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Introductory textbook/general reference in domain theory for professionals in computer science and logic.
Book Synopsis Mathematical Theory of Domains by : V. Stoltenberg-Hansen
Download or read book Mathematical Theory of Domains written by V. Stoltenberg-Hansen and published by Cambridge University Press. This book was released on 1994-09-22 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory textbook/general reference in domain theory for professionals in computer science and logic.
Download or read book Mathematical Theory of Domains written by and published by . This book was released on 1999 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Domains are mathematical structures for information and approximation; they combine order-theoretic, logical, and topological ideas and provide a natural framework for modelling and reasoning about computation. The theory of domains has proved to be a useful tool for programming languages and other areas of computer science, and for applications in mathematics. Included in this proceedings volume are selected papers of original research presented at the 2nd International Symposium on Domain Theory in Chengdu, China. With authors from France, Germany, Great Britain, Ireland, Mexico, and China, the papers cover the latest research in these sub-areas: domains and computation, topology and convergence, domains, lattices, and continuity, and representations of domains as event and logical structures. Researchers and students in theoretical computer science should find this a valuable source of reference. The survey papers at the beginning should be of particular interest to those who wish to gain an understanding of some general ideas and techniques in this area.
Book Synopsis Domain Theory, Logic and Computation by : Guo-Qiang Zhang
Download or read book Domain Theory, Logic and Computation written by Guo-Qiang Zhang and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domains are mathematical structures for information and approximation; they combine order-theoretic, logical, and topological ideas and provide a natural framework for modelling and reasoning about computation. The theory of domains has proved to be a useful tool for programming languages and other areas of computer science, and for applications in mathematics. Included in this proceedings volume are selected papers of original research presented at the 2nd International Symposium on Domain Theory in Chengdu, China. With authors from France, Germany, Great Britain, Ireland, Mexico, and China, the papers cover the latest research in these sub-areas: domains and computation, topology and convergence, domains, lattices, and continuity, and representations of domains as event and logical structures. Researchers and students in theoretical computer science should find this a valuable source of reference. The survey papers at the beginning should be of particular interest to those who wish to gain an understanding of some general ideas and techniques in this area.
Graduate text on mathematical foundations of programming languages, and operational and denotational semantics.
Book Synopsis Domains and Lambda-Calculi by : Roberto M. Amadio
Download or read book Domains and Lambda-Calculi written by Roberto M. Amadio and published by Cambridge University Press. This book was released on 1998-07-02 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate text on mathematical foundations of programming languages, and operational and denotational semantics.
This unique book on modern topology looks well beyond traditional treatises and explores spaces that may, but need not, be Hausdorff. This is essential for domain theory, the cornerstone of semantics of computer languages, where the Scott topology is almost never Hausdorff. For the first time in a single volume, this book covers basic material on metric and topological spaces, advanced material on complete partial orders, Stone duality, stable compactness, quasi-metric spaces and much more. An early chapter on metric spaces serves as an invitation to the topic (continuity, limits, compactness, completeness) and forms a complete introductory course by itself. Graduate students and researchers alike will enjoy exploring this treasure trove of results. Full proofs are given, as well as motivating ideas, clear explanations, illuminating examples, application exercises and some more challenging problems for more advanced readers.
Book Synopsis Non-Hausdorff Topology and Domain Theory by : Jean Goubault-Larrecq
Download or read book Non-Hausdorff Topology and Domain Theory written by Jean Goubault-Larrecq and published by Cambridge University Press. This book was released on 2013-03-28 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book on modern topology looks well beyond traditional treatises and explores spaces that may, but need not, be Hausdorff. This is essential for domain theory, the cornerstone of semantics of computer languages, where the Scott topology is almost never Hausdorff. For the first time in a single volume, this book covers basic material on metric and topological spaces, advanced material on complete partial orders, Stone duality, stable compactness, quasi-metric spaces and much more. An early chapter on metric spaces serves as an invitation to the topic (continuity, limits, compactness, completeness) and forms a complete introductory course by itself. Graduate students and researchers alike will enjoy exploring this treasure trove of results. Full proofs are given, as well as motivating ideas, clear explanations, illuminating examples, application exercises and some more challenging problems for more advanced readers.
This monograph studies the logical aspects of domains as used in de notational semantics of programming languages. Frameworks of domain logics are introduced; these serve as foundations for systematic derivations of proof systems from denotational semantics of programming languages. Any proof system so derived is guaranteed to agree with denotational se mantics in the sense that the denotation of any program coincides with the set of assertions true of it. The study focuses on two categories for dena tational semantics: SFP domains, and the less standard, but important, category of stable domains. The intended readership of this monograph includes researchers and graduate students interested in the relation between semantics of program ming languages and formal means of reasoning about programs. A basic knowledge of denotational semantics, mathematical logic, general topology, and category theory is helpful for a full understanding of the material. Part I SFP Domains Chapter 1 Introduction This chapter provides a brief exposition to domain theory, denotational se mantics, program logics, and proof systems. It discusses the importance of ideas and results on logic and topology to the understanding of the relation between denotational semantics and program logics. It also describes the motivation for the work presented by this monograph, and how that work fits into a more general program. Finally, it gives a short summary of the results of each chapter. 1. 1 Domain Theory Programming languages are languages with which to perform computa tion.
