№ 1 (64) (2024)

In this work, modified Gerasimov–Caputo formulas were obtained for the first time. The modified formulas take into account the value of the derivative of the function at zero with an order of one less than the order of the derivative under the sign of the Gerasimov–Caputo integral. Without taking into account the new term in the Gerasimov–Caputo formulas, it is not always possible to calculate the fractional derivative on any order interval and for any function. The paper also describes a simple numerical algorithm with the Gaussian quadrature formula, which allows one to calculate the fractional derivative with double precision. tables of fractional derivatives for the sine and cosine functions have been compiled. Moreover, the first half of the tables (in the interval of order (0,1)) and the second half of the tables (in the interval of order (1,2)) were obtained by programs using different algorithms. In the work, an absolute error in calculating the fractional derivative of 10–15 was achieved.

The gyrostat moves around a fixed point under the forces influence in pseudo-Euclidean space with signature (3,1). The resulting moment of the external forces system and the gyrostatic moment are specified relative to the coordinate orthoreper, invariably associated with the gyrostat carrier, and are constant. Three types of gyrostat motion are given, in each of which the resulting force vector-moment is collinear to of the main axis of the gyrostat inertia, and the gyrostatic moment is orthogonal to this axis. The vector manifold of the gyrostat angular velocities and the field of its phase trajectories in the state space are found with the parametric integration method using. Integration of the gyrostat motion equations is carried out in quadratures and elliptic functions of time.

Automatic digital controllers that ensure the operation of autonomous (on-board or embedded) devices must use robust or adaptive algorithms. To compile a program in C language that implements modern effective control algorithms, model-based design technology (MOP technology) is used, the essence of which is that first a simulation computer model of the automatic control system is being compiled and debugged in a higher-level language, and then the controller operation code for the microprocessor is generated. The article provides an overview of robust and adaptive algorithms that can be used in on-board automatic control systems. Computer models of control systems were built using these algorithms in MATLAB and SimInTech packages, as examples of the initial stages of model-based design technology.

The development of user-to-user communication methods, such as social media, has resulted in the amount of inaccurate information reaching record levels. This problem affects not only regular users of social media, but also the media, which may refer to such messages as a source of information. The spread of false information leads to both financial and life-threatening problems. It is almost impossible to trace these messages manually and therefore it is required to create an algorithm that can perform this process automatically. The purpose of this paper is to try to create such an algorithm for the Russian language using machine learning methods. The data on which the models are based is a sample of data that has undergone the process of manual annotation. The sample has undergone the process of preparation and balancing. From this sample, 29 attributes were obtained which can be divided into 3 categories: user, text and distribution. These attributes and were applied to obtain classification models that are able to predict with sufficiently high probability. The result of this work is an algorithm for predicting the presence of inaccurate information in a social network post.