Theory Of Semigroups And Applications

Author : Kalyan B. Sinha,Sachi Srivastava
Publisher : Springer
Page : 169 pages
File Size : 47,7 Mb
Release : 2017-07-12
Category : Mathematics
ISBN : 9789811048647

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Theory of Semigroups and Applications by Kalyan B. Sinha,Sachi Srivastava Pdf

The book presents major topics in semigroups, such as operator theory, partial differential equations, harmonic analysis, probability and statistics and classical and quantum mechanics, and applications. Along with a systematic development of the subject, the book emphasises on the explorations of the contact areas and interfaces, supported by the presentations of explicit computations, wherever feasible. Designed into seven chapters and three appendixes, the book targets to the graduate and senior undergraduate students of mathematics, as well as researchers in the respective areas. The book envisages the pre-requisites of a good understanding of real analysis with elements of the theory of measures and integration, and a first course in functional analysis and in the theory of operators. Chapters 4 through 6 contain advanced topics, which have many interesting applications such as the Feynman–Kac formula, the central limit theorem and the construction of Markov semigroups. Many examples have been given in each chapter, partly to initiate and motivate the theory developed and partly to underscore the applications. The choice of topics in this vastly developed book is a difficult one, and the authors have made an effort to stay closer to applications instead of bringing in too many abstract concepts.

Author : Amnon Pazy
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461255611

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Semigroups of Linear Operators and Applications to Partial Differential Equations by Amnon Pazy Pdf

Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications, and the last two chapters give a connected account of the applications to partial differential equations.

Author : Abdallah Assi,Pedro A. García-Sánchez
Publisher : Springer
Page : 106 pages
File Size : 42,8 Mb
Release : 2016-08-25
Category : Mathematics
ISBN : 9783319413303

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Numerical Semigroups and Applications by Abdallah Assi,Pedro A. García-Sánchez Pdf

This work presents applications of numerical semigroups in Algebraic Geometry, Number Theory, and Coding Theory. Background on numerical semigroups is presented in the first two chapters, which introduce basic notation and fundamental concepts and irreducible numerical semigroups. The focus is in particular on free semigroups, which are irreducible; semigroups associated with planar curves are of this kind. The authors also introduce semigroups associated with irreducible meromorphic series, and show how these are used in order to present the properties of planar curves. Invariants of non-unique factorizations for numerical semigroups are also studied. These invariants are computationally accessible in this setting, and thus this monograph can be used as an introduction to Factorization Theory. Since factorizations and divisibility are strongly connected, the authors show some applications to AG Codes in the final section. The book will be of value for undergraduate students (especially those at a higher level) and also for researchers wishing to focus on the state of art in numerical semigroups research.

Author : Phillipe Clement
Publisher : CRC Press
Page : 476 pages
File Size : 43,6 Mb
Release : 2020-12-22
Category : Mathematics
ISBN : 9781000154214

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semigroup theory and applications by Phillipe Clement Pdf

This book contains articles on maximal regulatory problems, interpolation spaces, multiplicative perturbations of generators, linear and nonlinear evolution equations, integrodifferential equations, dual semigroups, positive semigroups, applications to control theory, and boundary value problems.

Author : Alfred Hoblitzelle Clifford
Publisher : Cambridge University Press
Page : 180 pages
File Size : 43,7 Mb
Release : 1996-05-16
Category : Mathematics
ISBN : 0521576695

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Semigroup Theory and Its Applications by Alfred Hoblitzelle Clifford Pdf

This volume contains survey papers by the invited speakers at the Conference on Semigroup Theory and Its Applications which took place at Tulane University in April, 1994. The authors represent the leading areas of research in semigroup theory and its applications, both to other areas of mathematics and to areas outside mathematics. Included are papers by Gordon Preston surveying Clifford's work on Clifford semigroups and by John Rhodes tracing the influence of Clifford's work on current semigroup theory. Notable among the areas of application are the paper by Jean-Eric Pin on applications of other areas of mathematics to semigroup theory and the paper by the editors on an application of semigroup theory to theoretical computer science and mathematical logic. All workers in semigroup theory will find this volume invaluable.

