The theory of multidimensional continuous and discrete systems is applied to derive a parametric description of musical sounds from a physical model of real or virtual string instruments. The mathematical representation of this model is given by a partial differential equation for a vibrating string. Suitable functional transformations with respect to time and space turn this partial differenti...

In this paper we develop a multi-objective model to optimally control the lead time of a multistage assembly system. The multistage assembly system is modeled as an open queueing network, whose service stations represent manufacturing or assembly operations. The arrival processes of the individual parts of the product, which should be assembled to each other in assembly stations, are assumed to...

We give the precise conditions under which a periodic discrete-time linear state-space system can be transformed into a time-invariant one by a change of basis. Thus our theory is the discrete-time counterpart of the classical theory of Floquet transforms developed by Floquet and Lyapunov in the 1800s for continuous-time systems. We state and prove a necessary and sufficient condition for a “di...

The existing modeling methods using Petri Nets‎, ‎have been successfully applied to model and analyze dynamic systems‎. ‎However‎, ‎these methods are not capable of modeling all dynamic systems such as systems with the current sample time signals‎, ‎systems including various subsystems and multi-mode systems‎. ‎This paper proposes Hybrid Time Delay Petri Nets (HTDPN) to solve the problem‎. ‎In ...