Book Synopsis Logic of Domains by : G. Zhang
Download or read book Logic of Domains written by G. Zhang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph studies the logical aspects of domains as used in de notational semantics of programming languages. Frameworks of domain logics are introduced; these serve as foundations for systematic derivations of proof systems from denotational semantics of programming languages. Any proof system so derived is guaranteed to agree with denotational se mantics in the sense that the denotation of any program coincides with the set of assertions true of it. The study focuses on two categories for dena tational semantics: SFP domains, and the less standard, but important, category of stable domains. The intended readership of this monograph includes researchers and graduate students interested in the relation between semantics of program ming languages and formal means of reasoning about programs. A basic knowledge of denotational semantics, mathematical logic, general topology, and category theory is helpful for a full understanding of the material. Part I SFP Domains Chapter 1 Introduction This chapter provides a brief exposition to domain theory, denotational se mantics, program logics, and proof systems. It discusses the importance of ideas and results on logic and topology to the understanding of the relation between denotational semantics and program logics. It also describes the motivation for the work presented by this monograph, and how that work fits into a more general program. Finally, it gives a short summary of the results of each chapter. 1. 1 Domain Theory Programming languages are languages with which to perform computa tion.
Book Synopsis Cartesian Closed Categories of Domains by : A. Jung
Download or read book Cartesian Closed Categories of Domains written by A. Jung and published by . This book was released on 1989 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Quadrature domains were singled out about 30 years ago by D. Aharonov and H.S. Shapiro in connection with an extremal problem in function theory. Since then, a series of coincidental discoveries put this class of planar domains at the center of crossroads of several quite independent mathematical theories, e.g., potential theory, Riemann surfaces, inverse problems, holomorphic partial differential equations, fluid mechanics, operator theory. The volume is devoted to recent advances in the theory of quadrature domains, illustrating well the multi-facet aspects of their nature. The book contains a large collection of open problems pertaining to the general theme of quadrature domains.
Book Synopsis Quadrature Domains and Their Applications by : Peter Ebenfelt
Download or read book Quadrature Domains and Their Applications written by Peter Ebenfelt and published by Springer Science & Business Media. This book was released on 2006-03-10 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quadrature domains were singled out about 30 years ago by D. Aharonov and H.S. Shapiro in connection with an extremal problem in function theory. Since then, a series of coincidental discoveries put this class of planar domains at the center of crossroads of several quite independent mathematical theories, e.g., potential theory, Riemann surfaces, inverse problems, holomorphic partial differential equations, fluid mechanics, operator theory. The volume is devoted to recent advances in the theory of quadrature domains, illustrating well the multi-facet aspects of their nature. The book contains a large collection of open problems pertaining to the general theme of quadrature domains.
Whenever two or more objects or entities—be they bubbles, vortices, black holes, magnets, colloidal particles, microorganisms, swimming bacteria, Brownian random walkers, airfoils, turbine blades, electrified drops, magnetized particles, dislocations, cracks, or heterogeneities in an elastic solid—interact in some ambient medium, they make holes in that medium. Such holey regions with interacting entities are called multiply connected. This book describes a novel mathematical framework for solving problems in two-dimensional, multiply connected regions. The framework is built on a central theoretical concept: the prime function, whose significance for the applied sciences, especially for solving problems in multiply connected domains, has been missed until recent work by the author. This monograph is a one-of-a-kind treatise on the prime function associated with multiply connected domains and how to use it in applications. The book contains many results familiar in the simply connected, or single-entity, case that are generalized naturally to any number of entities, in many instances for the first time. Solving Problems in Multiply Connected Domains is aimed at applied and pure mathematicians, engineers, physicists, and other natural scientists; the framework it describes finds application in a diverse array of contexts. The book provides a rich source of project material for undergraduate and graduate courses in the applied sciences and could serve as a complement to standard texts on advanced calculus, potential theory, partial differential equations and complex analysis, and as a supplement to texts on applied mathematical methods in engineering and science.
Book Synopsis Solving Problems in Multiply Connected Domains by : Darren Crowdy
Download or read book Solving Problems in Multiply Connected Domains written by Darren Crowdy and published by SIAM. This book was released on 2020-04-20 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whenever two or more objects or entities—be they bubbles, vortices, black holes, magnets, colloidal particles, microorganisms, swimming bacteria, Brownian random walkers, airfoils, turbine blades, electrified drops, magnetized particles, dislocations, cracks, or heterogeneities in an elastic solid—interact in some ambient medium, they make holes in that medium. Such holey regions with interacting entities are called multiply connected. This book describes a novel mathematical framework for solving problems in two-dimensional, multiply connected regions. The framework is built on a central theoretical concept: the prime function, whose significance for the applied sciences, especially for solving problems in multiply connected domains, has been missed until recent work by the author. This monograph is a one-of-a-kind treatise on the prime function associated with multiply connected domains and how to use it in applications. The book contains many results familiar in the simply connected, or single-entity, case that are generalized naturally to any number of entities, in many instances for the first time. Solving Problems in Multiply Connected Domains is aimed at applied and pure mathematicians, engineers, physicists, and other natural scientists; the framework it describes finds application in a diverse array of contexts. The book provides a rich source of project material for undergraduate and graduate courses in the applied sciences and could serve as a complement to standard texts on advanced calculus, potential theory, partial differential equations and complex analysis, and as a supplement to texts on applied mathematical methods in engineering and science.
This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.
Book Synopsis Domain Decomposition Methods - Algorithms and Theory by : Andrea Toselli
Download or read book Domain Decomposition Methods - Algorithms and Theory written by Andrea Toselli and published by Springer Science & Business Media. This book was released on 2006-06-20 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.
