2023.4

The paper considers the algebraic properties of the Hadamard product (Shur product, componentwise product) of error-correcting linear codes. We discuss the question of the complexity of constructing the basis of Hadamard’s product by known bases of factors. Also, we introduce the concept of quotients, quasi quotients, and maximal (concerning inclusion) quasi quotient from the Hadamard division of one linear code to another. We establish an explicit form of the maximal quasi quotients of the Hadamard division. It proved the criterion of existence for a given code of an inverse code in a semiring formed by linear codes of length n with operations of sum and Hadamard product of codes. We also describe the explicit form of codes with an inverse code in this semiring.

The problem of maximizing the horizontal coordinate of a point mass moving in a vertical plane under the influence of gravity, viscous friction, curve reaction force and thrust is considered. It is assumed that state constraints are imposed on the trajectory inclination angle. The system of equations belongs to a certain type, which allows us to reduce the optimal control problem with constraints on the phase variable to the optimal control problem with control constraints. The sequence and number of inclusions of phase constraints in the optimal trajectory and synthesis of optimal control are determined.

The lower bound for bilinear complexity of multiplication of arbitrary matrices over finite fields is improved.

The article deals with the task of testing drugs for bioequivalence. Bioequivalence studies underlie the reproduction of drugs that have confirmed their efficacy and safety. The main method for testing the bioequivalence hypothesis is the procedure of two one-way Schuirmann tests. Due to inaccurate data, as well as omitted data at the drug trial stage, the Schuirmann criterion allows for errors that exceed a given probability of error of the first kind. Such situations are dangerous for patients who may receive a drug that is not equivalent to the original drug. The authors presented a new criterion that is more sensitive to differences in characteristics affecting the bioavailability of drugs, which reduces patient risk. Note that the new criterion generalizes the classical Schuirmann criterion, preserving its useful properties.

The task of urgent detection of pathogen microorganisms in the human body is a relevant problem in the field of medicine. An approach based on seeding the biomaterial into the media nutritious and monitoring the bacterial colony growth is on the popular side by today’s standards. At the same time it possesses a set of downsides, caused generally by the human factor, introducing possible mistakes to medical verdicts. This work is dedicated to the development of intelligent data-driven technologies for processing microbiological analysis data in the form of photographic images of Petri dishes. Such technologies must allow reducing the dependence on the human factor as well as increasing the key factor quality of the analysis. The results of the conducted experiments allow making a conclusion that developed heuristic and neural network methods for detection and classification of the microorganism colonies surpass existing approaches and allow automating the key stages of the microbiological analysis as well as introducing proposed methods in practice.

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. Also it was shown that there is no universal polynomials for the class of linear functions depending on two arguments for any even k. In this paper we prove that polynomial xy + xz + yz is universal for classes of linear functions depending on three arguments for arbitrary odd k and polynomial xy + zw is universal for classes of linear functions depending on four arguments for any k.

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.