Construction of New Exact Rational Solutions to the Veselov–Novikov Equation and New Exact Rational Potentials for the Two-Dimensional Schrödinger Stationary Equation by the $$\overline \partial $$ -Dressing Method

With the help of the Zakharov–Manakov $\overline \partial $ -dressing method, the scheme of obtaining exact rational solutions to the well-known two-dimensional Veselov–Novikov integrable nonlinear equation and exact rational potentials for the two-dimensional Schrödinger stationary equation corresponding to wave functions with multiple poles is developed. As an example, new exact rational nonsingular and singular solutions to the Veselov–Novikov equation and the corresponding exact rational potentials for the two-dimensional Schrödinger stationary equation with multiple second-order poles are obtained.     

Three-dimensional numerical simulation of the characteristics of a ramjet power plant with a continuous-detonation combustor in supersonic flight

Multi-variant three-dimensional numerical simulations demonstrate the feasibility of the continuous- detonation process in an annular combustor of a ramjet power plant operating on hydrogen as fuel and air as oxidant in conditions of flight at a Mach number of M ₀ = 5.0 and an altitude of 20 km. Conceptual schemes of an axisymmetric power plant, 400 mm in external diameter and 1.3 to 1.5 m in length, with a supersonic intake, divergent annular combustor, and outlet nozzle with a frusto-conical central body are proposed. Calculations of the characteristics of the internal and external flows, with consideration given to the finite rate of turbulent-molecular mixing of the fuel mixture components with each other and with the combustion products, as well as the finite rate of chemical reactions and the viscous interaction of the flow with the bounding surfaces, have shown that, in these flight conditions, the engine of such a power plant has the following performance characteristics: the thrust, 10.7 kN; specific thrust, 0.89 (kN s)/kg; specific impulse, 1210 s; and specific fuel?consumption 0.303 kg/(N h). In this case, the combustor can operate with one detonation wave traveling in the annular channel at an average velocity of 1695 m/s, which corresponds to a detonation wave rotation frequency of 1350 Hz. It is shown that, an operating combustor has regions with subsonic flow of detonation products, but the flow is supersonic throughout its outlet section.     

Dissociative electron capture and level width of quasistationary molecular states

Perturbation theory is applied to give the cross section for dissociative capture e+A₂A+A^–. From the requirement of quantitative agreement with experiment, the level widths for the quasistationary states are estimated as ₁1.2 eV; ₂0.2 eV; ₃0.05 eV for the first three terms for H ₂ ^– .Visiting worker from the Boris Kidri Institute of Nuclear Sciences, Belgrade.     

Influence of the temperature on polyelectrolyte microcapsules: Light scattering and confocal microscopy data

The influence of heating on polyelectrolyte (PE) microcapsules consisting of an even or uneven number of alternating layers of poly(allylamine) and poly(styrenesulfonate) is investigated by the light scattering and confocal microscopy techniques. In the formation of PE microcapsules, CaCO₃ microspherulites are used as “core” dispersed particles. It is established that the capsules decrease in size with increasing temperature and time of heating, irrespective of whether they consist of an even or uneven number of layers. The sensitivity of PE microcapsules to heat is estimated in terms of the activation energy of changes in parameters of their initial structure on heating. It is shown that PE microcapsules consisting of an uneven number of layers are more sensitive to heating as compared to those consisting of an even number of layers. A plausible mechanism is proposed for changes in structure parameters of the microcapsules on heating.     

The asymptotic behavior of the spectral function of an operator in Lp with discrete spectrum

The asymptotic behavior in L ^p ,where 1 p + ,of the spectral function of a perturbed discrete operator, defined on an n-dimensional compact manifold, is found. Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 16, pp. 182–185, 1992.     

Identification of mineral waters using impedance spectroscopy and projection to latent structures

A method is proposed for the rapid identification of mineral waters by impedance spectroscopy combined with chemometric experimental data processing by projection to latent structures. Measurement conditions are optimized and performance characteristics are estimated. Possibilities of the extraction of qualitative and quantitative information on the concentrations of metal ions and anions in water, determination of the nature of mineral waters, degree of mineralization, and conformity to standard samples are shown.     

Synthesis and Magnetic Properties of the Core–Shell Fe3O4/CoFe2O4 Nanoparticles

Physics of the Solid State - The Fe3O4/CoFe2O4 nanoparticles with a core–shell structure with an average size of 5 nm have been obtained by codeposition from the iron and cobalt chloride...     

Nature of chaos in conservative and dissipative systems of the Duffing-Holmes oscillator

We show that the chaotic dynamics of the conservative Duffing-Holmes oscillator obeys the universal Feigenbaum-Sharkovskii-Magnitskii theory of passage to chaos in dynamical systems of ordinary differential equations. Moreover, the cascades of bifurcations of the conservative and dissipative oscillators are continuously related to each other. Our study uses the stable control method, which permits rapidly stabilizing nearly any periodic solution and dynamically changing system parameters without moving far away from that periodic solution.