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Author: Victor I. Varshavsky
Publisher: Springer Science & Business Media
ISBN: 9400904878
Category : Computers
Languages : en
Pages : 427
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Book Description
'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.
Author: Victor I. Varshavsky
Publisher: Springer Science & Business Media
ISBN: 9400904878
Category : Computers
Languages : en
Pages : 427
Get Book Here
Book Description
'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.
Author: Victor I Varshavsky
Publisher:
ISBN: 9789400904880
Category :
Languages : en
Pages : 428
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Book Description
Author: Jörg Desel
Publisher: Springer Science & Business Media
ISBN: 3540222618
Category : Mathematics
Languages : en
Pages : 857
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Book Description
This tutorial volume originates from the 4th Advanced Course on Petri Nets, ACPN 2003, held in Eichstätt, Germany in September 2003. In addition to lectures given at ACPN 2003, additional chapters have been commissioned to give a well-balanced presentation of the state of the art in the area. This book will be useful as both a reference for those working in the area as well as a study book for the reader who is interested in an up-to-date overview of research and development in concurrent and distributed systems; of course, readers specifically interested in theoretical or applicational aspects of Petri nets will appreciate the book as well.
Author: Jordi Cortadella
Publisher: Springer
ISBN: 3540361901
Category : Computers
Languages : en
Pages : 355
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Book Description
As CMOS semiconductor technology strides towards billions of transistors on a single die new problems arise on the way. They are concerned with the - minishing fabrication process features, which a?ect for example the gate-to-wire delay ratio. They manifest themselves in greater variations of size and operating parameters of devices, which put the overall reliability of systems at risk. And, most of all, they have tremendous impact on design productivity, where the costs of utilizing the growing silicon ‘real estate’ rocket to billions of dollars that have to be spent on design, veri?cation, and testing. All such problems call for new - sign approaches and models for digital systems. Furthermore, new developments in non-CMOS technologies, such as single-electron transistors, rapid single-?- quantum devices, quantum dot cells, molecular devices, etc. , add extra demand for new research in system design methodologies. What kind of models and design methodologies will be required to build systems in all these new technologies? Answering this question, even for each particular type of new technology generation, is not easy, especially because sometimes it is not even clear what kind of elementary devices are feasible there. This problem is of an interdisciplinary nature. It requires an bridges between di?erent scienti?c communities. The bridges must be built very quickly, and be maximally ?exible to accommodate changes taking place in a logarithmic timescale.
Author: Luciano Lavagno
Publisher: Springer Science & Business Media
ISBN: 1461532124
Category : Technology & Engineering
Languages : en
Pages : 353
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Book Description
Since the second half of the 1980s asynchronous circuits have been the subject of a great deal of research following a period of relative oblivion. The lack of interest in asynchronous techniques was motivated by the progressive shift towards synchronous design techniques that had much more structure and were much easier to verify and synthesize. System design requirements made it impossible to eliminate totally the use of asynchronous circuits. Given the objective difficulty encountered by designers, the asynchronous components of electronic systems such as interfaces became a serious bottleneck in the design process. The use of new models and some theoretical breakthroughs made it possible to develop asynchronous design techniques that were reliable and effective. This book describes a variety of mathematical models and of algorithms that form the backbone and the body of a new design methodology for asyn chronous design. The book is intended for asynchronous hardware designers, for computer-aided tool experts, and for digital designers interested in ex ploring the possibility of designing asynchronous circuits. It requires a solid mathematical background in discrete event systems and algorithms. While the book has not been written as a textbook, nevertheless it could be used as a reference book in an advanced course in logic synthesis or asynchronous design.
Author: A.A. Tuganbaev
Publisher: Springer Science & Business Media
ISBN: 9401150869
Category : Mathematics
Languages : en
Pages : 368
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Book Description
A module M is called distributive if the lattice Lat(M) of all its submodules is distributive, i.e., Fn(G + H) = FnG + FnH for all submodules F,G, and H of the module M. A module M is called uniserial if all its submodules are comparable with respect to inclusion, i.e., the lattice Lat(M) is a chain. Any direct sum of distributive (resp. uniserial) modules is called a semidistributive (resp. serial) module. The class of distributive (resp. semidistributive) modules properly cont.ains the class ofall uniserial (resp. serial) modules. In particular, all simple (resp. semisimple) modules are distributive (resp. semidistributive). All strongly regular rings (for example, all factor rings of direct products of division rings and all commutative regular rings) are distributive; all valuation rings in division rings and all commutative Dedekind rings (e.g., rings of integral algebraic numbers or commutative principal ideal rings) are distributive. A module is called a Bezout module or a locally cyclic module ifevery finitely generated submodule is cyclic. If all maximal right ideals of a ring A are ideals (e.g., if A is commutative), then all Bezout A-modules are distributive.
