The article considers exact and periodic solutions of nonlinear electrodynamics problems for ferromagnetic and ferroelectric media. The method of decomposition by Jacobi elliptic functions is used to obtain solutions. The solutions to the problems are found using sn ξ — sine amplitude, cn ξ — cosine amplitude, and dn ξ — delta amplitude of the Jacobi function.

This paper presents a systematic analysis of contemporary directions in the application of artificial intelligence (AI) technologies to urological practice and pharmaceutical research. The principal domains of intelligent-algorithm deployment are examined, encompassing automated medical image analysis, the development of predictive models based on machine learning methods, the utilisation of robotic surgical systems, and the integration of digital platforms for remote patient monitoring. Particular attention is paid to the role of hybrid neuro-fuzzy architectures such as ANFIS in clinical decision support and to the ethical and regulatory challenges accompanying the adoption of AI in healthcare. The study evaluates the current state and future prospects of AI-driven approaches in urology and highlights their potential to enhance diagnostic accuracy, optimise therapeutic decision-making, and improve patient outcomes.

This study develops a hybrid modeling framework for geothermal heat flow prediction in the tectonically active Dushanbe Basin by integrating Grey Wolf Optimization (GWO) with an Adaptive Neuro-Fuzzy Inference System (ANFIS). The proposed approach addresses the challenges of nonlinear relationships, sparse measurements, and uncertainty in geothermal datasets. Borehole-derived parameters, including depth, water temperature, thermal conductivity, and measured heat flow, were used as model inputs, with predicted heat flow as the output variable.

In this paper, generalized Jacobi elliptic functions sn ω(z), cn ω(z), dn ω(z) are applied to the construction of particular solutions of certain classes of elliptic systems of partial differential equations of second order on the complex plane C with Cauchy–Riemann operators 2∂_z = ∂_x + i∂_y, 2∂_z̄ = ∂_x − i∂_y, the Laplace operator Δ = 4∂_z(∂_z̄) = ∂_xx + ∂_yy, and the Bitsadze operator 4∂²_z̄ = 4∂_z̄(∂_z̄) = ∂_xx − ∂_yy + 2i∂²_xy, where the variables z = x + iy, z̄ = x − iy are independent.

This paper examines the velocity and equilibrium temperature of a stationary wave of filtration combustion of gases as a function of the fuel-equivalent ratio. Calculations of the stationary wave velocity and equilibrium temperature were performed using previously obtained relationships. The calculations revealed that positive values of the hydrogen-air mixture wave velocity, and consequently, superadiabatic equilibrium temperatures, occur only for sufficiently saturated or extremely fuel-lean mixtures. During combustion of a methane-air mixture, both copropagation and counterpropagation of the combustion wave occur. The equilibrium temperature of the methane-air mixture is higher than that of hydrogen-air and propane-air mixtures, and the superadiabatic temperature is achieved in the fuel-rich region, at less saturated mixture compositions. The stationary wave of filtration combustion of a propane-air mixture predominantly propagates in a counterpropagation direction and exhibits subadiabatic equilibrium combustion temperatures.