Vol 65, No 4 (2025)

The article continues the development of a new approach to evaluate approximation parameters, in which the distance of the approximating function from the given finite set of points is estimated by a vector criterion, its components are the modules of residuals at all points. The vector criterion is used to define the distance preference ratio, and the best approximation function is considered to be nondominant with respect to this ratio. Compared to the first article of the authors (“Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki”, 2022), which is devoted to parametric methods, the present article offers nonparametric methods for several preference relations, including the Pareto relation and the relation generated by the information about the equality of criteria. Computational problems are considered and the relations between the introduced approximating functions and classical ones are investigated. Calculated examples are provided.

The problem of short-wave asymptotics of the Helmholtz equation with a localized right-hand side in the form of a rapidly decreasing function is considered in the article. We present an algorithm for calculating rays using the variational method and the wave field applying the canonical Maslov operator method for given boundary conditions. This approach is used for model examples, including those with a logarithmic feature of the ray family. In addition, we consider applications of the variational method for calculating rays in the illuminated region and in the caustic shadow region.

In this paper, we consider three Cauchy problems for (N + 1) dimensional nonlinear Sobolevtype equations arising in the theory of magnetic vibrations in ferrites. We obtain results on the existence and uniqueness of weak solutions to these problems that are local in time, as well as on the existence and uniqueness of weak solutions to these problems, and on destroying these solutions.

Two algorithms for broadband optical monitoring of the deposition of optical coatings are considered: the first one is without solving the additional inverse problem for refining the thicknesses of already deposited layers, the second one is with its solution. It is shown that refinement of the thicknesses of already deposited layers reduces errors in the layer thicknesses, but does not always provide a more accurate implementation of the required spectral properties of the coating. It is demonstrated for the first time that when choosing a control algorithm, the presence of the error self-compensation effect should be taken into account.

In the paper, we study the dependences of the linear increment of drift-dissipative instability in the equatorial region of the Earth ionosphere on helio-geomagnetic conditions, ionospheric parameters, and characteristics of equatorial plasma bubbles, on the fronts of which small-scale plasma inhomogeneities can develop. In the works of both the authors of the article and numerous studies by other authors, a high degree of correlation of the F-scattering phenomenon with the presence of plasma bubbles in the equatorial F-region of the ionosphere has been revealed. The classical explanation of F-scattering is related to the appearance and development of small-scale inhomogeneities on the fronts of equatorial plasma bubbles. The time period favorable for the generation and development of equatorial plasma bubbles is from one to two hours. The study was carried out in the form of a series of computational experiments, using the original two–dimensional mathematical and numerical model of Rayleigh-Taylor instability development developed earlier by the authors. Numerical simulations were performed for geophysical conditions favorable for the development of equatorial plasma bubbles in the equatorial F-region of the Earth ionosphere. This work is a continuation of the authors’ research. In contrast to the previous works of the authors, this paper examines the features of the increment of drift-dissipative instability depending on a wide range of conditions and parameters of the low-latitude ionosphere.

The paper is devoted to mathematical modeling of indoor pedestrian flows. The model under consideration is an analogue of the CTM transport macromodel. The current work explores the possibility of identifying split factors that were previously considered a priori given. These coefficients denote the proportions in which a flow of people is divided when moving to other rooms from the current one. We propose an identification algorithm based on interval estimates of both forward and backward reachability sets. The algorithm is illustrated with a numerical example.