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Finitely Supported Mathematics, Alexandru


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Цена: 10760.00р.
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Автор: Alexandru
Название:  Finitely Supported Mathematics
ISBN: 9783319422817
Издательство: Springer
Классификация:





ISBN-10: 3319422812
Обложка/Формат: Hardback
Страницы: 185
Вес: 0.46 кг.
Дата издания: 2016
Язык: English
Издание: 1st ed. 2017
Иллюстрации: VII, 185 p.
Размер: 234 x 156 x 13
Читательская аудитория: Professional & vocational
Основная тема: Computer Science
Подзаголовок: An Introduction
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: In this book the authors present an alternative set theory dealing with a more relaxed notion of infiniteness, called finitely supported mathematics (FSM). It has strong connections to the Fraenkel-Mostowski (FM) permutative model of Zermelo-Fraenkel (ZF) set theory with atoms and to the theory of (generalized) nominal sets. More exactly, FSM is ZF mathematics rephrased in terms of finitely supported structures, where the set of atoms is infinite (not necessarily countable as for nominal sets). In FSM, sets are replaced either by `invariant sets (sets endowed with some group actions satisfying a finite support requirement) or by `finitely supported sets (finitely supported elements in the powerset of an invariant set). It is a theory of `invariant algebraic structures in which infinite algebraic structures are characterized by using their finite supports. After explaining the motivation for using invariant sets in the experimental sciences as well as the connections with the nominal approach, admissible sets and Gandy machines (Chapter 1), the authors present in Chapter 2 the basics of invariant sets and show that the principles of constructing FSM have historical roots both in the definition of Tarski `logical notions and in the Erlangen Program of Klein for the classification of various geometries according to invariants under suitable groups of transformations. Furthermore, the consistency of various choice principles is analyzed in FSM. Chapter 3 examines whether it is possible to obtain valid results by replacing the notion of infinite sets with the notion of invariant sets in the classical ZF results. The authors present techniques for reformulating ZF properties of algebraic structures in FSM. In Chapter 4 they generalize FM set theory by providing a new set of axioms inspired by the theory of amorphous sets, and so defining the extended Fraenkel-Mostowski (EFM) set theory. In Chapter 5 they define FSM semantics for certain process calculi (e.g., fusion calculus), and emphasize the links to the nominal techniques used in computer science. They demonstrate a complete equivalence between the new FSM semantics (defined by using binding operators instead of side conditions for presenting the transition rules) and the known semantics of these process calculi.The book is useful for researchers and graduate students in computer science and mathematics, particularly those engaged with logic and set theory.
Дополнительное описание: Introduction.- Fraenkel-Mostowski Set Theory: A Framework for Finitely Supported Mathematics.- Algebraic Structures in Finitely Supported Mathematics.- Extended Fraenkel-Mostowski Set Theory.- Process Calculi in Finitely Supported Mathematics.- References



Least-Squares Finite Element Methods

Автор: Pavel B. Bochev; Max D. Gunzburger
Название: Least-Squares Finite Element Methods
ISBN: 0387308881 ISBN-13(EAN): 9780387308883
Издательство: Springer
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Цена: 16769.00 р.
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Описание: Since their emergence finite element methods have become one of the most versatile and powerful methodologies for the approximate numerical solution of PDEs. Today finite element methods are in common use for incompressible fluid flow, heat, transfer, electromagnetics, and convection-diffusion-reaction problems, to name a few. This book is written with the premise that there is a real, existing need to put least-squares finite elemenet methods on a common mathematically sound foundation. It is intended to give both the researcher and the practitioner a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems. Appendices provide results from functional analysis and standard finite theory which are used in various places in the book.

Finite Mathematics - Models and Applications

Автор: Morris
Название: Finite Mathematics - Models and Applications
ISBN: 1119015502 ISBN-13(EAN): 9781119015505
Издательство: Wiley
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Цена: 19158.00 р.
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Описание: Finite Mathematics: Models and Applications connects fundamental mathematical modeling skills and decision making concepts to their everyday applicability and features real-world examples from a variety of areas from business, finance, and management to the life and social sciences.

Handbook of Finite State Based Models and Applications

Название: Handbook of Finite State Based Models and Applications
ISBN: 1138199354 ISBN-13(EAN): 9781138199354
Издательство: Taylor&Francis
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Цена: 9492.00 р.
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Описание:

Applicable to any problem that requires a finite number of solutions, finite state-based models (also called finite state machines or finite state automata) have found wide use in various areas of computer science and engineering. Handbook of Finite State Based Models and Applications provides a complete collection of introductory materials on finite state theories, algorithms, and the latest domain applications. For beginners, the book is a handy reference for quickly looking up model details. For more experienced researchers, it is suitable as a source of in-depth study in this area.

The book first introduces the fundamentals of automata theory, including regular expressions, as well as widely used automata, such as transducers, tree automata, quantum automata, and timed automata. It then presents algorithms for the minimization and incremental construction of finite automata and describes Esterel, an automata-based synchronous programming language for embedded system software development.

Moving on to applications, the book explores regular path queries on graph-structured data, timed automata in model checking security protocols, pattern matching, compiler design, and XML processing. It also covers other finite state-based modeling approaches and applications, including Petri nets, statecharts, temporal logic, and UML state machine diagrams.


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