The series is divergent; therefore we may be able to do something with it O. Heaviside One service mathematics has rendered thl human race. It has put common sense back where it belongs. on the topmost shelf nexl to the dusty canister labelled 'discarded non• sense'.
## Eric T. Bell
Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non• Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and fO! other sciences.
Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com• puter science ... .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
This series, Mathematics and Its Applications, started in 1977. Now that over one hundre<i volumes have appeared it seems opportune to reexamine its scope. At 1he time I wrote "Growing specialization and diversification have brought a host of monographs and textbooks on . increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drasticaIly in recent years: measure theory is used (non-triviaIly) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as 'experimental mathematics', 'CFD', 'completely integrable systems', 'chaos, synergetics and large-scale order', which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics."
By and large, all this still applies today. It is still true that at first sight mathematics seems rathel fragmented and that to find, see, and exploit the deeper underlying interrelations more effort i~ needed and so are books that can help mathematicians and scientists do so. Accordingly MIA wil continue to try to make such books available.
If anything, the description I gave in 1977 is now an understatement. To the examples 0: interaction areas one should add string theory where Riemann surfaces, algebraic geometry, modu• lar functions, knots, quantum field theory, Kac-MOody algebras, monstrous moonshine (and more: all come together. And to the examples of things which can be usefully applied let me add the topic 'finite geometry'; a combination of words which sounds like it might not even exist, let alone be applicable. And yet it is being applied: to statistics via designs, to radar/sonar detection arrays (vi! finite projective planes), and to bus connections of VLSI chips (via difference sets). There seems t( be no part of (50-caIled pure) mathematics that is not in immediate danger of being applied. And accordingly, the applied mathematician needs to be aware of much more. Besides analysis ane numerics, the traditional workhorses, he may need all kinds of combinatorics, algebra, probability and so on.
In addition, the applied scientist needs to cope increasingly with the nonlinear world and th. extra mathematical sophistication that this requires. For that is where the rewards are. Linea models are honest and a bit sad and depressing: proportional efforts and results. It is in the non v The shortest path between two truths in the real domain passes through the complex domain.
## J. Hadamard
La physique ne nous donne pas seuIement l' occasion de resoudre des problemes ... eUe nous fait pressentir la solution.
H. Poincare Russum, September 1989 Never lend books, for no one ever returns them; the only books I have in my library are books that other folk have lent me. Anatole France The function of an expert is not to be more right than other people. but to be wrong for more sophisticated reasons. David Butler Michiel Hazewinkel CONTENTS Preface to the English Edition Xl From the Editor xv Chapter 1 Introduction Chapter 2 Asynchronous processes and their interpretation 2.1 Asynchronous processes 2.1.1 Definition 2.1.2 Some subclasses 2.1.3 Reposition 2.1.4 Structured situations 2.1.5 An asynchronous process as a metamodel 2.

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zlib/Engineering/Victor I. Varshavsky (auth.), Victor I. Varshavsky (eds.)/Self-Timed Control of Concurrent Processes: The Design of Aperiodic Logical Circuits in Computers and Discrete Systems_2111462.pdf

V I Varshavskiĭ; M A Kishinevskiĭ; Alex Yakovlev; et al

edited by Victor I. Varshavsky

Springer Science + Business Media BV

Springer International Publishing

Kluwer Academic Publishers

Mathematics and Its Applications (Soviet Series), 0169-6378 -- 52, Mathematics and Its Applications (Soviet Series) -- 52., Dordrecht, Netherlands, 1990

Mathematics and its applications (Kluwer Academic Publishers), v. 52, Dordrecht ; Boston, ©1990

Softcover reprint of the original 1st ed. 1990, 2011

Springer Nature, Dordrecht, 2012

Netherlands, Netherlands

Cham, 20uu

lg957563

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'Et moi ... ~ si j'avait su comment en revenir. One service mathematics has rendered thl je n'y serais point aile: human race. It has put common sense back where it belongs. on the topmost shelf nexl Jules Verne to the dusty canister labelled 'discarded non· The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non· Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and fO! other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com· puter science ... '; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series

Front Matter....Pages i-xviii
Introduction....Pages 1-11
Asynchronous Processes and Their Interpretation....Pages 12-42
Self-Synchronizing Codes....Pages 43-63
Aperiodic Circuits....Pages 64-113
Circuit Modelling of Control Flow....Pages 114-188
Composition of Asynchronous Processes and Circuits....Pages 189-214
The Matching of Asynchronous Processes and Interface Organization....Pages 215-242
Analysis of Asynchronous Circuits and Processes....Pages 243-280
Anomalous Behaviour of Logical Circuits and the Arbitration Problem....Pages 281-308
Fault Diagnosis and Self-Repair in Aperiodic Circuits....Pages 309-328
Typical Examples of Aperiodic Design Modules....Pages 329-363
Back Matter....Pages 364-408

Mathematics and its Applications
Erscheinungsdatum: 02.10.2011

2013-08-01