Author : Ioan I. Vrabie
Publisher : Elsevier
Page : 386 pages
File Size : 48,5 Mb
Release : 2003-03-21
Category : Mathematics
ISBN : 9780080530048

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Co-Semigroups and Applications by Ioan I. Vrabie Pdf

The book contains a unitary and systematic presentation of both classical and very recent parts of a fundamental branch of functional analysis: linear semigroup theory with main emphasis on examples and applications. There are several specialized, but quite interesting, topics which didn't find their place into a monograph till now, mainly because they are very new. So, the book, although containing the main parts of the classical theory of Co-semigroups, as the Hille-Yosida theory, includes also several very new results, as for instance those referring to various classes of semigroups such as equicontinuous, compact, differentiable, or analytic, as well as to some nonstandard types of partial differential equations, i.e. elliptic and parabolic systems with dynamic boundary conditions, and linear or semilinear differential equations with distributed (time, spatial) measures. Moreover, some finite-dimensional-like methods for certain semilinear pseudo-parabolic, or hyperbolic equations are also disscussed. Among the most interesting applications covered are not only the standard ones concerning the Laplace equation subject to either Dirichlet, or Neumann boundary conditions, or the Wave, or Klein-Gordon equations, but also those referring to the Maxwell equations, the equations of Linear Thermoelasticity, the equations of Linear Viscoelasticity, to list only a few. Moreover, each chapter contains a set of various problems, all of them completely solved and explained in a special section at the end of the book. The book is primarily addressed to graduate students and researchers in the field, but it would be of interest for both physicists and engineers. It should be emphasised that it is almost self-contained, requiring only a basic course in Functional Analysis and Partial Differential Equations.

Author : John M Howie,Nik Ruskuc
Publisher : World Scientific
Page : 290 pages
File Size : 44,9 Mb
Release : 1998-12-08
Category : Electronic
ISBN : 9789814545433

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Semigroups And Applications by John M Howie,Nik Ruskuc Pdf

This volume contains contributions from leading experts in the rapidly developing field of semigroup theory. The subject, now some 60 years old, began by imitating group theory and ring theory, but quickly developed an impetus of its own, and the semigroup turned out to be the most useful algebraic object in theoretical computer science.

Author : Kalyan Bidhan Sinha,Sachi Srivastava
Publisher : Unknown
Page : 167 pages
File Size : 47,7 Mb
Release : 2017
Category : Semigroups
ISBN : 9386279630

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Theory of Semigroups and Applications by Kalyan Bidhan Sinha,Sachi Srivastava Pdf

This book combines the spirit of a textbook and of a monograph on the topic of Semigroups and their applications. It is expected to have potential users across a broad spectrum including operator theory, partial differential equations, harmonic analysis, probability and statistics and classical and quantum mechanics. A reasonable amount of familiarity with real analysis, including the Lebesgue-integration theory, basic functional analysis and bounded linear operators is assumed. However, any discourse on a theory of semigroups needs an introduction to unbounded linear operators, some elements of which have been included in the Appendix, along with the basic ideas of the Fourier transform and of Sobolev spaces. The chapters 4 through 6 contain advanced material, not often found in textbooks, but which have many interesting applications such as the Feynman-Kac formula, the central limit theorem and the construction of Markov semigroups. The exercises are given in the text as the topics are developed, so that the interested reader can be persuaded to solve these as a part of learning that topic.

Author : Alfred Hoblitzelle Clifford,G. B. Preston
Publisher : American Mathematical Soc.
Page : 370 pages
File Size : 46,6 Mb
Release : 1961
Category : Group theory
ISBN : 9780821802724

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The Algebraic Theory of Semigroups, Volume II by Alfred Hoblitzelle Clifford,G. B. Preston Pdf

Author : Robert Alicki,K. Lendi
Publisher : Springer Science & Business Media
Page : 138 pages
File Size : 51,9 Mb
Release : 2007-04-23
Category : Science
ISBN : 9783540708605

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Quantum Dynamical Semigroups and Applications by Robert Alicki,K. Lendi Pdf

Reinvigorated by advances and insights the quantum theory of irreversible processes has recently attracted growing attention. This volume introduces the very basic concepts of semigroup dynamics of open quantum systems and reviews a variety of modern applications. Originally published as Volume 286 (1987) in Lecture in Physics, this volume has been newly typeset, revised and corrected and also expanded to include a review on recent developments.

Author : Jerome A. Goldstein
Publisher : Courier Dover Publications
Page : 320 pages
File Size : 44,9 Mb
Release : 2017-05-17
Category : Mathematics
ISBN : 9780486822228

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Semigroups of Linear Operators and Applications by Jerome A. Goldstein Pdf

Advanced graduate-level treatment of semigroup theory explores semigroups of linear operators and linear Cauchy problems. The text features challenging exercises and emphasizes motivation, heuristics, and further applications. 1985 edition.

Author : Olexandr Ganyushkin,Volodymyr Mazorchuk
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 47,9 Mb
Release : 2008-12-10
Category : Mathematics
ISBN : 9781848002814

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Classical Finite Transformation Semigroups by Olexandr Ganyushkin,Volodymyr Mazorchuk Pdf

The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It covers the following topics on the examples of the three classical finite transformation semigroups: transformations and semigroups, ideals and Green's relations, subsemigroups, congruences, endomorphisms, nilpotent subsemigroups, presentations, actions on sets, linear representations, cross-sections and variants. The book contains many exercises and historical comments and is directed first of all to both graduate and postgraduate students looking for an introduction to the theory of transformation semigroups, but also to tutors and researchers.

