Mathematical Theory of Domains PDF Download
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Author: V. Stoltenberg-Hansen
Publisher: Cambridge University Press
ISBN: 9780521383448
Category : Computers
Languages : en
Pages : 366
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Book Description
Introductory textbook/general reference in domain theory for professionals in computer science and logic.
Author: V. Stoltenberg-Hansen
Publisher: Cambridge University Press
ISBN: 9780521383448
Category : Computers
Languages : en
Pages : 366
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Book Description
Introductory textbook/general reference in domain theory for professionals in computer science and logic.
Author: Roberto M. Amadio
Publisher: Cambridge University Press
ISBN: 0521622778
Category : Computers
Languages : en
Pages : 504
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Book Description
Graduate text on mathematical foundations of programming languages, and operational and denotational semantics.
Author: Jean Goubault-Larrecq
Publisher: Cambridge University Press
ISBN: 1107328772
Category : Mathematics
Languages : en
Pages : 499
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Book Description
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.
Author: G. Zhang
Publisher: Springer Science & Business Media
ISBN: 1461204453
Category : Computers
Languages : en
Pages : 264
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Book Description
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.
Author: Darren Crowdy
Publisher: SIAM
ISBN: 1611976154
Category : Mathematics
Languages : en
Pages : 457
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Book Description
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.
Author: Andrea Toselli
Publisher: Springer Science & Business Media
ISBN: 3540266623
Category : Mathematics
Languages : en
Pages : 454
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Book Description
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.
Author: Robert E. Greene
Publisher: Springer Science & Business Media
ISBN: 0817646221
Category : Mathematics
Languages : en
Pages : 310
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Book Description
This work examines a rich tapestry of themes and concepts and provides a comprehensive treatment of an important area of mathematics, while simultaneously covering a broader area of the geometry of domains in complex space. At once authoritative and accessible, this text touches upon many important parts of modern mathematics: complex geometry, equivalent embeddings, Bergman and Kahler geometry, curvatures, differential invariants, boundary asymptotics of geometries, group actions, and moduli spaces. The Geometry of Complex Domains can serve as a “coming of age” book for a graduate student who has completed at least one semester or more of complex analysis, and will be most welcomed by analysts and geometers engaged in current research.
Author: Alistair Sutcliffe
Publisher: CRC Press
ISBN: 0805839518
Category : Computers
Languages : en
Pages : 419
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Book Description
Is this book about patterns? Yes and no. It is about software reuse and representation of knowledge that can be reapplied in similar situations; however, it does not follow the classic Alexandine conventions of the patterns community--i.e. Problem- solution- forces- context- example, etc. Chapter 6 on claims comes close to classic patterns, and the whole book can be viewed as a patterns language of abstract models for software engineering and HCI. So what sort of patterns does it contain? Specifications, conceptual models, design advice, but sorry not code. Plenty of other C++ code pattern books (see PLOP series). Nearest relative in published patterns books are Fowler's (1995) Analysis Patterns: Reusable object models and Coad, North and Mayfield. What do you mean by a Domain Theory? Not domains in the abstract mathematical sense, but domains in the knowledge--natural language sense, close to the everyday meaning when we talk about the application domain of a computer system, such as car rental, satellite tracking, whatever. The book is an attempt to answer the question ' what are the abstractions behind car rental, satellite tracking' so good design solutions for those problems can be reused. I work in industry, so what's in it for me? A new way of looking at software reuse, ideas for organizing a software and knowledge reuse program, new processes for reusing knowledge in requirements analysis, conceptual modeling and software specification. I am an academic, should I be interested? Yes if your research involves software engineering, reuse, requirements engineering, human computer interaction, knowledge engineering, ontologies and knowledge management. For teaching it may be useful for Master courses on reuse, requirements and knowledge engineering. More generally if you are interested in exploring what the concept of abstraction is when you extend it beyond programming languages, formal specification, abstract data types, etc towards requirements and domain knowledge. ADDITIONAL COPY: Based on more than 10 years of research by the author, this book is about putting software reuse on a firmer footing. Utilizing a multidisciplinary perspective--psychology and management science, as well as software--it describes the Domain Theory as a solution. The domain theory provides an abstract theory that defines a generic, reusable model of domain knowledge. Providing a comprehensive library of reusable models, practice methods for reuse, and theoretical insight, this book: *introduces the subject area of reuse and software engineering and explains a framework for comparing different reuse approaches; *develops a metric-oriented framework to assess the reuse claims of three competing approaches: patterns, ERPs, and the Domain Theory OSMs (object system models); *explains the psychological background for reuse and describes generic tasks and meta-domains; *introduces claims that provide a representation of design knowledge attached to Domain Theory models, as well as being a schema for representing reusable knowledge in nearly any form; *reports research that resulted from the convergence of the two theories; *describes the methods, techniques, and guidelines of design for reuse--the process of abstraction; and *elaborates the framework to investigate the future of reuse by different paradigms, generation of applications from requirements languages, and component-based software engineering via reuse libraries.
Author: Ichiro Satake
Publisher: Princeton University Press
ISBN: 1400856809
Category : Mathematics
Languages : en
Pages : 340
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Book Description
This book is a comprehensive treatment of the general (algebraic) theory of symmetric domains. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: Stephen D. Fisher
Publisher: Courier Corporation
ISBN: 0486151107
Category : Mathematics
Languages : en
Pages : 292
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Book Description
A high-level treatment of complex analysis, this text focuses on function theory on a finitely connected planar domain. Clear and complete, it emphasizes domains bounded by a finite number of disjoint analytic simple closed curves. The first chapter and parts of Chapters 2 and 3 offer background material, all of it classical and important in its own right. The remainder of the text presents results in complex analysis from the far, middle, and recent past, all selected for their interest and merit as substantive mathematics. Suitable for upper-level undergraduates and graduate students, this text is accessible to anyone with a background in complex and functional analysis. Author Stephen D. Fisher, a professor of mathematics at Northwestern University, elaborates upon and extends results with a set of exercises at the end of each chapter.
