In the world, air pollution ranks among the primary sources of risk to human health and the environment. To assess the risk of impact of atmospheric pollution, a comprehensive research cycle was designed to develop a unified ecosystem for monitoring air pollution in industrial cities in Kazakhstan. Research involves analyzing data for the winter period from 20 automated monitoring stations (AMS) located in Almaty and conducting chemical-analytical studies of snowmelt water samples from 22 points to identify such pollutants as fine particulate matters, petroleum products, and heavy metals. Research includes a bio-experiment involving the cultivation of watercress on samples of melt water collected from snow cover to examine the effects of pollution on plants. In the framework of this research, we determined API based on data obtained from AMS. In order to determine the influence of atmospheric pollution on the environment, a multiple regression model was developed using machine learning algorithms to reveal the relationship between the bio-experiment data and data on pollutants of chemical-analytical research. The results revealed a wide spread of pollutants in the snow cover of the urban environment, a correlation between pollutants in the snow cover and the airspace of the city, and their negative impact on flora.

In this paper, we consider an elliptic equation with strongly varying coefficients. Interest in the study of these equations is connected with the fact that this type of equation is obtained when using the fictitious domain method. In this paper, we propose a special method for the numerical solution of elliptic equations with strongly varying coefficients. A theorem is proved for the rate of convergence of the iterative process developed. A computational algorithm and numerical calculations are developed to illustrate the effectiveness of the proposed method.

In the paper, we study the elliptical type equation with strongly changing coefficients. We are interested in studying such equation because the given type equations are yielded when we use the fictitious domain method. In this paper we suggest a special method for numerical solution of the elliptic equation with strongly changing coefficients. We have proved the theorem for the assessment of developed iteration process convergence rate. We have developed computational algorithm and numerical calculations have been done to illustrate the effectiveness of the suggested method.

This article addresses the critical issue of harmful impurity dispersion in industrial facility atmospheres, considering point sources and factoring in photochemical changes. Conjugate equations are employed to assimilate pollutant data into the transfer equations' right side. Boundary conditions derive from global models like weather research and forecasting (WRF) and system for integrated modeling of atmospheric composition (SILAM), customized for the unique characteristics of an industrial city's pollutants. To encompass anthropogenic heat sources and surface heterogeneity, the model incorporates differential schemes for the atmospheric boundary layer, transport equations, and impurity transformation equations. Parameters for photochemical transformations, varying with weather and time of day, are derived from Ust-Kamenogorsk. A cloud-based geoinformation system (GIS) is developed for monitoring and forecasting air pollution. It assimilates data sources and accounts for photochemical transformations, enabling visualization of diverse weather and environmental scenarios. The article presents numerical modeling results of impurity spread and transformation influenced by mesometeorological processes, topography, and water resources within a specific city.

In this paper, the Cauchy problem for the Helmholtz equation, also known as the continuation problem, is considered. The continuation problem is reduced to a boundary inverse problem for a well-posed direct problem. A generalized solution to the direct problem is obtained and an estimate of its stability is given. The inverse problem is reduced to an optimization problem solved using the gradient method. The convergence of the Landweber method with respect to the functionals is compared with the convergence of the Nesterov method. The calculation of the gradient in discrete form, which is often used in the numerical solutions of the inverse problem, is described. The formulation of the conjugate problem in discrete form is presented. After calculating the gradient, an algorithm for solving the inverse problem using the Nesterov method is constructed. A computational experiment for the boundary inverse problem is carried out, and the results of the comparative analysis of the Landweber and Nesterov methods in a graphical form are presented.