Author : John L. Rhodes,Chrystopher L. Nehaniv
Publisher : World Scientific
Page : 293 pages
File Size : 48,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9789812836960

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Applications of Automata Theory and Algebra by John L. Rhodes,Chrystopher L. Nehaniv Pdf

This book was originally written in 1969 by Berkeley mathematician John Rhodes. It is the founding work in what is now called algebraic engineering, an emerging field created by using the unifying scheme of finite state machine models and their complexity to tie together many fields: finite group theory, semigroup theory, automata and sequential machine theory, finite phase space physics, metabolic and evolutionary biology, epistemology, mathematical theory of psychoanalysis, philosophy, and game theory. The author thus introduced a completely original algebraic approach to complexity and the understanding of finite systems. The unpublished manuscript, often referred to as "The Wild Book," became an underground classic, continually requested in manuscript form, and read by many leading researchers in mathematics, complex systems, artificial intelligence, and systems biology. Yet it has never been available in print until now. This first published edition has been edited and updated by Chrystopher Nehaniv for the 21st century. Its novel and rigorous development of the mathematical theory of complexity via algebraic automata theory reveals deep and unexpected connections between algebra (semigroups) and areas of science and engineering. Co-founded by John Rhodes and Kenneth Krohn in 1962, algebraic automata theory has grown into a vibrant area of research, including the complexity of automata, and semigroups and machines from an algebraic viewpoint, and which also touches on infinite groups, and other areas of algebra. This book sets the stage for the application of algebraic automata theory to areas outside mathematics. The material and references have been brought up to date bythe editor as much as possible, yet the book retains its distinct character and the bold yet rigorous style of the author. Included are treatments of topics such as models of time as algebra via semigroup theory; evolution-complexity relations applicable to both ontogeny and evolution; an approach to classification of biological reactions and pathways; the relationships among coordinate systems, symmetry, and conservation principles in physics; discussion of "punctuated equilibrium" (prior to Stephen Jay Gould); games; and applications to psychology, psychoanalysis, epistemology, and the purpose of life. The approach and contents will be of interest to a variety of researchers and students in algebra as well as to the diverse, growing areas of applications of algebra in science and engineering. Moreover, many parts of the book will be intelligible to non-mathematicians, including students and experts from diverse backgrounds.

Author : John Rhodes,Benjamin Steinberg
Publisher : Springer Science & Business Media
Page : 674 pages
File Size : 53,5 Mb
Release : 2009-04-05
Category : Mathematics
ISBN : 9780387097817

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The q-theory of Finite Semigroups by John Rhodes,Benjamin Steinberg Pdf

This comprehensive, encyclopedic text in four parts aims to give the reader — from the graduate student to the researcher/practitioner — a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research. The q-theory of Finite Semigroups presents important techniques and results, many for the first time in book form, thereby updating and modernizing the semigroup theory literature.

Author : Jacek Banasiak,Adam Bobrowski,Mirosław Lachowicz
Publisher : Springer
Page : 338 pages
File Size : 55,6 Mb
Release : 2014-11-20
Category : Mathematics
ISBN : 9783319121451

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Semigroups of Operators -Theory and Applications by Jacek Banasiak,Adam Bobrowski,Mirosław Lachowicz Pdf

Many results, both from semi group theory itself and from the applied sciences, are phrased in discipline-specific languages and hence are hardly known to a broader community. This volume contains a selection of lectures presented at a conference that was organised as a forum for all mathematicians using semi group theory to learn what is happening outside their own field of research. The collection will help to establish a number of new links between various sub-disciplines of semigroup theory, stochastic processes, differential equations and the applied fields. The theory of semigroups of operators is a well-developed branch of functional analysis. Its foundations were laid at the beginning of the 20th century, while the fundamental generation theorem of Hille and Yosida dates back to the forties. The theory was, from the very beginning, designed as a universal language for partial differential equations and stochastic processes, but at the same time it started to live as an independent branch of operator theory. Nowadays, it still has the same distinctive flavour: it develops rapidly by posing new ‘internal’ questions and in answering them, discovering new methods that can be used in applications. On the other hand, it is influenced by questions from PDEs and stochastic processes as well as from applied sciences such as mathematical biology and optimal control, and thus it continually gathers a new momentum. Researchers and postgraduate students working in operator theory, partial differential equations, probability and stochastic processes, analytical methods in biology and other natural sciences, optimization and optimal control will find this volume useful.