Articles

A one-line queueing system with two priority classes, relative priority, Poissonian input flow with random intensity and infinite number of places in queue for waiting is studied. The current intensity value is taken at the beginning of the time reckoned for the arrival of the next requirement. Successive values of the flow intensity form a Markov chain of a special kind. The heavy traffic limiting distribution of the queue length for the least priority class is obtained.

The paper describes algorithms for converting linear control systems with interval parameters from the state space representations to the form of transfer functions and vice versa. The results are accompanied by computational examples demonstrating the possibilities and limitations of the proposed approach.

The article discusses the development of a system for identifying the channel of information leakage from a document photo taken from a computer screen via digital watermarks integrated into the image on the monitor. The article also presents the results of an experimental study to prove the properties of the algorithm and its resistance to deliberate attacks.

Recurrent sequences over a set of integers are considered, in which arbitrary superpositions of polynomial functions and functions close to polynomial ones are used as generating functions, — almost polynomial recurrent sequences. A series of functions of the form b · ji(x) is distinguished. Each of these functions, together with polynomial functions, allows us to construct generating functions that make it possible to determine almost polynomial recurrent sequences that simulate calculations on Minsky machines. Based on this result, algorithmically unsolvable problems related to these almost polynomial recurrent sequences are formulated. Consequences are obtained that significantly expand the range of functions capable of generating recurrent sequences with algorithmically unsolvable problems.

This paper is devoted to the problem of separation of mixtures of probability distributions. An optimization method is proposed as an alternative to the EM-algorithm (Expectation-Maximization) for statistical estimation of mixture parameters. The idea of approximating the distribution of increments (logarithms) of financial data by a mixture of normal laws is considered. The practical application of such an approximation to the problems of calculating and predicting volatility, as well as to the problem of calculating the risk measure (Value at Risk), is presented. The results obtained allow us to conclude that the application of mixtures of normal distributions to the description of financial data is adequate.

The article deals with localization methods of inverse magnetoencephalography tasks. Localization methods are important in real clinical practice. During neurosurgical interventions, various areas of the brain can be damaged, including non-recoverable areas. Since the location of functional areas in the human brain is individual, the doctor must be able to localize these areas in the preoperative period with high accuracy. The developed methods serve the solution of such an important problem.

Similarity transformations are the main part of matrix theory, which studies numerous classes of special matrices. Accordingly, there are many ways of describing such classes. In most cases, one can verify whether a matrix belongs to the required class by a rational calculation, that is, by a finite algorithm using only arithmetical operations.

The use of a large number of drones set us the tasks of correct, transparent, and high-performance modeling of their collective activity within the framework of swarm behavior. For this, an example of transitioning from the description of the control system of a single drone to the behavior of a swarm of identical drones based on Hadamard algebra (product) was developed and given. It was found that the use of such an approach increases the performance of the model by dozens of times and allows modeling of swarm systems with a very large number of agents.

We study the existence of an implicit function, defined by an equation G(x, σ) = 0, in a neighborhood of an abnormal point (x0, σ0). We prove that if some λ-truncation of the mapping F(x) = G(x, σ0) is regular in a certain direction, then the sought implicit function exists.

The paper considers the problem of feedback control for a group of several quadrocopters. The main goal is to transfer this group from a given initial position to a given target position for a fixed period of time, provided that at each intermediate time instant the quadrocopters must be in a small neighborhood of a fixed smooth curve in space. A centralized group control scheme is used. The main difficulty here is the complex, nonlinear mathematical model, describing the movement of each individual aircraft. It is necessary to develop computationally efficient algorithms for approximate search for feedback control, which allow to cope simultaneously with nonlinear dynamics, point-to-point constraints on control parameters, as well as state constraints arising in connection with group motion (in particular, due to the requirements of pairwise collision avoidance). Modifications of ellipsoidal calculus methods are used here to construct such algorithms.

It is considered the question about continuity of optimal time, as the function of initial state, for linear control objects. We obtained some generalization of the Theorems 21, 22 from the second Chapter of monograph E.B.Lee, L.Markus “Foundations of Optimal Control Theory,” J.Wiley and Sons, 1967, connected with continuity of optimal time, as the function of initial state, for linear controlled objects. In the article we broadly use the apparatus of support functions from Convex Analysis. Our results are obtained in more constructive form than another general results In this direction. In the first part we consider stationary case and in the second part it is considered non-stationary case.

Approximate bilinear algorithms for multiplication of 2 × 3 and 3 × 4 matrices (complexity 18), 2 × 4 and 4×4 matrices (complexity 24), 2×5 and 5×4 matrices (complexity 30) are presented, and approximate bilinear algorithms for multiplication of 2×n and n×4 matrices (complexity 6n) over field of characteristic zero gotten via them.

Dirichlet boundary value problem for the elliptic equation in a rectangle with a noninteger degeneration and analytic coefficients is considered. Applying the method of spectral isolation of singularities, the formal solution to the problem is constructed as a series which exhibits its non-analytic dependence with respect to y at the origin. Green’s function method verifies the convergence of the series to the classical solution of the considered problem.

The time optimal control problem with a state constraint investigates in the article. The object’s behavior is described by a system of second-order differential equations. The coefficient matrix for state variables has zero eigenvalues. The state constraint is linear. An admissible control is a piecewise continuous function that takes values from a given compact set. Sets of controllability to the origin are constructed for time intervals of various lengths.

It was proved earlier that product xy is a universal function for the class of linear functions depending on two arguments if k = 6l±1. In the paper we prove that there is no universal polynomials for the class of linear functions depending on two arguments for any even k.