Moisil The Algebraic Theory of Switching Circuits

1. Auflage 2014
ISBN: 978-1-4831-6076-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 720 Seiten, Web PDF

Reihe: International Series in Pure and Applied Mathematics

The Algebraic Theory of Switching Circuits covers the application of various algebraic tools to the delineation of the algebraic theory of switching circuits for automation with contacts and relays. This book is organized into five parts encompassing 31 chapters. Part I deals with the principles and application of Boolean algebra and the theory of finite fields (Galois fields). Part II emphasizes the importance of the sequential operation of the automata and the variables associated to the current and to the contacts. This part also tackles the recurrence relations that describe operations of the network and the principles of the so-called characteristic equations. Part III reviews the study of networks with secondary elements other than ordinary relays, while Part IV focuses on the fundamentals and application of multi-position contacts. Part V considers several topics related to circuit with electronic elements, including triodes, pentodes, transistors, and cryotrons. This book will be of great value to practicing engineers, mathematicians, and workers in the field of computers.

Autoren/Hrsg.

Moisil, Gr. C.

Inhaltsverzeichnis

1;Front Cover;1
2;The Algebraic Theory of Switching Circuits;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface to the English edition;12
6;Preface to the Romanian edition;17
7;PART ONE;22
7.1;CHAPTER 1. INTRODUCTION;24
7.1.1;1. Congruences of integers;24
7.1.2;2. Variables associated to elements of switching circuits;33
7.1.3;3 . Functions;39
7.1.4;4. Polynomials congruent with respect to a modulus;48
7.1.5;5. Functions generated by polynomials;51
7.2;CHAPTER 2. NETWORKS WITH BIPOSITION CONTACTS;55
7.2.1;1. Theory of functions in &^(2);55
7.2.2;2. Series-parallel networks;64
7.2.3;3 . Boolean Algebras;78
7.2.4;4. Combinational series-parallel networks;84
7.2.5;5. Shunt networks;93
7.2.6;6. Simplifieation of series-parallel networks with biposition contacts;96
7.3;CHAPTER 3. IDEAL OPERATION OF ORDINARY RELAYS;98
7.3.1;1. Description of the sequential operation;98
7.3.2;2. Characteristic equation of an ideal relay;100
7.3.3;3. Analysis of the operation of networks with ideal relays;104
7.3.4;4. The principle of determinism;108
7.3.5;5. Synthesis of series-parallel networks for relay operating programmes;119
7.3.6;6. Analysis and synthesis of shunt networks;124
7.3.7;7· Analysis of the sequential operation of bridge networks;127
7.4;CHAPTER 4. THE OPERATION OF BISTABLE RELAYS;129
7.5;CHAPTER 5. OPERATION OF RELAYS WITH REDUCED SELF-HOLDING CURRENT;136
7.6;CHAPTER 6. NETWORKS WITH THREE.POSITION CONTACTS;144
7.6.1;1. Theory of functions in @5 (3);144
7.6.2;2 . Series-parallel networks with three-position contacts;153
7.6.3;3 . Algebra of the series-parallel two-terminals with three-position contacts;160
7.6.4;5 · Antisymmetric series-parallel two-terminals with contacts and rectifiers;173
7.6.5;6. Three-valued Lukasiewicz Algebras;176
7.6.6;7. Simplification of series-parallel networks with three-position contacts;181
7.7;CHAPTER 7. IDEAL OPERATION OF POLARIZED RELAYS;182
7.7.1;1. Characteristic equation of an ideal polarized relay;182
7.7.2;2. Analysis of the operation of networks with ideal polarized relays;186
7.7.3;3. The principle of determinism;190
