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Constraint Theory Multidimensional Mathematical Model Management

:	George Friedman
:	Constraint Theory Multidimensional Mathematical Model Management
:	Springer-Verlag
:	9780387276502
:	1
:	CHF 162.20
:

:	Allgemeines, Lexika
:	English

:	188
:	Wasserzeichen
:	PC/MAC/eReader/Tablet
:	PDF

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 .

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