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Author: Anatolij Ivanovic Mal'cev
Publisher: Springer Science & Business Media
ISBN: 364265374X
Category : Mathematics
Languages : en
Pages : 331
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Book Description
As far back as the 1920's, algebra had been accepted as the science studying the properties of sets on which there is defined a particular system of operations. However up until the forties the overwhelming majority of algebraists were investigating merely a few kinds of algebraic structures. These were primarily groups, rings and lattices. The first general theoretical work dealing with arbitrary sets with arbitrary operations is due to G. Birkhoff (1935). During these same years, A. Tarski published an important paper in which he formulated the basic prin ciples of a theory of sets equipped with a system of relations. Such sets are now called models. In contrast to algebra, model theory made abun dant use of the apparatus of mathematical logic. The possibility of making fruitful use of logic not only to study universal algebras but also the more classical parts of algebra such as group theory was dis covered by the author in 1936. During the next twenty-five years, it gradually became clear that the theory of universal algebras and model theory are very intimately related despite a certain difference in the nature of their problems. And it is therefore meaningful to speak of a single theory of algebraic systems dealing with sets on which there is defined a series of operations and relations (algebraic systems). The formal apparatus of the theory is the language of the so-called applied predicate calculus. Thus the theory can be considered to border on logic and algebra.
Author: Anatolij Ivanovic Mal'cev
Publisher: Springer Science & Business Media
ISBN: 364265374X
Category : Mathematics
Languages : en
Pages : 331
Get Book Here
Book Description
As far back as the 1920's, algebra had been accepted as the science studying the properties of sets on which there is defined a particular system of operations. However up until the forties the overwhelming majority of algebraists were investigating merely a few kinds of algebraic structures. These were primarily groups, rings and lattices. The first general theoretical work dealing with arbitrary sets with arbitrary operations is due to G. Birkhoff (1935). During these same years, A. Tarski published an important paper in which he formulated the basic prin ciples of a theory of sets equipped with a system of relations. Such sets are now called models. In contrast to algebra, model theory made abun dant use of the apparatus of mathematical logic. The possibility of making fruitful use of logic not only to study universal algebras but also the more classical parts of algebra such as group theory was dis covered by the author in 1936. During the next twenty-five years, it gradually became clear that the theory of universal algebras and model theory are very intimately related despite a certain difference in the nature of their problems. And it is therefore meaningful to speak of a single theory of algebraic systems dealing with sets on which there is defined a series of operations and relations (algebraic systems). The formal apparatus of the theory is the language of the so-called applied predicate calculus. Thus the theory can be considered to border on logic and algebra.
Author: A. I. Malcev
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3112756355
Category : Mathematics
Languages : en
Pages : 332
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Book Description
No detailed description available for "Algebraic Systems".
Author: Heinrich Hertz
Publisher:
ISBN:
Category : Mechanics, Analytic
Languages : en
Pages : 316
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Book Description
Author: Razvan Diaconescu
Publisher: Springer Science & Business Media
ISBN: 3764387084
Category : Mathematics
Languages : en
Pages : 377
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Book Description
This book develops model theory independently of any concrete logical system or structure, within the abstract category-theoretic framework of the so called ‘institution theory’. The development includes most of the important methods and concepts of conventional concrete model theory at the abstract institution-independent level. Consequently it is easily applicable to a rather large diverse collection of logics from the mathematical and computer science practice.
Author: Graham Cormode
Publisher: Springer Science & Business Media
ISBN: 1848827652
Category : Computers
Languages : en
Pages : 469
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Book Description
Data networking now plays a major role in everyday life and new applications continue to appear at a blinding pace. Yet we still do not have a sound foundation for designing, evaluating and managing these networks. This book covers topics at the intersection of algorithms and networking. It builds a complete picture of the current state of research on Next Generation Networks and the challenges for the years ahead. Particular focus is given to evolving research initiatives and the architecture they propose and implications for networking. Topics: Network design and provisioning, hardware issues, layer-3 algorithms and MPLS, BGP and Inter AS routing, packet processing for routing, security and network management, load balancing, oblivious routing and stochastic algorithms, network coding for multicast, overlay routing for P2P networking and content delivery. This timely volume will be of interest to a broad readership from graduate students to researchers looking to survey recent research its open questions.
