This work proposes an expanded 3D Euler model for calculating the spatiotemporal evolution of pollutant concentrations released into the atmosphere under changing meteorological conditions. The model, alongside the advection-diffusion equation, combines in a single system: Stokes’ law deposition (for solid particles), temperature-dependent chemical decomposition according to Arrhenius’ law, retention by plants (passive sink), precipitation washout (rainout), terrain-dependent resistance, and parameterization of turbulent diffusion based on Pasquill-Gifford stability classes. The numerical solution employs upwind/QUICK convective fluxes, central difference diffusion, and a time step stabilized by the CFL criterion. Scenarios covering various wind directions and speeds demonstrate the role of terrain in flow direction and atmospheric-related dispersion characteristics. The model is mass-balanced.

This paper proposes a Context-adaptive Audio-Visual Neural Network (CAVN) model for anomaly detection in public safety systems. Existing approaches primarily rely on visual data and employ simple fusion strategies for combining modalities, which leads to limitations in capturing complex semantic relationships. The proposed model consists of four main components: a visual feature extraction module based on SlowFast architecture, an audio feature extraction module based on Audio Spectrogram Transformer (AST), a fusion module based on bidirectional cross-attention mechanism, and a temporal context aggregation module based on Transformer encoder. The main scientific novelty of the model lies in the adaptive modality balancing mechanism, which dynamically adjusts the relative importance of modalities under different conditions (dark/bright, noisy/quiet). Experimental results demonstrate that the proposed CAVN model outperforms existing methods by in overall accuracy and by in dark conditions. Ablation studies confirmed the contribution of each module to the overall performance.

A mathematical and numerical model is presented for the process of liquid solution filtration in a cylindrical porous filter. The model is based on the Brinkman-Darcy equations, describing fluid motion in a porous medium with porosity and permeability linked through the Kozeny-Carman relation. The transport of dissolved substances is governed by the advection-diffusion-reaction system, complemented by the LDF kinetics and the Langmuir isotherm for adsorption. The model also incorporates a clogging (colmatation) equation that accounts for particle deposition and temporal reduction of filter porosity. A finite-difference numerical algorithm with iterative pressure correction using the conjugate gradient method is developed, ensuring stability according to the Courant-Friedrichs-Lewy criterion. The proposed approach enables analysis of the coupled hydrodynamic, mass transfer, and adsorption phenomena, allowing for assessment of filtration efficiency and prediction of filter lifespan in liquid purification systems.

The paper presents a mathematical model of pollutant dispersion in turbulent airflows within the atmospheric boundary layer. The model is based on the advection–diffusion equation and the system of Navier–Stokes equations, complemented by the ???? − ???? turbulence model. In this formulation, the model provides an accurate description of the spatiotemporal dynamics of pollutant concentration. A point emission source is introduced through the Dirac delta function, which makes it possible to correctly represent localized pollutant releases. For the numerical solution of the problem, an algorithm based on a finite-difference scheme with directional (upwind) flux approximation and iterative pressure correction using the conjugate gradient method is proposed. Boundary and initial conditions are formulated for the near-surface atmospheric layer, taking into account the spatial inhomogeneity of the wind field and the vertical gradient of turbulent energy. The developed model ensures a stable solution and can be applied to analyze pollutant dispersion dynamics, forecast air quality, and optimize urban ventilation systems under various meteorological conditions.

This paper formalizes and extends the classic concept of the "Middle Turkic"language (Karimov–Mutalov, 1992) by applying tools from corpus and computational linguistics. The proposed model frames the selection of an "optimal"form for a linguistic unit as a multi-criteria optimization problem over a set of factors, including frequency, prevalence, simplicity, cultural compatibility, and a matrix of interlingual mutual intelligibility. To ensure stability and interpretability, the model introduces soft (softmax) and "saturating" weights, domain and diachronic modifiers, and inter-language "fairness"constraints. The model achieves up to 89% accuracy in linguistic form selection, a 78% intelligibility level, high grammatical consistency (0.92), and a high assimilation rate (0.85). The paper concludes by discussing the model’s potential applications in machine translation, its limitations, and directions for future validation.

The problems of forecasting the pollutant concentration in the atmosphere by means of mathematical modeling remain one of the most relevant scientific areas. Such a conclusion can be drawn from the analysis of scientific publications related to the problems of mathematical modeling of complex processes of mass transfer in the atmosphere. In this regard, the aim of this study is to develop a mathematical model for the transport and diffusion of emissions of polluting particles of technogenic and natural origin and an effective numerical algorithm for solving the problem with a high-order approximation in time and space variables. A feature of the proposed mathematical apparatus is that, in addition to the main factors, the model takes into account the phenomenon of the capture of aerosol particles by elements of vegetation in the land environment. The solution algorithm is based on the method for splitting the original problem into physical factors: advection, diffusion, and absorption of a substance in the air mass of the atmosphere. Computational experiments were conducted using real meteorological parameters and data on sources of atmospheric pollution. An analysis of the results of numerical calculations showed their good agreement with the data of field measurements and the results obtained by other authors. Thus, the adequacy of the developed mathematical model and the accuracy of the numerical algorithm were sufficiently substantiated. In the course of experiments, the influence of the main factors on the process of transfer and diffusion of particles of harmful substances in the atmosphere was established. Particular attention was paid to the study of how the green cover on the terrain affects the propagation of particle concentration fields; what portion of pollutants can be absorbed by vegetation elements compared to other types of the underlying surface. The practical outcome of the study is the possibility of developing recommendations to support decision-making on maintaining the ecological balance of the environment in industrial regions and protecting it from the possible negative impact of technogenic factors.