Developing Agent Interaction Protocols with PRALU

The purpose of the paper is to explore the possibility of applying existing formal theories of description and design of distributed and concurrent systems to interaction protocols for real-time multi-agent systems. In particular it is shown how the language PRALU, proposed for description of parallel logical control algorithms and rooted in the Petri net formalism, can be used for the modeling of complex concurrent conversations between agents in a multi-agent system. It is demonstrated with a known example of English auction on how to specify an agent interaction protocol using considered means.

Powers and Logarithms

There are applied power mappings in algebras with logarithms induced by a given linear operator D in order to study particular properties of powers of logarithms. Main results of this paper will be concerned with the case when an algebra under consideration is commutative and has a unit and the operator D satisfies the Leibniz condition, i.e. D(xy) = xDy + yDx for x, y ∈ dom D. Note that in the Number Theory there are well-known several formulae expressed by means of some combinations of powers of logarithmic and antilogarithmic mappings or powers of logarithms and antilogarithms (cf. for instance, the survey of Schinzel S[1].

Fractional Derivatives and Fractional Powers as Tools in Understanding Wentzell Boundary Value Problems for Pseudo-Differential Operators Generating Markov Processes

Mathematics Subject Classification: 26A33, 31C25, 35S99, 47D07.

Bounds for Fractional Powers of Operators in a Hilbert Space and Constants in Moment Inequalities

Mathematics Subject Classification: 47A56, 47A57,47A63