In this paper we consider the Spanne type boundedness of sublinear operators and prove the Adams type boundedness theorems for these operators and also give BMO (bounded mean oscillation space) estimates for their commutators in generalized Morrey spaces on Heisenberg groups. The boundedness conditions are formulated in terms of Zygmund type integral inequalities. Based on the properties of the...

Recently it has been shown that the conventional notions of stability in the sense of Lyapunov and asymptotic stability can be used to characterize the stability properties of a class of “logical” discrete event systems (DES). Moreover, it has been shown that stability analysis via the choice of appropriate Lyapunov functions can be used for DES and can be applied to several DES applications in...

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...

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.

in this paper, a complete description concerning linear operators of banach spaces with range in lipschitz algebras $lip_al(x)$ is provided. necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. finally, a lower bound for the essential norm of such operators is obtained.