Mathematical Theory Of Domains
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Mathematical Theory Of Domains
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Author : V. Stoltenberg-Hansen
language : en
Publisher: Cambridge University Press
Release Date : 1994-09-22
Mathematical Theory Of Domains written by V. Stoltenberg-Hansen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-09-22 with Computers categories.
Introductory textbook/general reference in domain theory for professionals in computer science and logic.
Mathematical Theory Of Domains
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Author :
language : en
Publisher:
Release Date : 1999
Mathematical Theory Of Domains written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
Logic Of Domains
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Author : G. Zhang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Logic Of Domains written by G. Zhang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
The Domain Theory
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Author : Alistair Sutcliffe
language : en
Publisher: CRC Press
Release Date : 2002-03-01
The Domain Theory written by Alistair Sutcliffe and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-03-01 with Computers categories.
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.
Solving Problems In Multiply Connected Domains
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Author : Darren Crowdy
language : en
Publisher: SIAM
Release Date : 2020-04-20
Solving Problems In Multiply Connected Domains written by Darren Crowdy and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-20 with Mathematics categories.
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.
Domains And Lambda Calculi
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Author : Roberto M. Amadio
language : en
Publisher: Cambridge University Press
Release Date : 1998-07-02
Domains And Lambda Calculi written by Roberto M. Amadio and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-02 with Computers categories.
Graduate text on mathematical foundations of programming languages, and operational and denotational semantics.
Asymptotic Theory Of Dynamic Boundary Value Problems In Irregular Domains
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Author : Dmitrii Korikov
language : en
Publisher: Springer Nature
Release Date : 2021-04-01
Asymptotic Theory Of Dynamic Boundary Value Problems In Irregular Domains written by Dmitrii Korikov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-01 with Mathematics categories.
This book considers dynamic boundary value problems in domains with singularities of two types. The first type consists of "edges" of various dimensions on the boundary; in particular, polygons, cones, lenses, polyhedra are domains of this type. Singularities of the second type are "singularly perturbed edges" such as smoothed corners and edges and small holes. A domain with singularities of such type depends on a small parameter, whereas the boundary of the limit domain (as the parameter tends to zero) has usual edges, i.e. singularities of the first type. In the transition from the limit domain to the perturbed one, the boundary near a conical point or an edge becomes smooth, isolated singular points become small cavities, and so on. In an "irregular" domain with such singularities, problems of elastodynamics, electrodynamics and some other dynamic problems are discussed. The purpose is to describe the asymptotics of solutions near singularities of the boundary. The presented results and methods have a wide range of applications in mathematical physics and engineering. The book is addressed to specialists in mathematical physics, partial differential equations, and asymptotic methods.
A Second Course In Complex Analysis
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Author : William A. Veech
language : en
Publisher: Courier Corporation
Release Date : 2008-01-24
A Second Course In Complex Analysis written by William A. Veech and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-24 with Mathematics categories.
A clear, self-contained treatment of important areas in complex analysis, this text is geared toward upper-level undergraduates and graduate students. Chiefly classical in content, it emphasizes the geometry of complex mappings. Additional topics include modular function, Hadamard product theorem, and prime number theorem. 1967 edition.
Elliptic Problems In Nonsmooth Domains
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Author : Pierre Grisvard
language : en
Publisher: SIAM
Release Date : 2011-10-20
Elliptic Problems In Nonsmooth Domains written by Pierre Grisvard and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-20 with Mathematics categories.
Originally published: Boston: Pitman Advanced Pub. Program, 1985.
Mathematics Education As A Research Domain A Search For Identity
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Author : Anna Sierpinska
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematics Education As A Research Domain A Search For Identity written by Anna Sierpinska and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Education categories.
No one disputes how important it is, in today's world, to prepare students to un derstand mathematics as weII as to use and communicate mathematics in their future lives. That task is very difficult, however. Refocusing curricula on funda mental concepts, producing new teaching materials, and designing teaching units based on 'mathematicians' common sense' (or on logic) have not resulted in a better understanding of mathematics by more students. The failure of such efforts has raised questions suggesting that what was missing at the outset of these proposals, designs, and productions was a more profound knowledge of the phenomena of learning and teaching mathematics in sociaIIy established and cuIturaIIy, politicaIIy, and economicaIIy justified institutions - namely, schools. Such knowledge cannot be built by mere juxtaposition of theories in disci plines such as psychology, sociology, and mathematics. Psychological theories focus on the individual learner. Theories of sociology of education look at the general laws of curriculum development, the specifics of pedagogic discourse as opposed to scientific discourse in general, the different possible pedagogic rela tions between the teacher and the taught, and other general problems in the inter face between education and society. Mathematics, aside from its theoretical contents, can be looked at from historical and epistemological points of view, clarifying the genetic development of its concepts, methods, and theories. This view can shed some light on the meaning of mathematical concepts and on the difficulties students have in teaching approaches that disregard the genetic development of these concepts.