Graph theory in modern engineering; computer aided design, control, optimization, reliability analysis, Volume 98 (Mathematics in Science and Engineering)

✍ Scribed by Henley (editor)

• Publisher: Academic Press
• Year: 1973
• Tongue: English
• Leaves: 320
• Category: Library

✦ Table of Contents

Front Cover
Graph Theory in Modern Engineering
Copyright Page
Contents
Preface
Acknowledgments
Nomenclature
Chapter 1. Basic Concepts
Directed Graphs
Flow Graphs for Differential Equations
Further Terminology
Chapter 2. Construction and Analysis of Signal Flow Graphs
Signal-Flow-Graph Reduction and the Solution of Equations
Flow-Graph Algebra
Loop Elimination and Equation Solving by Equation Reduction
Mason’s Rule
Applying Mason’s Rule
Application of Mason’s Rule to Dynamic Systems
References
Chapter 3. Systematic Analysis of Large Flow Graphs
Determining Specific Paths and Loops
Determining Specific Paths
List Processing Approach to Determining Paths
Evaluation of Gains
Removing Unnecessary Paths from the List Structure
Evaluating Determinants in Mason’s Formula
Computing the Determinants Corresponding to Specific Paths as Required by Mason’s Rule
Computing Transmittances
Implementing the Algorithms
References
Chapter 4. Frequency Response Analysis
Final Value Theorem
Initial Value Theorem
Substitution Rule
Bode Diagrams
A Typical Application
Other Stability Criteria
Reference
Chapter 5. Sensitivity Analysis
Sensitivity Analysis in General
Derivation of Network Functions
Deriving Sensitivity Functions
Applying Sensitivity Functions to Structural Analysis
Gain and Phase Sensitivity
Pole and Zero Sensitivity
Sensitivities via Structural Methods
Sensitivities for Large Parameter Variations
Transfer Functions and Sensitivities in Static Systems
References
Chapter 6. Examples and Further Applications
Closed-Form Solution of an Absorption Column
Sensitivity Analysis of a Heat Exchanger Network
Continuous Stirred Tank Reactor
Eigenvalue Problems
Ordering Recycle Calculations
Transportation Problems
References
Chapter 7. Linear and Nonlinear Programming
General Form of LP Problems
Simplex Solution by Signal-Flow-Graph Methods
Example Problems
Discussion of Solution Procedure (MASNLP)
An Advantage of MASNLP
Dual Simplex Method
Postoptimal Analysis
Sensitivity Analysis
Nonlinear Systems
Method of Feasible Directions
A Heat Exchanger Problem
Solution to the Heat Exchanger System
Results and Discussion
References
Chapter 8. Ranking by Flow-Graph Methods
Tennis Rankings
Implementation Difficulties
A Solution to the Implementation Problem
Reference
Chapter 9. Undirected Graphs
Undirected Graphs
Trees
Logic Trees
Branch and Bound Methods
Trees-Further Theorems and Definitions
Disconnecting Sets and Cut-Sets
Bipartite Graphs
Assigning Output Sets
References
Chapter 10. Matrix Representation of Graphs
Nondirected Graphs
Digraphs
References
Chapter 11. Branch and Eound. Search Tree Methods
Formal Definition of the Branch and Bound Technique
The Traveling Salesman Problem
Integer Programming and Pseudo-Boolean Progrhmming
Generalization of the Branch and Bound Method
Bidding Contest Problem
Conclusion
References
Chapter 12. Process Reliability Analysis by Flow-Graph Methods
Module Representation of Reliability Graphs
Principle of Path Enumeration and Sensitivity Calculation Methods
Basic Algorithm
Path Finding Algorithm
System Reliability
Comparison with State Enumeration Algorithm
Examples
Extension to System MTBF Calculation
Conclusions
References
Appendix A. Matrix Theory
Appendix B. Linearization of Equations
Appendix C. Derivation of Mason’s Rule
Appendix D. Boolean and Modulo-2 Algebra
Appendix E. Linear Programming
Appendix F. The Coates Flow Graph
Appendix G. The Fibonacci Search Method
Appendix H. Glossary of Graph Nomenclature
Appendix I. Computer Programs for Chapters 1-6
Appendix J. Computer Programs for Chapter 7
BIBLIOGRAPHY
INDEX