Power Algebras Over Semirings

Author : Jonathan S. Golan
Publisher : Springer
Page : 206 pages
File Size : 45,6 Mb
Release : 2013-01-07
Category : Mathematics
ISBN : 940159242X

Get Book

Power Algebras over Semirings by Jonathan S. Golan Pdf

This monograph is a continuation of several themes presented in my previous books [146, 149]. In those volumes, I was concerned primarily with the properties of semirings. Here, the objects of investigation are sets of the form RA, where R is a semiring and A is a set having a certain structure. The problem is one of translating that structure to RA in some "natural" way. As such, it tries to find a unified way of dealing with diverse topics in mathematics and theoretical com puter science as formal language theory, the theory of fuzzy algebraic structures, models of optimal control, and many others. Another special case is the creation of "idempotent analysis" and similar work in optimization theory. Unlike the case of the previous work, which rested on a fairly established mathematical foundation, the approach here is much more tentative and docimastic. This is an introduction to, not a definitative presentation of, an area of mathematics still very much in the making. The basic philosphical problem lurking in the background is one stated suc cinctly by Hahle and Sostak [185]: ". . . to what extent basic fields of mathematics like algebra and topology are dependent on the underlying set theory?" The conflicting definitions proposed by various researchers in search of a resolution to this conundrum show just how difficult this problem is to see in a proper light.

Author : Jonathan S. Golan
Publisher : Springer Science & Business Media
Page : 207 pages
File Size : 43,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401592413

Get Book

Power Algebras over Semirings by Jonathan S. Golan Pdf

This monograph is a continuation of several themes presented in my previous books [146, 149]. In those volumes, I was concerned primarily with the properties of semirings. Here, the objects of investigation are sets of the form RA, where R is a semiring and A is a set having a certain structure. The problem is one of translating that structure to RA in some "natural" way. As such, it tries to find a unified way of dealing with diverse topics in mathematics and theoretical com puter science as formal language theory, the theory of fuzzy algebraic structures, models of optimal control, and many others. Another special case is the creation of "idempotent analysis" and similar work in optimization theory. Unlike the case of the previous work, which rested on a fairly established mathematical foundation, the approach here is much more tentative and docimastic. This is an introduction to, not a definitative presentation of, an area of mathematics still very much in the making. The basic philosphical problem lurking in the background is one stated suc cinctly by Hahle and Sostak [185]: ". . . to what extent basic fields of mathematics like algebra and topology are dependent on the underlying set theory?" The conflicting definitions proposed by various researchers in search of a resolution to this conundrum show just how difficult this problem is to see in a proper light.

Author : K. Glazek
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 44,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401599641

Get Book

A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences by K. Glazek Pdf

This volume presents a short guide to the extensive literature concerning semir ings along with a complete bibliography. The literature has been created over many years, in variety of languages, by authors representing different schools of mathematics and working in various related fields. In many instances the terminology used is not universal, which further compounds the difficulty of locating pertinent sources even in this age of the Internet and electronic dis semination of research results. So far there has been no single reference that could guide the interested scholar or student to the relevant publications. This book is an attempt to fill this gap. My interest in the theory of semirings began in the early sixties, when to gether with Bogdan W ~glorz I tried to investigate some algebraic aspects of compactifications of topological spaces, semirings of semicontinuous functions, and the general ideal theory for special semirings. (Unfortunately, local alge braists in Poland told me at that time that there was nothing interesting in investigating semiring theory because ring theory was still being developed). However, some time later we became aware of some similar investigations hav ing already been done. The theory of semirings has remained "my first love" ever since, and I have been interested in the results in this field that have been appearing in literature (even though I have not been active in this area myself).