7.7.4;4. Synthesis of networks with polarized relays;190
7.7.5;5. Polarized relays with two operating positions of the contacts;194
7.8;CHAPTER 8. ACTUAL OPERATION OF ORDINARY RELAYS;196
7.9;CHAPTER 9. NETWORKS WITH FIVE-POSITION CONTACTS;201
7.9.1;1. Theory of functions in ®$(5);201
7.9.2;2. Five-position contacts;203
7.9.3;3. Actual operation of a polarized relay;205
7.9.4;4. Actual operation of networks with ordinary relays, with break-before-make and make-before-break contacts;212
8;PART TWO;216
8.1;CHAPTER 10. CONGRUENCES WITH RESPECT TO A DOUBLE MODULUS;218
8.2;CHAPTER 11. NETWORKS WITH TWO ORDINARY RELAYS;221
8.2.1;I. The field &^(2.;221
8.2.2;2. Theory of functions in ®5 (22);225
8.2.3;3· Equations of the second and third degree in (22);229
8.2.4;5. Networks wiih two ordinary relays;238
8.2.5;6. Combinational series-parallel networks with contacts and rectifiers;243
8.3;CHAPTER 12. NETWORKS WITH THREE ORDINARY RELAYS;254
8.3.1;1. The field;254
8.3.2;2. The theory of functions in @5 (2»);259
8.3.3;3· Combinational networks with three push-buttons;261
8.3.4;4. Networks with three ordinary relays;264
8.4;CHAPTER 13. NETWORKS WITH FOUR ORDINARY RELAYS;270
8.4.1;1. The field &%{2^;270
8.4.2;2 . The theory of functions in ©5(2«);276
8.4.3;3. Relalions between ©3Í2*<) and ©3(22);278
8.4.4;4. Combinational networks with four push-buttons;280
8.4.5;5. Networks with four relays;282
8.5;CHAPTER 14. NETWORKS WITH TWO POLARIZED RELAYS;288
8.5.1;1. The field;288
8.5.2;2. Theory of functions in &^13^;292
8.5.3;3. Combinational networks with two three-position push-buttons;298
8.6;CHAPTER 15. NETWORKS WITH THREE POLARIZED RELAYS;305
8.6.1;1. The field ©5(3^);305
8.6.2;2 . Theory of functions in ©5(3^);307
8.6.3;3. Combinational networks with three three-position push-buttons;317
8.6.4;4· Networks with three polarized relays;322
8.7;CHAPTER 16. ACTUAL OPERATION OF NETWORKS WITH TWO POLARIZED RELAYS;327
8.7.1;1. The field ©5(5^);327
8.7.2;2 . Theory of functions in (52);332
8.7.3;3. Networks with two polarized relays;343
8.8;CHAPTER 17. SIMULTANEOUS USE OF SEVERAL DIFFERENT FIELDS;348
8.8.1;1. The Cartesian product;348
8.8.2;2. Theory oí functions in 6Jg (2) . &^ (3);351
8.8.3;3. Bistable relays;355
8.8.4;4. Actual operation of ordinary relays;356
8.8.5;5. Actual operation of polarized relays;357
8.8.6;6. Working function of a two-terminal having both two-position and three-position contacts;359
8.8.7;7. Networks with ordinary and polarized relays;362
9;PART THREE;370
9.1;CHAPTER 18. NETWORKS WITH MULTI-POSITION CONTACTS;372
9.1.1;1. Functions whose domain is finite and whose range is a field;372
9.1.2;2. Functions of several variables;379
9.1.3;3. Working function of a multi-position contact;380
9.1.4;4. Series-parallel connection of multi-position contacts;384
9.1.5;5· Working function of a series-parallel two-terminal with contacts;385
9.1.6;6. Analysis of combinational series-parallel networks with multi-position contacts;388
9.1.7;7. Synthesis of combinational series-parallel networks with multi-position contacts;391
9.1.8;8. Working function of a series-parallel two-terminal with multi-position contacts and rectifiers;393
9.1.9;9. Working function of an antisymmetric series-parallel two terminal with rectifiers and multi-position contacts;395
9.2;CHAPTER 19. SEQUENTIAL OPERATION OF NETWORKS WITH MULTI-POSITION CONTACTS;397
9.2.1;1· Sequential operation of multi-position contacts;397
9.2.2;2 . Locking contacts;398
9.2.3;3. Functions whose argument and values are integers;399
