New methods for proving the existence and stability of periodic solutions in singularly perturbed delay systems

We carry out a detailed analysis of the existence, asymptotics, and stability problems for periodic solutions that bifurcate from the zero equilibrium state in systems with large delay. The account is based on a specific meaningful example given by a certain scalar nonlinear second-order differential-difference equation that is a mathematical model of a single-circuit RCL oscillator with delay in a feedback loop.     

New methods for proving the existence and stability of periodic solutions in singularly perturbed delay systems

We carry out a detailed analysis of the existence, asymptotics, and stability problems for periodic solutions that bifurcate from the zero equilibrium state in systems with large delay. The account is based on a specific meaningful example given by a certain scalar nonlinear second-order differential-difference equation that is a mathematical model of a single-circuit RCL oscillator with delay in a feedback loop. Original Russian Text ? A.Yu. Kolesov, E.F. Mishchenko, N.Kh. Rozov, 2007, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Vol. 259, pp. 106–133.     

Chaotic buffering and its mathematical models

We propose a general idea of obtaining different chains of coupled oscillators with chaotic buffering. As examples, we consider chains of diffusively coupled generalized cubic Schrödinger equations and nonlinear telegraph equations. We also give examples of systems that have an infinite-dimensional chaotic attractor.     

Asymmetric nitrogen

The¹H NMR spectra ofO-derivatives of 1-hydroxy-2,2-bis(trifluoromethyl)aziridine containing such substituents as EtO₂CCH₂, (R/S)-RO₂CCH(Me) (R=Me, Prⁱ, or Bu^t), (R/S)-H₂NC(O)CH(Me), and (R)-H₂NC(O)CH(Me) were analyzed. Both of the diastereomerically pure amides of the latter type were isolated. The validity of the¹H NMR criteria, which were suggested for the determination of absolute configurations of diastereomers ofN-alkoxyaziridines, was confirmed by X-ray diffraction study of the (R,R)-amide.     

Synthesis of hydrocarbons from CO and H2 on supported nickel-palladium catalysts

The use of an Ni-Pd/Al₂O₃ catalyst in the synthesis of C₁-C₄ hydrocarbons from CO and H₂ permits us to increase the selectivity and total yield of these products by a factor of 1.5–2.0 relative to the corresponding nickel and palladium catalysts. The optimal temperatures and CO/H₂ ratios for obtaining hydrocarbons were determined. A structure was proposed for the active sites of the bimetallic catalyst.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 7, pp. 1689–1691, July, 1991.     

Quantum model of the magnetic dynamics of single-domain particles for describing their magnetization curves and Mössbauer spectra in a weak magnetic field

A universal approach to describing the equilibrium magnetization curves and relaxation Mössbauer spectra of magnetic nanoparticles is proposed for consistent analysis of magnetometry and gamma-resonance experimental data, based solving a quantum-mechanical problem for a particle with spin S that has intrinsic magnetic anisotropy and is positioned in an external magnetic field.