58
9.9;2.8 CHAPTER SUMMARY;64
9.10;2.9 PROBLEMS FOR THE INTERESTED STUDENT;65
10;Chapter 3 GENERAL RESULTS;67
10.1;From Protomath to Math to Metamath;67
10.2;3.1 LANGUAGE AND MATHEMATICS;67
10.3;3.2 MOST GENERAL TRUSTWORTHY RESULTS;69
10.4;3.3 CLASSES OF RELATIONS;74
10.5;3.4 MANAGER AND ANALYST REVISITED;77
10.6;3.5 CHAPTER SUMMARY;78
10.7;3.6 PROBLEMS FOR THE GENERAL STUDENT;78
11;Chapter 4 REGULAR RELATIONS;79
11.1;Searching for the Kernels of Constraint;79
11.2;4.1 COGNITIVE BARRIERS TO CIRCUITS;79
11.3;4.2 NODE, KNOT AND BASIC NODAL SQUARE SANCTIFICATION;81
11.4;4.3 USEFUL PROPERTIES OF BIPARTITE GRAPHS;90
11.5;4.4 CORNERING THE CULPRIT KERNELS; TEN EASY PIECES;97
11.6;4.5 CONTINUING THE PURSUIT INSIDE THE CIRCUIT CLUSTERS ( cc);105
11.7;4.6 LOCATING BNSs IN MINUTES, NOT UNIVERSE LIFETIMES;108
11.8;4.7 COMPARISON OF COMPUTATIONAL COMPLEXITY; TRILLIONS AND TRILLIONS OF TIMES FASTER;109
11.9;4.8 ZERO CONSTRAINT ALL ALONG THE COMPUTATIONAL PATH;114
11.10;4.9 RECAPITULATION OF COMPUTATIONAL FLOW;116
11.11;4.10 GENERAL PROCEDURE FOR DETERMINING CONSISTENCY AND ALLOWABILITY IN A MODEL OF REGULAR RELATIONS;118
11.12;4.11 SUMMARY OF CHAPTER AND CONSTRAINT THEORY TOOLKIT;122
11.13;4.12 QUERIES FOR THE REGULAR STUDENT;127
12;Chapter 5 DISCRETE AND INTERVAL RELATIONS;129
12.1;The Diminished Utility of Metamodels;129
12.2;5.1 Metamodel Issues and Perspectives;129
12.3;5.2 The General Taxonomy and Primary Property of Discrete Relations;130
12.4;5.3 Boolean Relations;130
12.5;5.4 Topological Implications;136
12.6;5.5 Allowability of Discrete Computations;138
12.7;5.6 Inequality Relations;140
12.8;5.7 Summary;143
12.9;5.8 PROBLEMS FOR THE DISCRETE STUDENT;145
13;Chapter 6 THE LOGICAL STRUCTURE OF CONSTRAINT THEORY;146
13.1;A Compact Summary;146
13.2;6.1 Overview;146
13.3;6.2 Postulates and Philosophical Assumptions;146
13.4;6.3 Definitions;147
13.5;6.4 Theorems;147
13.6;6.5 Graphs of the Logical Structure of Constraint Theory;148
13.7;6.6 Completeness;148
14;Chapter 7 EXAMPLES OF CONSTRAINT THEORY APPLIED TO REAL- WORLD PROBLEMS;153
14.1;7.1 Apologies Not Required;153
14.2;7.2 Cost as an independent variable (CAIV);153
14.3;7.3 The Kinematics of Free-Fall Weapons;161
14.4;7.4 The Deflection of an Earth-Threatening Asteroid Employing Mass Drivers;166
15;Chapter 8 MANAGER AND ANALYST MEET AGAIN;173
15.1;Gists and Schizophrenia;173
16;Appendix A COMPUTATIONAL REQUEST DISAPPOINTMENTS; RESULTS OF THE USC ALLOWABILITY PROJECT;178
17;Appendix B GRAPH THEORY OVERVIEW;186
17.1;Why was the Bipartite Graph Chosen?;186
18;Appendix C THE LOGIC OF "IF" AND "IF AND ONLY IF";190
19;Appendix D VECTOR SPACES APPLIED TO GRAPH THEORY;192
20;References;195
21;Index;197