Wayne Wymore A. Mathematical Theory of Systems Engineering

New York: John Wiley and Sons, Inc., 1967. — 365 p.A pioneering book in general sysyem theory.Set Theoretic Concepts,
Function Theoretic Concepts,
Notation for Sets of Real Numbers,
Cartesian Products,
Exercises
Systems s
Admissible Sets of Input Functions,
System Theoretic Notions,
The Assemblage,
The Relation between a System and an Assemblage,Alternate Statement of System Consistency Requirements,Existence of Discrete Systems,
System Models for Complete Sequential Machines,Semigroups,
Turing Machines,
System Models for Turing Machines,
Exercises
Modeling of Systems
A System Model of an Adder
A System Model of a Multiplier
A System Model of a Scalor
A System Model of an Integrator
A System Model of the Initial Condition Mode
A System Model of a Differentiator
A System Model of a Stieltjes Integrator
A System Model of a Retail Sales Operation
A System Model of an Information Retrieval System
A System Model of a Catch Basin
Existence of Memory of Length d,
Memory of Length d,
A System Model of an Open Pit Mine
A System Model of a Human Operator Tracking
A System Model of a Human Organization
Exercises
Comparison of Systems
Structural Comparison,
System Properties of Homomorphs,
Relation between Sets of Transition Functions under Homo
morphism,
System Equivalence,
Relation between Homomorph and Alternative,
Orderings,
Order on a Set of Systems Generated by Homomorphism,State Equivalence,
Reduction of S to a Distinguished Set of States,
Input Equivalence,
Input Equivalence If Z Is State-Distinguished,
Input Equivalence If T = R and Z Is State-Distinguished,Input Bases,
Step Functions,
Operational Criterion for a Reliable Input Base,
An Fwithout a Reliable Input Base,
Zorn’s , a Postulate
The Axiom of Choice,
Existence of Input Bases,
Reduction of F to an Input-Distinguished Set,
General Reduction ,
Reduction of F through P for Discrete Systems,
Technical System Specifications,
Existence of a System Satisfying Consistent Technical System
Specifications, CONTENTS Xi
Existence of a System Better Satisfying Explicit, Consistent
Technical System Specifications,
Specification Satisfaction Is Implied by Homomorphism,Exercises
Coupling of Systems
Admissible Sets of Input Functions Generated by Projections,Feedback Couples,
A Condition Equivalent to Time Determinedness,
The Resultant of a Feedback Couple Is Well Defined,Representation of Any Time-Determined System As a Result
ant,
Cartesian Products of Admissible Sets of Input Functions,n-System Couples,
The Resultant of an n-System Couple Is Well Defined,The Resultant of an n-System Couple Is a System,
Synthesis of Two-System Couples from Cascade and Feedback
Couples,
Infinite System Couples,
Exercises
Subsystems and Components
Subsystems and Decomposition,
Decomposition of a Disjunction,
Existence of Maximal Decompositions,
Components and Resolution,
Conjunctive Resolutions,
Every Conjunctive Resolution Determines a Two-Couple
Conjunctive Resolution,
Structure of Z Due to a Two-Couple Conjunctive Resolution
of Z,
Existence of Parallel Resolutions,
Structure of Z Due to a Conjunctive Resolution of Z of
Arbitrary Size,
The Homomorphic Image of an Input Base, xii CONTENTS
Construction of a Complementary Conjunctive Component
through Input Bases,
Dual Systems,
The Dual of a System Is a System and Every System Is a Dual,Reachability and Determination,
Duality of AND and OR,
Exercises
Discrete Systems
Discreteness,
Primitive Sample Data ,
Canonical Discreteness Is General,
n-Couples among Discrete Systems Are n-System Couples,Existence of a Computation for the Maximal Decomposition,Existence of Cascade Resolutions of a Discrete System,Exercises
Appendix: Table of Symbols