Message sequence charts are a widely used notation to express requirements specifications of multi-agent systems. The semantics of message sequence charts can be defined algebraically in the theory of agents and insertion functions. Using this algebra, one can split message sequence chart scenarios into sets of Hoare triples consisting of precondition, the specification of a finite process, and a postcondition. We refer to such triples as "basic protocols." In this paper, we discuss tools to prove properties of systems described as basic protocols, such as the completeness (at each of its stages the system behavior has a possible continuation) and consistency (at each stage the system behavior is deterministic) of the specification, or the correspondence of the specified behavior to given scenarios. Together, these tools constitute a powerful environment for the formal verification of requirements specifications expressed through message sequence charts. *

SUMMARY Mechanisms of stress transfer and probabilistic models have been widely investigated to explain earthquake clustering features. However, these approaches are still far from being able to link individual events and to determine the number of earthquakes caused by a single event. An alternative approach based on proximity functions allows us to generate hierarchical clustering trees and to identify pairs of nearest-neighbours between consecutive levels of hierarchy. Then, the productivity of an earthquake is the number of events of the next level to which it is linked. Using a relative magnitude threshold ΔM to account for scale invariance in the triggering process, we show that the ΔM-productivity attached to each event is a random variable that follows an exponential distribution. The exponential rate of this distribution does not depend on the magnitude of triggering events and systematically decreases with depth. These results could now be used to characterize active fault systems and improve epidemic models of seismicity.

The paper presents the results of research about specifics of gross domestic product production in Russia using the tool of econometrics -production functions apparatus. Also, there are quantitatively found answers on questions, which have theoretical and methodological significance. First question -what has a decisive influencing on the production of gross domestic product in Russia, whether it is stocks or investments into the main fund? It was found that the decisive influence on the production of gross domestic product in Russia comes from investments into the main fund. Weak dependency of gross domestic product in Russia on capital stocks explains the inappropriateness of using capital stocks as a parameter of fund in production functions. Second question -what is the exact type of indicators that is preferred to use for characterizing the components of production function in conditions of the Russian economy -cost or natural? It is defined that is it possible to use both -cost terms indicators and indexes

A new technique for testing professional skills and competencies as well as its practical applications are presented. The approach in question uses modeling and analyzing the spatio-temporal peculiarities of subjects' oculomotor activity, which are based on the representation of gaze movement on a stimulus surface with the aid of random continuous-time Markov processes with discrete states. The procedure of model parameters estimation provided with goodness-of-fit tests as well as the classifier-building technique, which makes it possible to assess a degree of correspondence between the observed gaze movement distribution and reference distributions identified for different diagnosed groups, were considered. Three examples of practical application of the suggested technique are given as illustrations: assessing a mathematical background level, studying differences in spatio-temporal gaze movement distributions identified for aircraft pilots with different flight proficiency, and assessing skill levels for dispatchers of building automatic control systems.

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