Aim: to consider the viscoelastic characteristics of a polymer hydrogel, namely, a polyvinylpyrrolidone and carboxymethylcellulose hydrogel, which were obtained for two values of the deformation amplitude in a fresh sample and in a swelled hydrogel sample.
Methodology. An approximation of the experimental data of dynamic measurements by the equations of the structural rheological model was carried out at individual intervals of the cyclic frequency of shear oscillations.
Results. The possibility of using the equations of the structural model to describe the frequency dependences of dynamic moduli is shown. The value of the coefficients of the rheological equations depends on both the deformation amplitude and the initial state of the hydrogel. Research implications. It is shown that the equations of the structural rheological model are capable of approximating the experimental data of dynamic measurements obtained for hydrogel samples at different deformation amplitudes.

Aim is to demonstrate that the principle of least action follows from the stability requirement. This means that it is possible to obtain fundamental laws of physics from stability, since they are derived from the principle of least action.
Methodology. A variational principle is considered which generalizes the classical principle of least action to any reference frames, including random non-inertial ones, and requires not only the first variation of the action function to be zero, but also the second variation of the action function to be non-negative.
Results. The principle of least action can be used to obtain the main fundamental laws of physics, therefore it can be argued that they follow from the stability requirement.
Research implications. The significance of the study lies in the fact that the axiomatic introduction of the stability principle leads to the axiomatics of mechanics, electrodynamics and other areas of physics.

Aim is to create a molecular dynamics model of the (001) Ni atomic block that can be used to study sputtering.
Methodology. The molecular dynamics method, the Box-Muller method to generate random numbers from normal distribution, the embedded atom method, the Fletcher-Reeves conjugate gradient method, the parabola approximation and the golden section methods to find the minimum of a function, and the Velocity Verlet method are used.
Results. A program for molecular dynamics modeling with preliminary relaxation of the atomic block has been created. The lattice constant and surface binding energy were calculated for blocks of different sizes. The correctness of the model has been shown.
Research implications. The results can be used by other researchers in developing similar models. In addition, the model created in the work will be used in practice in our future works to study the ejection of atoms during sputtering from the (001) Ni face.

Aim is to correct the value of the radius of the helium atom.
Methodology. A semi-classical approach is used, which is quite sufficient for the purpose of the work.
Results. The need to eliminate double standards when determining the angular momentum of quantum systems leads to the fact that the quantum of angular momentum ћ is assigned not to each electron of the helium atom, but to their quantum set. The consequence of this is the correction of the value of the radius of the helium atom, which turned out to be almost four times smaller than the tabulated value. A corrected formula for the radius of the helium atom has been found: r_1,2 = [1 + (1 + 7α²)]a₀/14 = 7,56∙10^–12 (м).
Research implications lie in the fact that the size of the helium atom is of significant importance, in particular for membrane technologies.

Aim is to characterize andesite, a volcanic mineral similar in structure and chemical composition to lunar regolith, under shock compression conditions at loading speeds of up to 800 m/s.
Methodology. Flat andesite samples were subjected to a one-dimensional impact by a striker accelerated in a pneumatic throwing device. The laser Doppler interferometry method was used to measure the velocity profiles of the free surface of the samples when a shock compression wave was released onto it in the pressure range from 0.5 to 1.9 GPa. The time of compression wave passage in samples of a given thickness was measured.
Results. For the first time, Hugoniot adiabats were obtained for bulk samples (with an average grain size of (80–90) microns, with grain sizes from 400 microns to several hundred nanometers) and monolithic andesite at relatively low impact velocities from 250 to 800 m/s. The surface velocity profiles at the ‘sample – diagnostic window’ boundary at the moment of the shock compression wave exit were obtained. A comparison with the Martian regolith analogue was made. It has been found that at mass velocities less than 350 m/s, a region of adiabatic compression occurs, in which only deformation of the substance without phase transitions in it takes place. At a pressure of 1.9 GPa, an elastic precursor was detected, which is typical for the region of elastic deformation.
Research implications. The results obtained are important for the development of engineering and numerical models of the properties of lunar soils in the interaction of landers with them in upcoming expeditions.

Aim is to provide a general idea of the comparison of methods and algorithms for decision-making in a fuzzy information situation in risk management.
Methodology. In the modern world, with a significant jump in the development of information technology and a significant increase in the volume of information, new means and methods for investing appear which in turn increases the number of situations with increased risks. Such situations require modern and timely solutions. Situational information processing algorithms help optimize the number of such situations and minimize them. And for the processed volume of risk situations, both classical methods of transmitting information and methods of transmitting and processing information using quantum technologies can be used.
Results. Digital and quantum methods of information transmission and processing are presented. Advantages and disadvantages when working with them are described.
Research implications. The described methods and algorithms can be applied and used in various spheres of the economy when working with increased risks of their forecasting and prevention.