We study Petri nets with Reset arcs (also Transfer and Doubling arcs) in combination with other extensions of the basic Petri net model. While Reachability is undecidable in all these extensions (indeed they are Turing-powerful), we exhibit unexpected frontiers for the decid-ability of Termination, Coverability, Boundedness and place-Boundedness. In particular, we show counter-intuitive separat...

In this paper, we establish some new sufficient conditions which guarantee the boundedness and the uniform boundedness of solutions of certain nonlinear and nonautonomous differential equations of second order. By defining appropriate Liapunov functions, we obtain some new results on the subject, and examples are also provided to illustrate the feasibility of the proposed results. By this work,...

In order to apply the concept of boundedness, so crucial in the theory of metric spaces, to the case of a general topological space Hu Sze-Tsen introduced the notions of a bornological space and of boundedness for a mapping of bornological spaces. In this work we discuss two alternative approaches how the concepts of bornology and boundedness can be extended to the case of fuzzy sets and many-v...

background and aims. lichen planus (lp) is a relatively common, chronic dermato-mucosal disease that often affects the oral mucosa. among bacterial infections affecting lp, helicobacter pylori has recently been proposed as an important etiologic factor. the present study was designed to evaluate the association of lp and h. pylori infection. materials and methods. this study included 30 patient...

in this paper we investigate the behavior of solutions, stable and unstable of the solutions a second-order rational difference equation. also we will discuss about the behavior of solutions a the rational system, we show these solutions may be stable or unstable.

In this paper we investigate stability and boundedness of solutions of some nonlinear differential equations of third order with delay. By constructing a Lyapunov functional, sufficient conditions for the stability and boundedness of solutions for equations considered are obtained.

We combine the globally exponentially attractive set with the iterative theory to discuss the boundedness of a Lorenz-Stenflo chaotic system. Firstly, We get a exponentially attractive set for this system. Then, we use iterative theory to get a refined boundedness for this system. Finally, the boundedness for y, z is applied to chaos synchronization. Numerical simulations are presented to show ...

The existence of shift for periodically correlated processes and its boundedness are investigated. Spectral criteria for these non-stationary processes to have such shifts are obtained.