A mechanism allowing the unique conversion of an event-based business process model of the ARIS EPC format into a monochrome Petri net is suggested. The Petri net ma¬trix representation resulting from this conversion allows investigating a business process topology and finding cycles and dead-ends. Moreover the Petri net matrix representation allows finding net invariants thus solving a task of finding all the business process development variants.

A dynamical model of laser generation based on monomode balance equations with delay is studied. Methods of a local analysis are used to build sets of quasinormal forms in the neighborhood of parame^ters bifurcation values. The possibility of the coexistence of a large number of steady oscillating states is shown.

The system of diffusion couplexl nonlinear differential-difference equations with delay modelling the elexctrical interacction of pulse neurons is studiexl. Given the spexxl of electrical processes in the system is high, the limit system, responsible for relaxation ccydes, is construcctexL Along with a synchronous cycle the system permits stable asynchronous ccydes, which asymptotics are presentexL

Some properties of formal languages (ACML) of automaton counter machines are investigated. We show that a class of these languages is closed with respect to the following operations: union, intersection by regular sets, concatenation, infinite iteration (Kleene star), homomorphism and inverse homomorphism. This means that the ACML-class is full-AFL (Abstract Family of Languages). Moreover, the class of ACML is closed with respect to intersection and substitution, but not closed with respect to conversion and complementation. We prove that an empty language problem and a word recognition problem are decidable for automaton counter machines, but inclusion and equivalence problems are not decidable. We compare the class of ACML with other formal language classes - regular, context-free, context-sensitive and Petri net languages.

The article is devoted to the problem of integer-valued balancing of a three-dimensional matrix. The reduction of this problem to the problem of finding a maximum flow in the multiple network of integer-valued balancing and the algorithm for this problem are suggested. Also, the comparative characteristic of two algorithms of integer-valued bal¬ancing is made according to the results of the computing experiments. NP-completeness of the problem of integer-valued balancing of a three-dimensional matrix is proved in the article. The problem of minimization of the errors of rounding off in the problem of integer-valued balancing is explored.

New facts characterizing the vertex set of 3-SAT problem relaxation polytope are established. In particular, the question of preservation of nonintegral vertices under additional linear constraints of stronger relaxations is examined.

The conception of Cloud Computing in Internet is presented on the base of the Computer Simulation Center.

The goal of this article is to consider the task of determining the execution frequency of program basic blocks. This task is important for such applications as program optimization, paralleling program execution, computing resources allocation, program compaction, and malicious software detection. A new method is proposed in the article for evaluation of basic block execution frequency based on the Monte Carlo method. The method proposed allows us to estimate a number of program runs to get the execution frequency with a given precision.

Dynamics of two diffusion coupled close oscillators occuring in nerve cell simulation is considered. The delay of passage the pulse in the connecting element between the oscillators is taken into account. For parameters close to critical values the normal form for amplitude and phase variables is constructed. Phase reconstructions of the normal form when changing the parameters describing connection element are analyzed. It is shown that, the introduction of delay leads to significant changes in the scenario of phase reconstructions.

The article secifies the ARTCP header format and describes the algorithm of the ARTCP connection establishment. Some aspects of TCP and ARTCP interaction are discussed. Presented a work plan to implement the ARTCP in Linux.