Author: Dajun Wang
Publisher: Springer Nature
ISBN: 9811313768
Category : Technology & Engineering
Languages : en
Pages : 404
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Book Description
This book focuses on the qualitative theory in structural mechanics, an area that remains underdeveloped. The qualitative theory mainly deals with the static deformation and vibrational modes of linear elastic structures, and cover subjects such as qualitative properties and the existence of solutions. Qualitative properties belong to one type of structure, are at the system level and of clear regularity, and often result from analytical derivation and logical reasoning. As for the existence of solutions, it addresses a fundamental issue in structural mechanics, and has far-reaching implications for engineering applications. A better understanding of qualitative properties can assist in both numerical computation and experimental studies. It also promotes the development of better dynamic designs for structures. At the same time, a sound grasp of the existence of solutions and related subjects can aid in quantitative analysis, and help researchers establish the theoretical background essential to their work. This book is among the few that is dedicated exclusively to the qualitative theory in structural mechanics and systematically introduces the important and challenging area to a wide audience, including graduate students in engineering.
Author: Fabien Durand
Publisher: Cambridge University Press
ISBN: 1108986099
Category : Mathematics
Languages : en
Pages : 594
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Book Description
This book is the first self-contained exposition of the fascinating link between dynamical systems and dimension groups. The authors explore the rich interplay between topological properties of dynamical systems and the algebraic structures associated with them, with an emphasis on symbolic systems, particularly substitution systems. It is recommended for anybody with an interest in topological and symbolic dynamics, automata theory or combinatorics on words. Intended to serve as an introduction for graduate students and other newcomers to the field as well as a reference for established researchers, the book includes a thorough account of the background notions as well as detailed exposition – with full proofs – of the major results of the subject. A wealth of examples and exercises, with solutions, serve to build intuition, while the many open problems collected at the end provide jumping-off points for future research.
Author: Rafael F. Schaefer
Publisher: Cambridge University Press
ISBN: 1108210732
Category : Technology & Engineering
Languages : en
Pages : 581
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Book Description
Gain a solid understanding of how information theoretic approaches can inform the design of more secure information systems and networks with this authoritative text. With a particular focus on theoretical models and analytical results, leading researchers show how techniques derived from the principles of source and channel coding can provide new ways of addressing issues of data security, embedded security, privacy, and authentication in modern information systems. A wide range of wireless and cyber-physical systems is considered, including 5G cellular networks, the Tactile Internet, biometric identification systems, online data repositories, and smart electricity grids. This is an invaluable guide for both researchers and graduate students working in communications engineering, and industry practitioners and regulators interested in improving security in the next generation of information systems.
Author: S. Shapiro
Publisher: Elsevier
ISBN: 0080880045
Category : Science
Languages : en
Pages : 237
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Book Description
``Platonism and intuitionism are rival philosophies of Mathematics, the former holding that the subject matter of mathematics consists of abstract objects whose existence is independent of the mathematician, the latter that the subject matter consists of mental construction... both views are implicitly opposed to materialistic accounts of mathematics which take the subject matter of mathematics to consist (in a direct way) of material objects...'' FROM THE INTRODUCTIONAmong the aims of this book are: - The discussion of some important philosophical issues using the precision of mathematics. - The development of formal systems that contain both classical and constructive components. This allows the study of constructivity in otherwise classical contexts and represents the formalization of important intensional aspects of mathematical practice. - The direct formalization of intensional concepts (such as computability) in a mixed constructive/classical context.
Author: Bloomsbury Publishing
Publisher: Bloomsbury Publishing USA
ISBN: 0313021422
Category : Political Science
Languages : en
Pages : 352
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Book Description
Privatization began in the 1970s with Carter's deregulation of some business, and increased with the Thatcher administration in the United Kingdom, the Reagan administration in the United States, and many communist and socialist countries. One area of concern in privatization is transportation—airports, water ports, roads, and mass transit. Privatization can be implemented in financing, construction, operation, and maintenance of the transportation system, the main motives being the belief that the private sector can be more efficient than the public sector, and because public funds are becoming less plentiful for a variety of reasons. The focus is on ideas and innovations for expanding the private role in transportation. Specifically covered are ideas and innovations for expanding the role of private sector in U.S. transportation projects, private financing of urban transportation, airport privatization, water port improvement, toll roads, and competitive contracting for transit services. The distinguished list of contributors includes the co-recipient of the 1996 Nobel Prize in Economics, William Vickrey. The audience for the work are scholars dealing with the discussions concerning the economics and politics of privatization, business people who are likely to be interested in potential opportunities, governmental regulators and staff, and policy makers.
