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Local triple derivations on real C*-algebras and JB*-triples
We study when a local triple derivation on a real JB*-triple is a triple
derivation. We find an example of a (real linear) local triple derivation on a
rank-one Cartan factor of type I which is not a triple derivation. On the other
hand, we find sufficient conditions on a real JB*-triple E to guarantee that
every local triple derivation on E is a triple derivation
Playing with Derivation Modes and Halting Conditions
In the area of P systems, besides the standard maximally parallel derivation
mode, many other derivation modes have been investigated, too. In this paper, many
variants of hierarchical P systems and tissue P systems using different derivation modes
are considered and the effects of using di erent derivation modes, especially the maximally
parallel derivation modes and the maximally parallel set derivation modes, on the
generative and accepting power are illustrated. Moreover, an overview on some control
mechanisms used for (tissue) P systems is given.
Furthermore, besides the standard total halting mode, we also consider different halting
conditions such as unconditional halting and partial halting and explain how the use
of different halting modes may considerably change the computing power of P systems
and tissue P systems
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