Overview

An up-to-date report on the status of important research topics in algebraic geometry and its applications, such as computational algebra and geometry, singularity theory algorithms, numerical solutions of polynomial systems, coding theory, communication networks, and computer vision. Contributions on more fundamental aspects of algebraic geometry include expositions related to counting points on varieties over finite fields, Mori theory, linear systems, Abelian varieties, vector bundles on singular curves, degenerations of surfaces, and mirror symmetry of Calabi-Yau manifolds.

Full Product Details

Author:   Geert Stremersch
Publisher:   Springer
Imprint:   Springer
Edition:   2001 ed.
Volume:   13
Dimensions:   Width: 15.50cm , Height: 1.40cm , Length: 23.50cm
Weight:   1.060kg
ISBN:  

9780792374862

ISBN 10:   079237486
Pages:   198
Publication Date:   30 September 2001
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. The Petri Net Model.- 1 Discrete event systems.- 2 Notation.- 3 Order theoretical preliminaries.- 4 Petri net definition.- 5 Petri nets as discrete event system models.- 6 Reachable sets.- 7 Graphical representation.- 8 Reachability via subsets of transitions.- 9 Other concurrency assumptions.- 10 A general Petri net definition.- 11 Notes and references.- 2. Supervisory Control.- 1 Control goal and architecture.- 2 Formal definition.- 3 Reachable sets under supervision.- 4 Maximally permissive control laws.- 5 Specific control sets.- 6 Linear inequalities as a legal set.- 7 Control design under the no concurrency assumption.- 8 Notes and references.- 3. Uncontrollable Events And Transitions.- 1 Introduction.- 2 Supervisory control laws.- 3 Specific concurrency and control assumptions.- 4 Maximally permissive control laws.- 5 Control design.- 6 The supremal controllable subset.- 7 Notes and references.- 4. Reduction Theorems.- 1 Intuition for A*.- 2 Invariance properties of the legal set.- 3 Sets of places and transitions.- 4 Reduction result for A*.- 5 Reduction of the control design.- 6 Structural and invariance properties of the legal set.- 7 Notes and references.- 5. Acyclic Petri Nets.- 1 Partitioning of the sets of places and transitions.- 2 Structure of the incidence matrices.- 3 Reachability in acyclic Petri nets.- 4 A reachability algorithm.- 5 Acyclic Petri nets free of choice places.- 6 Construction of the supremal controllable subset.- 7 Notes and references.- 6. Decomposition Of The Control Design.- 1 Introduction.- 2 Unions of legal sets.- 3 A uxiliary results.- 4 Proof of Theorem 6.1.- 5 Discussion.- 6 Control design.- 7 Notes and references.- 7. Continuous Versus Discrete Events.- 1 Continuous Petri nets.- 2 A subset of the supremal controllable subset.- 3 Construction of the supremal controllable subset.- 4 No synchronising transitions in NAuc.- 5 No choice places in NAuc.- 6 A third class.- 7 Structure of A*.- 8 Notes and references.- 8. Structural Linear Algebraic Control Design.- 1 Unobservable events.- 2 Overview of the approach.- 3 Intersection of a linear halfspace with the first orthant.- 4 Candidate sets A??.- 5 Maximal sets A??.- 6 Reduction of controllers with disjunctions.- 7 A subset of the supremal controllable subset.- 8 Notes and references.- References.

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