Closed Form Solutions of Integrable Nonlinear Evolution Equations

2010 Mathematics Subject Classification: 35Q55.

A Random Evolution Inclusion of Subdifferential Type in Hilbert Spaces

In this paper we study a nonlinear evolution inclusion of subdifferential type in Hilbert spaces. The perturbation term is Hausdorff continuous in the state variable and has closed but not necessarily convex values. Our result is a stochastic generalization of an existence theorem proved by Kravvaritis and Papageorgiou in [6].

Decision Trees for Applicability of Evolution Rules in Transition P Systems

Transition P Systems are a parallel and distributed computational model based on the notion of the cellular membrane structure. Each membrane determines a region that encloses a multiset of objects and evolution rules. Transition P Systems evolve through transitions between two consecutive configurations that are determined by the membrane structure and multisets present inside membranes. Moreover, transitions between two consecutive configurations are provided by an exhaustive non-deterministic and parallel application of active evolution rules subset inside each membrane of the P system. But, to establish the active evolution rules subset, it is required the previous calculation of useful and applicable rules. Hence, computation of applicable evolution rules subset is critical for the whole evolution process efficiency, because it is performed in parallel inside each membrane in every evolution step. The work presented here shows advantages of incorporating decision trees in the evolution rules applicability algorithm. In order to it, necessary formalizations will be presented to consider this as a classification problem, the method to obtain the necessary decision tree automatically generated and the new algorithm for applicability based on it.