Currently, 6 % of the total population of the planet has both types of diabetes mellitus, and 4% have bronchial asthma. It is predicted that the number of people with these diseases will increase every year. A large percentage of all those suffering from the above diseases are children. An urgent task is to develop a non-invasive method for diagnosing type 1 and type 2 diabetes, asthma and other diseases. An approach has been developed for preparing samples of human exhaled air for their subsequent analysis using a method based on infrared laser spectroscopy. The method used is described in detail in this work. Using an installation based on an infrared quantum cascade laser, the transmission spectra of human exhaled air are analyzed. From the obtained spectra, it is possible to calculate the concentrations of biomarker substances, deviations from the norm are associated with the development of certain diseases or pathologies in the patient. In this work, an analysis of existing types of air dehumidifiers was carried out, for example: capillary column, cryotrap, adsorption dehumidifiers, etc. A Nafion dehumidifier was chosen as the most optimal solution for use in an experimental setup with an infrared quantum cascade laser. Based on the results of studies of the spectra of exhaled air from patients with previously known diagnoses, a method for drying a sample of human exhaled air was developed and described, and the absolute humidity of the dried exhaled air sample was calculated

 A strongly nonlinear partial differential equation with three independent variables of the form 𝑢_𝑡 = = 𝑢_𝑥𝑥𝑢_𝑦𝑦−𝑢²_𝑥𝑦, which occurs in electron magnetohydrodynamics, isconsidered. Multiparameter transformations that preserve the form of this equation are described, as well as two- and one-dimensional reductions that lead to simpler partial differential equations with two independent variables (including stationary equations of the Monge–Ampere type and nonstationary heat equations) or ordinary differential equations. By methods of generalized separation of variables, exact solutions are constructed, many of which admit representation in elementary functions. More complex solutions are also considered, which are expressed in terms of solutions of linear diffusion-type equations.

The paper deals with one-dimensional linear homogeneous Klein–Gordon type equations with constant and proportional delay, which, in addition to the desired functions 𝑢(x, 𝑡), contain functions with constant delay of the form 𝑢(x, t – t), where t > 0 is the constant delay, and functions with proportional delay of the form 𝑢(x, 𝑝𝑡), where p is the proportionality coefficient. Exact solutions of such equations expressed in elementary functions are given. Initial boundary value problems with general initial data and homogeneous boundary conditions of the first, second and third kind, as well as mixed boundary conditions, are formulated. A detailed description of solving these problems using the method of separation of variables is provided. As a result, analytical formulas for solutions of initial boundary value problems for linear homogeneous Klein-Gordon type equations with constant and proportional delay are obtained.

The work uses a technique for representing solutions to a system of nonlinear equations of motion in the form of infinite trigonometric series of two spatial variables. The coefficients of the series are the desired functions of time, for which an infinite system of ordinary differential equations is written. The initial data are specified in the form of finite trigonometric sums. Approximate solutions to the stated Cauchy problems are also constructed in the form of finite segments of trigonometric series. For various initial data, the work considers specific nonstationary two-dimensional gas flows that are periodic in the spatial variables x, y and analyzes their properties.

The article is devoted to numerical studies of dense hot plasma flows in coaxial channels of plasma accelerators. Plasma is considered as a continuous electrically conducting medium, the behavior of which is described in terms of magnetic hydro dynamics (MHD). The work uses a mathematical model with nonstationary equations of “ideal” single-fluid magnetic hydro dynamics, obtained in a quasi-one-dimensional approximation. The purpose of the work is to study the influence of the geometry of the accelerator channel in the form of a nozzle and the external longitudinal magnetic field on the parameters of steady-state transonic super-Alfvénic acceleration MHD flows, which are of the greatest applied interest in the development of plasma engines. It has been demonstrated that a longitudinal magnetic field causes rotation of the flow and slightly reduces the acceleration characteristics of the channel. It has been established that the location of the “waist”, where the minimum cross-section of the channel is achieved, has practically no effect on the input and output flow values, but significantly affects the flow parameters inside the channel area. It is shown that the channel geometry affects the value of the critical longitudinal magnetic field corresponding to the boundary of the super-Alfvénic flow regime.

Currently, the research and development of an effective human-machine interface for robotic complexes is relevant. To increase the efficiency of controlling a robotic complex, several interfaces operating in parallel mode can be used. In particular, there is a multi-channel human-machine interface, which involves the interaction of several interfaces. There are various algorithms for the interaction of several interfaces aimed at selecting a command that needs to be sent to the robotic complex at a given time. To justify the feasibility of the interaction algorithms, it is necessary to apply a methodology for testing a multi-channel human-machine interface. This article considers different approaches to the implementation of this methodology: based on the statistical test method and based on modeling of results. Based on the results of statistics collection, confusion matrices are formed. In this article, different types of confusion matrices are considered, as well as metrics that can be used to evaluate the efficiency of the human-machine interface taking into account type I and II errors. In the case of modeling the results, this article are considered modeling based on the type of distribution and modeling based on generating a confusion matrix. Simulation of results can be used when it is impossible to collect large statistics, to check the feasibility of using interaction algorithms.