9.2.4;4. Discontinuous description of continuous phenomena;399
9.2.5;5. Flasher operation;403
9.3;CHAPTER 20. OPERATION OF NETWORKS WITH SLOW ACTING RELAYS;406
9.3.1;1. Networks with slow acting relays;406
9.3.2;2. Operation of a pressing installation;417
9.3.3;3 . A protection network with relays;422
9.4;CHAPTER 21. OPERATION OF NETWORKS WITH ROTARY SWITCHES;426
9.5;CHAPTER 22. OPERATION OF NETWORKS WITH ELECTRONIC TUBES;438
10;PART FOUR;454
10.1;CHAPTER 23. GENERAL THEORY OF THE SWITCHING CIRCUITS OPERATION;456
10.1.1;1. The general form of the recurrence equation for normally delayed relays;456
10.1.2;2. General form of the recurrence equations in the ease of slow acting elements;463
10.1.3;3. Reduction of networks with slow acting elements to normally delayed networks;464
10.1.4;4. Reduction of networks with multi-position contacts to networks with biposition contacts;468
10.2;CHAPTER 24. SYNTHESIS OF NETWORKS WITH GIVEN OPERATING CONDITIONS FOR THEIR OUTPUT ELEMENTS;473
10.3;CHAPTER 25. EXACT PROGRAMMES;523
10.3.1;1. Definition of exact programmes;523
10.3.2;2. Realization of an exact programme;528
10.3.3;3. Conditions of compatibility;532
10.3.4;4. Lemmas of formal logic;532
10.3.5;5. Analysis of the conditions ot compatibility;539
10.3.6;6. Compatible programmes;543
10.3.7;7. Theorems on realization;545
10.3.8;8. Simplification of an exact programme;550
10.3.9;9. Examples of simplification;556
10.4;CHAPTER 26. NORMAL PROGRAMMES;562
10.4.1;1. Definition of a normal programme;562
10.4.2;2. Strict transcription of a normal programme;566
10.4.3;3. Transcription of an exact programme into a normal programme;570
10.4.4;4. Transcription of a normal programme into an exact programme;572
10.4.5;5. Operating conditions and normal progranmes;578
10.4.6;6. The problem of a minimal realization;579
10.4.7;7. The reduction of an exact progranoime;585
10.5;CHAPTER 27. THE TECHNICAL CONDITION OF A PROPER OPERATION;593
10.5.1;1. Networks with ordinary relays;593
10.5.2;2. Difficulties;596
10.5.3;3. Networks with polarized relays;598
11;PART FIVE;602
11.1;CHAPTER 28. SYNONYMOUS NETWORKS;604
11.1.1;1. Definition of synonymous networks;604
11.1.2;2. Representation of symmetric groups;606
11.1.3;3. Systems of linear equations;612
11.1.4;4. Network classification;615
11.2;CHAPTER 29. SIMILAR NETWORKS;623
11.2.1;1. Transmutations;623
11.2.2;2 . Classification of networks with two push-buttons;631
11.2.3;3. Another method of network classification. Networks with two push-buttons;634
11.3;CHAPTER 30. ISOMORPHIC NETWORKS;636
11.3.1;1. Network isomorphism;636
11.3.2;2. The classification of autonomous networks with one relay;646
11.3.3;3. The classification of autonomous networks with two relays;650
11.3.4;4. Another classification .. the autonomous evolutions;664
11.4;CHAPTER 31. EQUIVALENT NETWORKS;669
11.4.1;ADDENDA;672
11.4.1.1;1. The notion of "elementary time interval";672
11.4.1.2;2. Automata with slow acting relays;673
11.4.1.3;3. Synchronous and asynchronous automata;674
11.4.1.4;4. Rapid and slow acting polarized relays;675
11.4.1.5;5. On the synthesis problem;676
11.4.2;A SURVEY OF THE ROMANIAN WORKS ON THE ALGEBRAIC THEORY OF AUTOMATA;678
11.4.2.1;ELEMENTS;678
11.4.2.2;GENERAL PROBLEMS;678
11.4.2.3;METHODS;678
11.4.3;BIBLIOGRAPHY OF ROMANIAN LITERATURE;688
11.4.3.1;BOOKS;688
11.4.3.2;PAPERS;689
11.4.3.3;DOCTOR THESIS;709
11.4.3.4;CIRCULAR LETTERS;709
12;INDEX;712
13;OTHER TITLES IN THE SERIES IN PURE AND APPLIED MATHEMATICS;718