The paper presents the results of studying the interaction of uranium-molybdenum alloys with corrosion-resistant steels in non-reactor diffusion experiments at temperatures of 700-850°C. A solid-phase interaction is observed in the U10Mo/Fe13Cr diffusion pair at an annealing temperature of 700°C. An increase in the annealing temperature above the eutectic transformation in the U-Fe system leads to a change in the diffusion pattern from bulk to grain boundary. The appearance of a liquid phase is observed, which crystallized into eutectic upon cooling. The growth rate of the interaction layer for diffusion pairs is described by a parabolic law. The results of the study of the effect of the molybdenum content in the uranium alloy on the kinetics of the growth of the interaction with Fe-Cr showed that the alloying of uranium with molybdenum up to 17 wt.% leads to a linear decrease in the growth rate of the entire interaction layer (K_tot) with corrosion-resistant steels, and the growth rate constant of the interaction layer in steel (Kp) decreases exponentially with an increase in the molybdenum content at a temperature of 750 °C, due to a decrease in the mutual diffusion coefficient in the U-Mo system with an increase in the molybdenum content. Kp decreases by 10 times, K_tot decreases by 30 times at a temperature of 750 ° C with an increase in the Mo content from 6 to 17 wt.%. Based on the results of the study of the structural and phase state of the interaction layer between uranium alloys and steels of various compositions, triple diagrams of the states of alloys of the following systems U-Mo-Fe, U-Mo-Fe(Cr), at temperatures of 750°C.

When transmitting analog signals through optical link, the signal quality deteriorates due to losses, nonlinear distortions, and noise, leading to a reduction in the effective number of bits in the transmitted signal subjected to analog-to-digital conversion. The papaer presents the results of an experimental study on the operation of a ultra-wideband ultra-high-frequency analog optical channel with a digital output. The aim of the work is to assess the signal transmission quality of the studied channel in terms of digital metrics. A comparison of the digitization results of the generator signal and the same signal transmitted through the analog optical link has been performed. By analyzing the radio frequency spectra of the digitized signals, the contribution of the optical part of the system to the change in signal quality has been evaluated. Measurements have shown that the level of nonlinear distortions and noise introduced into the signal by the optical channel was 14.7 dB, which is equivalent to a reduction in the effective number of bits by 2.44, primarily due to power losses in the optical part.

The Korteweg-de Vries-Burgers equation with a nonlinear source is studied. The Cauchy problem for this equation cannot be solved by the inverse scattering transform in the general case. Therefore, the equation is considered taking into account the traveling wave variables. The Painlevé test is applied to the resulting nonlinear ordinary differential equation to investigate its integrability. It is shown that general solutions of the nonlinear ordinary differential equation are expressed via the Weierstrass elliptic function and the first Painlevé transcendents under certain parameter constraints. The relationship between the Painlevé test and special methods for finding exact solutions of nonlinear differential equations is discussed. Special methods are used to construct analytical solutions with one and two arbitrary constants. Exact solutions with two arbitrary constants expressed in terms of the Weierstrass elliptic function are obtained. Exact solutions with one arbitrary constant of the Korteweg-de Vries-Burgers equation with a nonlinear source are found using the logistic function method. It is demonstrated that the family of equations for which exact solutions are found is significantly expanded by the use of special methods.

The generalized Chavi-Waddy-Kolokolnikov model used to describe the spatial and temporal dynamics of bacterial colonies is studied, taking into account possible “dispersion” – the mechanism responsible for migration and redistribution of the population in the environment. From a biological point of view, the model allows us to understand how bacterial cells, capable of collective movement, form ordered structures (e.g., clusters or waves) even in the presence of external disturbances. The main focus of the work is on the study of the dynamics of the bacterial colony system described by the generalized Chavi-Wadi-Kolokolnikov model. Thus, a numerical algorithm for mathematical modeling of these processes has been developed and its verification has been carried out on the basis of exact solutions of the model in the form of solitary waves. The influence of the problem parameters on the behavior of the bacterial colony system was investigated. In addition, the main attention in the work is paid to the study of bacterial self-organization processes, as well as to the classification of the dynamics of the system behavior for different values of the parameters of the problem under consideration.

