卷 25, 编号 2 (2024)

The work is devoted to the study of sets of aperiodic words over a finite alphabet. The set of aperiodic words can be considered as a dictionary of some finite formal language. The existence of infinite words in two-letter or three-letter alphabets that do not contain subwords that are third powers or, respectively, squares of other words was first discovered more than a hundred years ago. S.I. Adyan in 2010 constructed an example of an infinite sequence of irreducible words, each of which is the beginning of the next and does not contain word squares in a two-letter alphabet. S.E. Arshon established the existence of an n-digit asymmetric repetition-free sequence for an alphabet of at least three letters. In the monograph by S.I. Ad- yan proved that in an alphabet of two symbols there exist infinite 3-aperiodic sequences. In the works of other authors, generalizations of aperiodicity were considered, when not only the powers of some subwords were excluded. In the monograph by A.Yu. Olshansky proved the infinity of the set of 6-aperiodic words in a two-letter alphabet and obtained an estimate for the number of such words of any given length. The au- thor previously considered the case of a three-letter alphabet only in the case of 6-aperiodic words. In this article, we prove the infinity of the set of m-aperiodic words in the three-letter alphabet at $m\ge 4$ and obtain an estimate for the set of such words. The results can be applied when encoding information in space communications.

The reliability of ring current-collecting devices during a given service life plays a decisive role in the opera- tion of power supply systems of various equipment and largely depends on the strength and reliability of all its components, in particular, contact rings. One of the most important characteristics of ring current collectors is the contact resistance, which is reduced by using non-ferrous and precious materials with low resistance, while increasing the downforce between the rings of the current collector. With an increase in the compression force F of the contact ring, the resistance of the contacts decreases to a certain minimum value and practically does not decrease with further growth of the force. The dependence of the contact resistance on the compression force has the form of a power function, the coefficients of which are determined experimentally.

However, the operability of the contact rings in such severe conditions can be ensured in the case of low speeds and a small number of loading cycles by using the low-cycle fatigue area on the Weller curve. Having determined the coefficients of the equation of the inclined section on the Weller curve in the area of low-cycle fatigue, it is possible to determine the number of permissible loading cycles at a given stress level or solve the inverse problem of determining the permissible stress level if the number of loading cycles is known. To substantiate the correctness of the selected compressive force and the corresponding stresses, methods for calculating the fatigue margin coefficient, as well as a method for calculating the reliability of the ring material, are proposed. Reliability is estimated by the Gauss curve and is numerically expressed in the form of the probability of failure-free operation and the probability of failure, for which the corre- sponding theoretical dependencies are obtained.

According to the proposed methods, calculations of the rings of the current-collection device used in EX- PRESS-type spacecraft were performed, which showed the operability of the methods and allowed to ensure the required service life of the contact rings and their reliability. A very simple analytical formulation of the methods allows us to solve both verification and design calculations of rings, depending on the task at hand.

Currently, most small spacecraft (MCAS) are becoming increasingly relevant in the modern space industry. To successfully complete the tasks assigned to them, the ICS must be oriented in some way in space relative to the Earth. The orientation and stabilization system (SOS) is responsible for this task, which is necessary for monitoring and controlling the position of the MC in space.

At the moment, the tasks for the MCA basically do not require complex turning maneuvers and high orientation accuracy, therefore passive and combined SOS have become widespread for them. Such systems have a long service life, are characterized by simplicity, high reliability and low weight. One of the typical systems used in modern space technology is gravity systems. The principle of gravitational SOS is based on the use of gravity acting on a body and moments of inertia relative to three mutually orthogonal axes.

This article proposes a 3U CubeSat ICA project with a gravitational orientation system. The design of such a satellite requires a gravitational stabilization device, which is necessary to deploy the ICA after separating it from the launch vehicle, as well as to create a restoring moment. The gravitational device is supposed to be placed between the rigidly bonded 2U MC and the third U MCA.

The advantage of this design is the fact that it becomes possible to place more payload on the MC without overloading it with various devices for the orientation and stabilization system.

After the end of operation of the International Space Station in 2028, the Russian Federation plans to develop a national orbital station project. The Russian Space Station will differ from its predecessor in a greater practical aspect. One of the tasks assigned to the station will be the launch and management of a group of small satellites for remote sensing of the Earth, as well as the interaction and maintenance of prospective satellite groups. Due to the limited maneuverability of the orbital station and the potential for a malfunctioning device to be at a significant distance from it, the use of an autonomous spaceplane is proposed to increase the transportation and technical capabilities of the station.

In the research, two aerodynamic designs of the spaceplane are presented, and one of them is chosen based on the results of the aerodynamic and weight analysis. The spaceplane configuration and algorithms for its operation on the orbit and descent to the atmosphere are also presented. The goal of the research is to compare the trajectory parameters during the descent of the spacecraft from different descent orbits. For this purpose, a task was formulated to determine the dependence of the area of the descent corridor on the initial parameters. The area of the descent corridor is determined by the boundary conditions, which depend on the operational parameters of the spaceplane. A computational program is written to solve differential equations of flight dynamics of a spaceplane by Euler's method in general and by Runge-Kutta method in a computational case. The results of the research are presented as the dependence of the area of the descent corridor on the altitude of descent. Graphical representations of the primary parameters of the spaceplane descent for the computational case are also presented.

The article contains the results of research on the automation of control of the geometric characteristics of gears. The use of coordinate measuring machines can significantly improve the productivity and accuracy of measurements. However, their use for testing gears requires the use of special programs for carrying out and processing the results of measurements of products with complex surface shapes. The use of software for metrological control of the geometric characteristics of worm and bevel gears makes it possible to achieve high accuracy of control and measurement work. To automate the control of geometric characteristics of worm and bevel gears, an additional module has been created for the standard program. With its help, all points of the measured curved surface of gears, obtained by contact method according to a standard measurement program, are structured into a single data array with a measurement protocol. Based on these data, the module generates a profile of the measured surface of a wheel tooth and builds a geometric contour of the profile of the measured tooth. The result of the module's operation is the formation of a general profile of the entire gear and its comparison with the original (theoretical) profile of the gear as a whole. The control process itself is carried out in a short time interval, which makes it possible to use the proposed approach to automating the control of gear profiles in small-scale production.

Manganese chalcogenides, which are promising for the manufacture of thermoelements, are being studied. The current is measured in the temperature range of 80–500 K, in the absence of external voltage, which can be caused by a temperature gradient (thermopower), a change in electrical polarization (pyroelectric current), piezoelectric current (when the sample is deformed, a potential difference arises) or thermionic emission (thermal emission current) . Temperatures of current anomalies and their relationship with thermionic current and polarization current are found. A change in electrical polarization with temperature will cause a pyroelectric current. Compensation for excess electrical charge will result in local electrical polarization. Partial decompensation will cause the formation of an electric field in the sample. The critical temperatures for the disappearance of electric polarization were determined for different concentrations. In the region of concentration of thulium ions flowing through the lattice, the activation nature of the thermionic current was established and the activation energy was found. The pyroelectric current has a smaller value compared to the thermionic current. The current mechanism is determined by the emission of electrons from deep traps and the temperatures of the maximum thermionic current correlate with the temperatures at which IR absorption disappears. The electric current density and its value depend on the type of substituted rare earth element are calculated.