E-learning brings new dimensions to traditional education. This especially affects countries that, due to many factors, have historically been considered the “talent pool” for the world community. In this study, a model for financing e-education has been developed that is applicable to Russian realities. The model was built around the balance between demand (global politics, economics, and principles of sustainable development) and supply (sources of direct financing). As a result, a key challenge of improving the e-learning financing methodology and models, specifically the efficiency of government spending and private investing, demands the use of new approaches and mechanisms. To improve e-learning financing, a clear understanding of the applied purpose of public and private means is required. Responsibilities for the e-learning outcome of institutions that receive financing are linked to their status. An unclear understanding of these issues is more likely associated with the issue of transparency of financing than with inefficiency. The proposed model allows transforming the “standards” of financing both in the field of e-education and Russian education in general and presents a new vision of participants’ interaction in the educational process, taking into account a set of restrictions and market features.

This study examines the flow of hyperbolic nanofluid over a stretching sheet in three dimensions. The influence of velocity slip on the flow and heat transfer properties of a hyperbolic nanofluid has been investigated. The partial differential equations for nanoparticle solid concentration, energy, and motion were turned into ordinary differential equations. Nanoparticle mass fluxes at boundaries are assumed to be zero, unlike surface concentrations. The influence of the main parameters on flow characteristics, surface friction coefficients, and the Nusselt number has been visualized. The results suggest that Brownian motion has a negligible impact on the heat transfer rate. The ratio of the elastic force to the viscosity force was found to decrease the fluid velocity. The resulting thermophysical properties of nanofluids are in agreement with previous research. The present findings can be used to expand the potential for using nanofluids as a coolant in critical thermophysical and industrial installations.

The main aim of the study is to deepen understanding of quasilinear hyperbolic systems through the investigation of their asymptotic solutions, with specific objectives related to theoretical analysis, wave dynamics characterization, and practical applications in physics and engineering. The methods of mathematical analysis employed include asymptotic analysis, Taylor series expansions, and the formulation of transfer equations. The paper considers systems of quasilinear hyperbolic equations in partial derivatives of the first order with two independent variables. The main results of the paper are: 1) high-frequency asymptotic solutions of small amplitude for quasilinear hyperbolic systems of the first order were obtained. For fixed values of t and , values of the modulus are limited by р→∞, because the transfer equations depend on p. Thus, the moduli of the decomposition coefficients are bounded at p→∞ and at fixed u and ; 2) It has been established that for ui0= const, , , independent of t, the solution of the equation is greatly simplified because the coefficient а0 is constant. For the linear function , is also constant. Practical applications of the results lie in fields such as fluid dynamics, wave propagation, and materials science, where understanding dispersion phenomena is crucial.