Cybernetics and Systems Analysis

The states of a finite automaton are ordered by height. This order is shown to be graduated, and the well-known Cerny problem on the minimal length of reset words can be formulated in terms of global height. The problem is proved for automata with four ...

In the topology of information networks, problems arise of existence and implementation of a decomposition of some network into factor-graphs that have no common edges and to which certain specified features are assigned. Special attention is given to ...

Penalty and dummy-domain methods are used to approximate second-order elliptic variational inequalities with a restriction inside a domain by nonlinear boundary-value problems in a rectangle. Difference schemes, with the order of accuracy O(h^1/2) in the ...

A new approach is proposed to identify intersections of the Green functions of linear dynamic systems. State restoration and control problems are solved for such systems.

The authors analyze a stochastic programming problem where the random factor is a stationary ergodic sequence. The problem is approximated by minimizing an empirical function. It is proved that, under some conditions, the probability of large deviations ...

A model of a classical risk process describing the evolution of an insurance company's capital is generalized. Integral equations for the bankruptcy probability are derived. The method of successive approximations is used to solve these equations.

The relationships between arithmetical simulation of random processes, ergodic theory, and optimization are analyzed. Some new results are considered and their possible applications to optimization problems are described.

A complete description is given to the linearity space of Monge cone matrices and of all its minimum faces. The description makes it possible to completely characterize Monge matrices. Possible applications of the results obtained are discussed.

The properties of matrix-convex functions, which may take values from an expanded numerical axis, are analyzed. Matrix convexity is specified by a pair of matrices, a final set of matrices, or an infinite family of matrices. The results obtained are ...

A two-person zero sum noncooperative game with an interval uncertain strategy and a payoff function is considered. With the use of methods of an extended interval arithmetic, external estimates are obtained for generalized sets of lower and upper values ...

Parallel modifications of linear iteration schemes are proposed that are used to solve systems of liner algebraic equations and to achieve the time complexity equal to T = log₂ k · O(log₂ n), where k is the number of iterations of an original scheme and ...

In studying the surjectivity of set-valued mappings, a modification of the “acute-angle lemma” (or the “equilibrium theorem”) is used. This allows one to weaken the coerciveness condition. Some applications to differential equations (inclusions) with ...

This paper considers the problem of mathematical formalization and finding of explicit formulas for determination of risk functions in stock control models with goods of many kinds. The choice of the kind of goods and distribution of random variables ...

The class of polyhedral coherent risk measures that are used in making decisions under uncertainty is investigated. Operations are introduced on the measures of this class, and properties of these measures are studied. The problems of portfolio ...

Polynomial analogs of pseudoprime numbers are created (Fermat pseudoprimes, Euler pseudoprimes, and strong pseudoprimes). Some of their properties and interrelations are described. Efficient probabilistic algorithms of irreducibility testing are given ...

The paper deals with the solution of an equation that describes a particular case of the flow of the ideal liquid in which the vorticity is proportional to the flow function. To solve the equation, two methods are used, namely, the finite-difference ...

A version of the Newton method is presented. In constructing an auxiliary problem, constraints in the form of inequalities are not considered and the classical extremal problem is solved. Inequalities are taken into account owing to a special choice of ...