Author: Vadim Vasyukevich
Publisher: Springer Science & Business Media
ISBN: 3642216110
Category : Technology & Engineering
Languages : en
Pages : 134
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Book Description
This book is dedicated to new mathematical instruments assigned for logical modeling of the memory of digital devices. The case in point is logic-dynamical operation named venjunction and venjunctive function as well as sequention and sequentional function. Venjunction and sequention operate within the framework of sequential logic. In a form of the corresponding equations, they organically fit analytical expressions of Boolean algebra. Thus, a sort of symbiosis is formed using elements of asynchronous sequential logic on the one hand and combinational logic on the other hand. So, asynchronous logic is represented in the form of enhanced Boolean logic. The book contains initial concepts, fundamental definitions, statements, principles and rules needed for theoretical justification of the mathematical apparatus and its validity for asynchronous logic. Asynchronous operators named venjunctor and sequentor are designed for practical implementation. These basic elements are assigned for realizing of memory functions in sequential circuits. Present research work is the final stage of generalization and systematization of all those ideas and investigations, author’s interest to which alternately flashed up and faded over many years and for various reasons until formed “critical mass”, and all findings were arranged definitively as a mathematical basis of a theory appropriately associated under a common theme – asynchronous sequential logic, essentially classified as switching logic, which falls into category of algebraic logics.
Author: L.A. Lambe
Publisher: Springer Science & Business Media
ISBN: 1461541093
Category : Mathematics
Languages : en
Pages : 314
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Book Description
Chapter 1 The algebraic prerequisites for the book are covered here and in the appendix. This chapter should be used as reference material and should be consulted as needed. A systematic treatment of algebras, coalgebras, bialgebras, Hopf algebras, and represen tations of these objects to the extent needed for the book is given. The material here not specifically cited can be found for the most part in [Sweedler, 1969] in one form or another, with a few exceptions. A great deal of emphasis is placed on the coalgebra which is the dual of n x n matrices over a field. This is the most basic example of a coalgebra for our purposes and is at the heart of most algebraic constructions described in this book. We have found pointed bialgebras useful in connection with solving the quantum Yang-Baxter equation. For this reason we develop their theory in some detail. The class of examples described in Chapter 6 in connection with the quantum double consists of pointed Hopf algebras. We note the quantized enveloping algebras described Hopf algebras. Thus for many reasons pointed bialgebras are elsewhere are pointed of fundamental interest in the study of the quantum Yang-Baxter equation and objects quantum groups.
Author: Kunio Murasugi
Publisher: Springer Science & Business Media
ISBN: 9401593191
Category : Mathematics
Languages : en
Pages : 287
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Book Description
In Chapter 6, we describe the concept of braid equivalence from the topological point of view. This will lead us to a new concept braid homotopy that is discussed fully in the next chapter. As just mentioned, in Chapter 7, we shall discuss the difference between braid equivalence and braid homotopy. Also in this chapter, we define a homotopy braid invariant that turns out to be the so-called Milnor number. Chapter 8 is a quick review of knot theory, including Alexander's theorem. While, Chapters 9 is devoted to Markov's theorem, which allows the application of this theory to other fields. This was one of the motivations Artin had in mind when he began studying braid theory. In Chapter 10, we discuss the primary applications of braid theory to knot theory, including the introduction of the most important invariants of knot theory, the Alexander polynomial and the Jones polynomial. In Chapter 11, motivated by Dirac's string problem, the ordinary braid group is generalized to the braid groups of various surfaces. We discuss these groups from an intuitive and diagrammatic point of view. In the last short chapter 12, we present without proof one theorem, due to Gorin and Lin [GoL] , that is a surprising application of braid theory to the theory of algebraic equations.
Author: R. Krichevsky
Publisher: Springer Science & Business Media
ISBN: 9401736286
Category : Computers
Languages : en
Pages : 230
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Book Description
Objectives Computer and communication practice relies on data compression and dictionary search methods. They lean on a rapidly developing theory. Its exposition from a new viewpoint is the purpose of the book. We start from the very beginning and finish with the latest achievements of the theory, some of them in print for the first time. The book is intended for serving as both a monograph and a self-contained textbook. Information retrieval is the subject of the treatises by D. Knuth (1973) and K. Mehlhorn (1987). Data compression is the subject of source coding. It is a chapter of information theory. Its up-to-date state is presented in the books of Storer (1988), Lynch (1985), T. Bell et al. (1990). The difference between them and the present book is as follows. First. We include information retrieval into source coding instead of discussing it separately. Information-theoretic methods proved to be very effective in information search. Second. For many years the target of the source coding theory was the estimation of the maximal degree of the data compression. This target is practically bit today. The sought degree is now known for most of the sources. We believe that the next target must be the estimation of the price of approaching that degree. So, we are concerned with trade-off between complexity and quality of coding. Third. We pay special attention to universal families that contain a good com pressing map for every source in a set.
