Vol 31, No 1 (2025)

In the article we study the arithmetic nature of the coefficients of multiplicative eta-products, also called McKay functions. For some functions it is possible to establish Hecke correspondence between the coefficients of McKay and Hecke grossen-characters of imaginary quadratic fields. For other McKay functions such a correspondence is impossible but their coefficients can be represented as sums containing Hecke characters. The emerging Hecke characters are written out explicitly. In the article we write the first ten coefficients for all McKay functions. Calculations are based on Euler’s pentagonal formula. The article also talks about the connection between the coefficients of these functions and Shimura sums.

The problems’ solving of heat and mass transfer during the cyclic steam stimulation of the bottom-hole zone of the production wells allows us to control the process of high-viscous oil extracting. Based on the mechanics of multiphase systems development approaches, a mathematical model is formulated and a criterion method for the steam injection time determining into the bottomhole zone is proposed. Within the framework of this method, the following processes are crucial: heat transfer to the roof and bottom of the reservoir, the water-saturated zone increase during continuous injection, and the presence of a limiting pressure gradient in a non-Newtonian fluid. The developed model was tested on the synthetic data. The development dynamics of thermal, steam-water and oil-water fronts during injection in the radial formulation of the problem are investigated. The model was verified based on a comparison of the results obtained with calculations in a hydrodynamic simulator.

The article develops a method for organizing a logical-event hybrid model for analyzing socioinformational processes in their stages, event transformations and rapid disturbances. Specific situations with a non-stationary lifetime y of a series of non-overlapping generations are not described by continuous equations of mathematical biophysics. The use of multiparameter functional iterations with the effect of xn+1 = = ψ(r; xn)ξ(a; xn−i) + Θ[n], xmax = max ψ(x) ̸= max ξ(x) leads to a cascade of bifurcations with the coexistence of stable cycles and a set of transition points {ˆr, ˆa} "chaos⇔cycle", which goes beyond the essential interpretation of the trajectory behavior. The proposed method is relevant for modeling cases when y generations have different lengths of juvenile ontogenesis stages. The models are important for forecasting invasive processes of insects capable of mass outbreaks of reproduction, where the factor of generation wintering is in effect. Hybrid structures of equations are constructed that describe the dynamics of generations on adjacent uneven segments of ontogenesis depending on changes in mortality factors due to competition for resources, regulated by the growth rate of organisms. The hybrid model allows one to obtain pulsating dynamics of numbers, where transitions to the state of excessively numerous generations of "outbreaks" are interconnected with the survival of the wintering generation and the level of competitive mortality of the summer generation. The modeling method is relevant for populations supported by artificial reproduction and for cases where different social groups exhibit varying reproductive activity, which is reflected in the development of demographic waves, the disruption of social structures and the disruption of traditional interactions during the crisis of social structures.

In this work we investigate the temporal structure of the events in the spin physics detector (SPD) straw tracker at the JINR NICA. Using the Geant4 toolkit we simulate the response of the straw layers sensitive elements in the triggerfree regime of SPD. Using the simulation results we present a simple algorithm for the fast primary-vertex finding and estimate the efficiency and purity of the reconstruction.

Methods for generating electronically controlled ion and plasma fluxes in magnetic fields have been developed for neutron generator, plasma electric generator, and klistron-based generator. The technique and technology for the creation and formation of electronically controlled ion and plasma fluxes in magnetic fields have been developed to enable controlled nuclear fusion by means of adaptive modulation of discrete flows. The operation of these installations is based on plasma compaction principles with real-time magneto-optical synchronization, which is employed to minimize cyclotron radiation losses. This work provides a comprehensive methodology for experimental validation, focusing on high-energy photon detection (6–17 MeV range) and alpha particle shielding via 50 μm titanium foil, essential for industrialscale plasma generator testing. Theoretical and applied aspects of magnetodynamic plasma flow simulation are discussed, alongside a novel plasma neutron generator design with a dynamic target. The proposed electronically controlled plasma energy converter achieves a thermal output power of 8–25 kW and electrical power of 4–12 kW, surpassing conventional D-T systems in energy conversion efficiency (>50 %). A neutron generator with a plasma target impulse flux up to 10¹⁰ s⁻¹ is proposed, highlighting advancements over conventional D-T systems. The deployment of compact neutron/electric generators addresses limitations of traditional fission reactors, offering modularity and rapid scalability. Recent innovations include pulsed D-T generators and hybrid laser-plasma systems, yet energy conversion efficiency remains suboptimal (<30 %). Our work introduces an electronically controlled plasma generator utilizing lithium hydride evaporation and quadrupole magnetic discretization (Patent RU 2757666), achieving >50 % efficiency via adaptive ion flux synchronization. By addressing scalability challenges of traditional fission reactors, this technology offers modularity and rapid deployment capabilities, with applications ranging from isotope production to compact neutron sources.