Author : Jonathan S. Golan
Publisher : Springer Science & Business Media
Page : 243 pages
File Size : 41,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401703833

Get Book

Semirings and Affine Equations over Them by Jonathan S. Golan Pdf

Semiring theory stands with a foot in each of two mathematical domains. The first being abstract algebra and the other the fields of applied mathematics such as optimization theory, the theory of discrete-event dynamical systems, automata theory, and formal language theory, as well as from the allied areas of theoretical computer science and theoretical physics. Most important applications of semiring theory in these areas turn out to revolve around the problem of finding the equalizer of a pair of affine maps between two semimodules. In this volume, we chart the state of the art on solving this problem, and present many specific cases of applications. This book is essentially the third part of a trilogy, along with Semirings and their Applications, and Power Algebras over Semirings, both written by the same author and published by Kluwer Academic Publishers in 1999. While each book can be read independently of the others, to get the full force of the theory and applications one should have access to all three. This work will be of interest to academic and industrial researchers and graduate students. The intent of the book is to bring the applications to the attention of the abstract mathematicians and to make the abstract mathematics available to those who are using these tools in an ad-hoc manner without realizing the full force of the theory.

Author : Hanns Joachim Weinert
Publisher : World Scientific
Page : 371 pages
File Size : 53,6 Mb
Release : 1998-10-30
Category : Mathematics
ISBN : 9789814495691

Get Book

Semirings: Algebraic Theory And Applications In Computer Science by Hanns Joachim Weinert Pdf

This book provides an introduction to the algebraic theory of semirings and, in this context, to basic algebraic concepts as e.g. semigroups, lattices and rings. It includes an algebraic theory of infinite sums as well as a detailed treatment of several applications in theoretical computer science. Complete proofs, various examples and exercises (some of them with solutions) make the book suitable for self-study. On the other hand, a more experienced reader who looks for information about the most common concepts and results on semirings will find cross-references throughout the book, a comprehensive bibliography and various hints to it.

Author : Anonim
Publisher : Unknown
Page : 1156 pages
File Size : 42,7 Mb
Release : 2005
Category : Mathematics
ISBN : UOM:39015062317212

Get Book

Mathematical Reviews by Anonim Pdf

Author : Jonathan S. Golan
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 48,7 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9789401593335

Get Book

Semirings and their Applications by Jonathan S. Golan Pdf

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world. - Nikolai Ivanovich Lobatchevsky This book is an extensively-revised and expanded version of "The Theory of Semirings, with Applicationsin Mathematics and Theoretical Computer Science" [Golan, 1992], first published by Longman. When that book went out of print, it became clear - in light of the significant advances in semiring theory over the past years and its new important applications in such areas as idempotent analysis and the theory of discrete-event dynamical systems - that a second edition incorporating minor changes would not be sufficient and that a major revision of the book was in order. Therefore, though the structure of the first «dition was preserved, the text was extensively rewritten and substantially expanded. In particular, references to many interesting and applications of semiring theory, developed in the past few years, had to be added. Unfortunately, I find that it is best not to go into these applications in detail, for that would entail long digressions into various domains of pure and applied mathematics which would only detract from the unity of the volume and increase its length considerably. However, I have tried to provide an extensive collection of examples to arouse the reader's interest in applications, as well as sufficient citations to allow the interested reader to locate them. For the reader's convenience, an index to these citations is given at the end of the book .

Author : Anonim
Publisher : Unknown
Page : 1886 pages
File Size : 50,6 Mb
Release : 2000
Category : Books
ISBN : STANFORD:36105111050469

Get Book

American Book Publishing Record by Anonim Pdf

Author : Anthony Iarrobino,Vassil Kanev
Publisher : Springer
Page : 365 pages
File Size : 41,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540467076

Get Book

Power Sums, Gorenstein Algebras, and Determinantal Loci by Anthony Iarrobino,Vassil Kanev Pdf

This book treats the theory of representations of homogeneous polynomials as sums of powers of linear forms. The first two chapters are introductory, and focus on binary forms and Waring's problem. Then the author's recent work is presented mainly on the representation of forms in three or more variables as sums of powers of relatively few linear forms. The methods used are drawn from seemingly unrelated areas of commutative algebra and algebraic geometry, including the theories of determinantal varieties, of classifying spaces of Gorenstein-Artin algebras, and of Hilbert schemes of zero-dimensional subschemes. Of the many concrete examples given, some are calculated with the aid of the computer algebra program "Macaulay", illustrating the abstract material. The final chapter considers open problems. This book will be of interest to graduate students, beginning researchers, and seasoned specialists. Prerequisite is a basic knowledge of commutative algebra and algebraic geometry.

