Convergence estimates for the Magnus expansion I. Banach algebras

We review and provide simplified proofs related to the Magnus expansion, and improve convergence estimates. Observations and improvements concerning the Baker--Campbell--Hausdorff expansion are also made. In this Part I, we consider the general Banach algebraic setting. We show that the (cumulative) convergence radius of the Magnus expansion is $2$; and of the Baker--Campbell--Hausdorff series is $\mathrm C_2=2.89847930\ldots$.Comment: Part I of original submission arXiv:1709.01791v1, rewritten and expande

Spectral calculations on locally convex vector spaces I

We develop a holomorphic functional calculus for (multivalued linear) operators on locally convex vector spaces. This includes the case of fractional powers along Lipschitz curves.Comment: 18 page

Modular Analysis of Systems Composed of Semiautonomous Subsystems

This paper reviews a proposal for the modular analysis of Petri nets and its applicability to factory automation systems. It presents new algorithms to harness this modular analysis in the determination of reachable states with specified partial markings, to determine possible deadlocks, both global and local, and also liveness. These algorithms have been implemented in a prototype tool which has then been used to solve a problem in factory automation which, even for relatively simple configurations, can lead to state spaces beyond the capabilities of many analysis tools

A proposal for relative time petri nets

Copyright © 2005, IEEEPetri nets are a graph-based modelling formalism which has been widely used for the formal specification and analysis of concurrent systems. A common analysis technique is that of state space exploration (or reachability analysis). Here, every possible reachable state of the system is generated and desirable properties are evaluated for each state. This approach has the great advantage of conceptual simplicity, but the great disadvantage of being susceptible to state space explosion, where the number of states is simply too large for exhaustive exploration. Many reduction techniques have been suggested to ameliorate the problem of state space explosion. In the case of timed systems, the state space is infinite, unless analysis is restricted to a bounded time period. In this paper, we present a Petri net formalism based on the notion of relative time (as opposed to the traditional approach of dealing with absolute time). The goal is to derive a finite state space for timed systems which have repeating patterns of behaviour, even though time continues to advance indefinitely.Joseph Kuehn, Charles Lakos, Robert Esse