The article presents an original hybrid approach that integrates fuzzy cognitive maps and regression analysis for forecasting in weakly formalized systems characterized by high levels of uncertainty and complex, unstructured interrelationships among variables. The core idea of the approach lies in utilizing expert judgments, expressed through linguistic variables and fuzzy numbers, to adapt the weighting coefficients of the regression model. The weights obtained from cognitive analysis are incorporated into the procedure of multiparametric linear regression using the weighted least squares method. This integration enhances both the accuracy of forecasts and the interpretability of the model. The results of an empirical study conducted in the  statistical environment demonstrate that the proposed approach outperforms (  = 10.21%) not only classical single forecasting methods, such as linear regression (  = 13.80%) and neural network models, e.g., the multilayer perceptron (  = 31.24%), but also successfully competes with ensemble methods, including random forest (  = 12.35%) and gradient boosting (  = 7.75%). The proposed approach can be effectively applied to forecasting natural gas supply volumes to China, as well as to solving other tasks that require the integration of qualitative and quantitative data.

The article presents a new approach for modeling voltage noise of chemical power sources for the purpose of datasets augmentation. For the first time known machine learning methods were applied for modelling of the voltage noises of lithium-ion batteries: a generative adversarial neural network based on LSTM layers was designed for this task. A brief statistical and spectral analysis of experimental voltage fluctuations is given. A qualitative and quantitative study of synthetic noise signals is carried out based on the performed analysis of real data. It is shown how the classification of generated data by a deep neural network results in generation of noise characteristics for a given state of charge of the battery. It is recommended how to apply the proposed technique to improve precision of interpretation of voltage fluctuations in power sources. An experimental assessment of the method’s effectiveness is given: a decrease in the determination error of the battery’s state of charge from its noise went from 6.8% to 4.9%.

The solution of the one-dimensional problem on interaction of ice and hydrophilic liquid is studied. Unlike the well-known Stefan problem of freezing of pure water upon contact with ice, the phase  transition temperature is not constant and depends on the concentration of hydrophilic liquid. The  concentration obeys the diffusion equation. We use a linear equation for the equilibrium temperature  and concentration at the contact boundary. The temperature in ice and liquid is described by the  heat conduction equations. Heat and mass transfer occurs at the phase boundary and water from the  hydrophilic liquid freezes onto the surface of the ice, its concentration increases, or, conversely, ice  dissolves at the boundary and the concentration of the hydrophilic liquid decreases. It is determined  by the input parameters of the problem. By introducing a self-similar variable, partial differential  equations are reduced to ordinary differential equations. Analytical solutions for the temperature in ice and liquid, and the concentration of the hydrophilic liquid are obtained. A transcendental equation  determines the self-similar parameter, and is solved numerically.

Some properties of the new transcendental Lambert W function are presented: the definition of the function, its graph, coordinates of characteristic points, and simple identities. Several examples are given showing how the W function can be used to solve analytically transcendental equations that contain power, logarithmic, and exponential terms. A recently obtained solution of the comparison of two functional expressions of power type  and  is presented, which arises due to the generalization of the comparison of numbers  and . An exact solution of the new generalized comparison of more complex power expressions  and  on sets of positive real numbers  and  for positive values ​​of the exponent α is obtained for the first time. The solution is presented both as an exact formula using the Lambert W  function and using graphs.

A method is presented for analyzing the electrophysical characteristics of LEDs (hereinafter referred to as LEDs) made from various semiconductor materials of group AIIIBV under the influence of external factors (ionizing radiation, long-term operation, elevated temperature, electric fields, etc.). This technique is intended to determine the ohmic resistance of LEDs, and individual proportionality coefficients, which allow targeted investigation of degradation processes in LEDs. It is shown that characteristic areas of the operating current flow are distinguished on the volt-ampere characteristics (hereinafter referred to as I-V characteristics): the low-current region LT, the LED ohmic resistance region – R region, and the high-current region HT. It is shown that the sublinear section of the direct branch of the I-V characteristic of a device with a p-n junction can be extrapolated by a linear dependence, the slope of which is determined by its ohmic resistance. Physico-mathematical relationships have been determined for the ohmic resistance of LEDs made of any materials. For the studied LEDs based on AlGaInP (with and without multiple quantum wells), AlGaN with multiple quantum wells and single-crystal GaP, the ranges of cutoff voltages are determined when forward current flows. A technique is presented that can be used to analyze the operation of any devices whose operating principle is based on the use of a p-n junction and a Schottky barrier.