Author : Arthur James Wells
Publisher : Unknown
Page : 1270 pages
File Size : 44,9 Mb
Release : 2000
Category : English literature
ISBN : UOM:39015079755651

Get Book

The British National Bibliography by Arthur James Wells Pdf

Author : Manfred Droste,Werner Kuich,Heiko Vogler
Publisher : Springer Science & Business Media
Page : 614 pages
File Size : 48,6 Mb
Release : 2009-09-18
Category : Computers
ISBN : 9783642014925

Get Book

Handbook of Weighted Automata by Manfred Droste,Werner Kuich,Heiko Vogler Pdf

The purpose of this Handbook is to highlight both theory and applications of weighted automata. Weighted finite automata are classical nondeterministic finite automata in which the transitions carry weights. These weights may model, e. g. , the cost involved when executing a transition, the amount of resources or time needed for this,or the probability or reliability of its successful execution. The behavior of weighted finite automata can then be considered as the function (suitably defined) associating with each word the weight of its execution. Clearly, weights can also be added to classical automata with infinite state sets like pushdown automata; this extension constitutes the general concept of weighted automata. To illustrate the diversity of weighted automata, let us consider the following scenarios. Assume that a quantitative system is modeled by a classical automaton in which the transitions carry as weights the amount of resources needed for their execution. Then the amount of resources needed for a path in this weighted automaton is obtained simply as the sum of the weights of its transitions. Given a word, we might be interested in the minimal amount of resources needed for its execution, i. e. , for the successful paths realizing the given word. In this example, we could also replace the “resources” by “profit” and then be interested in the maximal profit realized, correspondingly, by a given word.

Author : Anthony Iarrobino,Vassil Kanev
Publisher : Springer
Page : 354 pages
File Size : 48,5 Mb
Release : 2014-03-12
Category : Mathematics
ISBN : 3662214865

Get Book

Power Sums, Gorenstein Algebras, and Determinantal Loci by Anthony Iarrobino,Vassil Kanev Pdf

This book treats the theory of representations of homogeneous polynomials as sums of powers of linear forms. The first two chapters are introductory, and focus on binary forms and Waring's problem. Then the author's recent work is presented mainly on the representation of forms in three or more variables as sums of powers of relatively few linear forms. The methods used are drawn from seemingly unrelated areas of commutative algebra and algebraic geometry, including the theories of determinantal varieties, of classifying spaces of Gorenstein-Artin algebras, and of Hilbert schemes of zero-dimensional subschemes. Of the many concrete examples given, some are calculated with the aid of the computer algebra program "Macaulay", illustrating the abstract material. The final chapter considers open problems. This book will be of interest to graduate students, beginning researchers, and seasoned specialists. Prerequisite is a basic knowledge of commutative algebra and algebraic geometry.

Author : Frank DeMeyer,Edward Ingraham
Publisher : Springer
Page : 606 pages
File Size : 44,5 Mb
Release : 1971
Category : Mathematics
ISBN : UCSC:32106008336387

Get Book

Separable Algebras Over Commutative Rings by Frank DeMeyer,Edward Ingraham Pdf

These lecture notes were prepared by the authors for use in graduate courses and seminars, based on the work of many earlier mathematicians. In addition to very elementary results, presented for the convenience of the reader, Chapter I contains the Morita theorems and the definition of the projective class group of a commutative ring. Chapter II addresses the Brauer group of a commutative ring, and automorphisms of separable algebras. Chapter III surveys the principal theorems of the Galois theory for commutative rings. In Chapter IV the authors present a direct derivation of the first six terms of the seven-term exact sequence for Galois cohomology. In the fifth and final chapter the authors illustrate the preceding material with applications to the structure of central simple algebras and the Brauer group of a Dedekind domain, and they pose problems for further investigation. Exercises are included at the end of each chapter.

Author : Anonim
Publisher : Unknown
Page : 844 pages
File Size : 42,8 Mb
Release : 1983
Category : Computers
ISBN : CORNELL:31924058222252

Get Book

RAIRO. by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 440 pages
File Size : 40,8 Mb
Release : 1983
Category : Computers
ISBN : UOM:39015049334314

Get Book

RAIRO, Revue Française D'automatique, D'informatique Et de Recherche Opérationnelle by Anonim Pdf