It is known that when a drop of water sitting on a cooled horizontal flat substrate freezes, a sharp conical tip appears on the top of this drop. The process of freezing of hydrogel ball segments pre-saturated with water was studied. The segments were placed on a horizontal cooling flat surface. The surface was cooled by the Peltier element. The sharp conical tips appearance on the tops of hydrogel ball segments was recorded for the first time. They are similar to the tips appearing on the frozen water drops. It was established by direct video visualization that upward solidification fronts are observed during the freezing of hydrogel ball segments. These fronts curvature and volumetric expansion of water in hydrogel nano-pores are the reasons of tips appearance during freezing. It was also found that the material of these tips after freezing is ice. At the same time, no traces of polyacrylamide were found in the tips.

A method has been developed for constructing exact solutions of complex nonautonomous nonlinear equations of mathematical physics, the coefficients of which explicitly depend on time, by using solutions with generalized or functional separation of variables of simpler autonomous equations of mathematical physics, the coefficients of which do not depend on time. Specific examples of constructing exact solutions of nonlinear equations of mathematical physics, the coefficients of which depend arbitrarily on time, are considered. It is shown that solutions with generalized and functional separation of variables of nonlinear equations of mathematical physics with constant delay can be used to construct exact solutions of more complex nonlinear equations of mathematical physics with variable delay of a general form. A number of nonlinear reaction-diffusion equations with variable delay are described, which allow exact solutions with generalized separation of variables

Artificial pulmonary ventilation (ALV) is considered one of the most important methods of intensive care, part of a set of measures to maintain the vital functions of the body in critical conditions. In connection with the creation of intelligent ventilation modes that increase the efficiency of control of ventilators, it is necessary to develop and apply various computational schemes for processing data on the values of the patient’s current indicators during mechanical ventilation. The paper discusses the problem of identifying abnormal emissions and leveling their negative impact on the identified significant characteristics of the calculated indicators necessary for adopting optimal values of ventilation flow parameters that ensure the most effective treatment of the patient. To solve this problem, the article discusses and applies several so-called robust methods and computational schemes based on them for identifying anomalous outliers in the values of indicators of the patient’s condition and determining their future values.

The problem of pulse propagation described by the nonlinear Schrödinger equation with non-Kerr nonlinearity of the third, fifth and seventh powers is considered. Optical solitons of the considered equation are found using simplest equations method and implicit functions method. The area of acceptable model parameters is illustrated. A modification of the split-step Fourier method is presented. Optical soliton propagation process is studied numerically. The validity of analytical calculations has been proven. The process of the interaction of a soliton pulse with a disturbance in the initial condition is analyzed. The process of the soliton pulse propogation in a medium with a random noise simulated. The stability of optical solitons of the cubic-quintic-septic nonlinear Schrodinger equation is proved. The influence of higher nonlinearity terms on the nonlinear Schrodinger equation solitary waves is studied. The soliton collisions in the presence of higher nonlinear terms are simulated. It is shown that in the presence of higher nonlinear terms, the solitons interact inelastically upon collision.

This article deals with fuzzy and fuzzy-PI controllers for the automatic power control system of a non-linear mathematical model of the VVER-1200 nuclear reactor. The power control systems loop includes a mathematical model of the electromagnetic stepper motor, a model of in-core and ex-core neutron flux sensors, and a refined mathematical model of the group 12 of control and protection system control rods, obtained by approximating experimental data using the Levenberg–Marquardt algorithm for nonlinear least-square problem. Based on the state-space model, 10 transfer function matrices of the nuclear reactor corresponding to the power range of 10 to 100 % of the nominal power were also determined, and 10 classical PI controllers were modelled to ensure stability margins of at least 60 degrees in phase and at least 10 decibels in amplitude for each power level of the plant. Simulation results show significant advantages of the developed fuzzy controllers both in the steady-state power maintenance mode considering noise in the neutron flux sensor channel, and in load-following mode at different power levels.

The object of the study is a family of three-dimensional dynamic five-element dissipative systems with one quadratic nonlinearity, an arbitrary parameter A and a parameter e, e² = 1. In systems of the specified family, the parameter A is included as a multiplier with a linear element (systems of the first class), or as a separate constant element (systems of the second class). A characteristic feature (from a qualitative point of view) of this family is the presence in it of systems with chaotic behavior, in particular, with strange attractors. The purpose of the study is to determine the nature of the moving singular points of solutions of the specified family. To analyze solutions to systems of the family under consideration, the Painlevé test was used, as well as reducing the systems to equivalent second- or third-order equations and comparing the latter with known nonlinear P‑type equations. Solutions of systems of the first class do not have the Painlevé property (despite the fact that the components of the solutions of some of them do not have moving singular points at all), or do not satisfy the Painlevé test. Similarly, solutions of systems of the second class either do not satisfy the Painlevé test or do not possess the Painlevé property, despite the fact that the components of the solutions of some systems do not have moving singular points at all. The presence of systems with chaotic behavior among the systems under consideration allows us to indicate autonomous third-order differential equations with chaotic behavior.

This paper describes a covert broadband communication system using surface acoustic wave delay lines (SAW delay lines). A matched filter consisting of ten SAW delay lines is designed. The delay lines consist of unidirectional transmit-receive and reflective interdigital converters (IDCs), having an operating frequency band of 2 MHz, a distance between central frequencies of 4 MHz, and operating in the frequency range 905 – 941 MHz. Based on these filters, a covert broadband communication system has been developed, which makes it possible to obtain an output signal 5 times higher than the noise level. The maximum signal delay is 13 µs, which is twice the delay between IDTs. The distance between the IDTs can be varied depending on the LS frequency. By setting delays in the LP in such a way that the total delay in the LP with the same frequencies is always the same, it is possible to create different matched filters in the same frequency range.