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Petri nets model concurrent and distributed systems where active components communicate through the production and absorption of various kinds of resources. Although the dynamic properties of such systems may be very complex, they may sometimes be connected to the static structure of a Petri net. Many properties are decidable, but their complexity may be huge. It is often opportune to restrict oneself to classes of systems, to partial algorithms, and to similar but simpler properties. Instead of analysing a given system, it is also possible to search for a system satisfying some desired properties by construction. This comprehensive textbook/reference presents and discusses these issues in-depth in the context of one of the most fundamental Petri net models, called place/transition nets. The presentation is fortified by means of many examples and worked exercises. Among topics addressed: • In which order may actions may be generated and scheduled? • What states and configurations may be reached in a concurrent system? • Which interesting classes of systems can be analysed relatively efficiently? • Is it possible to synthesise a system of some class from its behaviour? • How can systems be represented algebraically, compositionally, and concisely? This unique text, based on introductory as well as on advanced courses on distributed systems, will serve as an invaluable guide for students and (future) researchers interested in theoretical—as well as in practical—aspects of Petri nets and related system models. Eike Best has been a full professor (now retired) affiliated to Carl von Ossietzky Universität Oldenburg, Germany. Raymond Devillers has been a full professor (now retired) affiliated to Université Libre de Bruxelles, Belgium. The authors have a long record as collaborators in the fields of Petri nets and the semantics of concurrency.

Computer science --- Discrete mathematics. --- Dynamical systems. --- Mathematical models. --- Stochastic models. --- Discrete Mathematics in Computer Science. --- Dynamical Systems. --- Mathematical Modeling and Industrial Mathematics. --- Stochastic Modelling. --- Mathematics. --- Dynamics.

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Petri nets model concurrent and distributed systems where active components communicate through the production and absorption of various kinds of resources. Although the dynamic properties of such systems may be very complex, they may sometimes be connected to the static structure of a Petri net. Many properties are decidable, but their complexity may be huge. It is often opportune to restrict oneself to classes of systems, to partial algorithms, and to similar but simpler properties. Instead of analysing a given system, it is also possible to search for a system satisfying some desired properties by construction. This comprehensive textbook/reference presents and discusses these issues in-depth in the context of one of the most fundamental Petri net models, called place/transition nets. The presentation is fortified by means of many examples and worked exercises. Among topics addressed: • In which order may actions may be generated and scheduled? • What states and configurations may be reached in a concurrent system? • Which interesting classes of systems can be analysed relatively efficiently? • Is it possible to synthesise a system of some class from its behaviour? • How can systems be represented algebraically, compositionally, and concisely? This unique text, based on introductory as well as on advanced courses on distributed systems, will serve as an invaluable guide for students and (future) researchers interested in theoretical—as well as in practical—aspects of Petri nets and related system models. Eike Best has been a full professor (now retired) affiliated to Carl von Ossietzky Universität Oldenburg, Germany. Raymond Devillers has been a full professor (now retired) affiliated to Université Libre de Bruxelles, Belgium. The authors have a long record as collaborators in the fields of Petri nets and the semantics of concurrency.

Discrete mathematics --- Mathematics --- Classical mechanics. Field theory --- Planning (firm) --- Computer science --- Computer. Automation --- discrete wiskunde --- informatica --- mathematische modellen --- externe fixatie (geneeskunde --- wiskunde --- dynamica --- Petri nets. --- Discrete mathematics. --- Dynamics. --- Mathematical models. --- Stochastic models. --- Discrete Mathematics in Computer Science. --- Dynamical Systems. --- Mathematical Modeling and Industrial Mathematics. --- Stochastic Modelling. --- Mathematics.

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De conquête en conquête, entre la fin du XIIe et le début du XIIIe siècle, Gengis Khan et les Mongols s'emparent d'un territoire gigantesque, sans équivalent. L'armée mongole fait de la guerre une affaire mondiale, les cavaliers issus des steppes assujettissant aussi bien les royaumes de Chine que les régions d'Asie centrale. À sa mort en 1227, le Grand Khan laisse un empire aux bases solides que ses descendants vont continuer d'agrandir durant un siècle et demi.Au-delà de la maîtrise de la guerre, y compris par la terreur, l'héritage de cet empire nomade et de son fondateur est immense : il réalise la première unification du monde par son centre. C'est à comprendre la construction de cet ensemble unique que Jack Weatherford convie le lecteur, avec un sens du récit captivant.

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Tort and negligence --- Belgium