On the stability in periodic and almost periodic difference systems

In this paper we consider the system of difference equations

     

Effect of prepulses with various durations on the neutron yield in laser picosecond plasma

Experimental results on the effect of picosecond and nanosecond prepulses on the neutron yield in laser picosecond plasma on the surface of solid (CD₂)_n targets at a laser intensity of 10¹⁸ W/cm² are presented. It is demonstrated that the picosecond (nanosecond) prepulse decreases the neutron yield at a laser prepulse intensity of higher than 10¹³ (10¹²) W/cm². The estimates indicate three possible mechanisms for the realization of the observed effect: stimulated Mandelstam-Brillouin scattering of the main pulse by the preplasma, channels of the generation of fast ions, and their possible deceleration in the preplasma. The results of calculations are compared with the experimental data.     

Electrical transport and magnetic ordering in R 2Ti3Ge4 (R=Dy, Ho and Er) compounds

New R ₂Ti₃Ge₄ (R=Dy, Ho and Er) intermetallic compounds have been synthesized and characterized by X-ray diffraction and low temperature ac magnetic susceptibility, electrical resistivity and thermoelectric power measurements were carried out. The compounds crystallize in the parent, Sm₅Ge₄-type orthorhombic structure (space group Pnma) and lanthanide contraction is observed as one moves along the rare-earth series. The changeover from paramagnetic to antiferromagnetic phase happens at low temperatures and the ordering temperature scales with the de Gennes factor. The electrical resistivity is metallic with a negative curvature above 100 K. Thermopower displays a weak maximum at temperatures less than 50 K signifying the possible phonon and magnon drag effects.     

On the stability of invariant sets of systems with impulse effect

A system of differential equations with impulse effect is considered. It is assumed that this system has an invariant set M$M$. By means of the direct Lyapunov method, the necessary and sufficient conditions of its uniform asymptotic stability are obtained. The conditions on the perturbations of right hand sides of differential equations and impulse effects, under which the uniform asymptotic stability of the invariant set M$M$ of the “nonperturbed” system implies the uniform asymptotic stability of the invariant set of the “perturbed” system, are obtained. The stability properties of invariant sets of periodic systems are also studied.     

Rearrangement and decomposition of (CH3)3M (M = Si, Ge, Sn) ions: A DFT study

Pathways for the rearrangement and decomposition of the (CH₃)₃M⁺ (M = Si, Ge, Sn) ions are traced by the detection of stationary points on the potential energy surfaces of these ions by the B3LYP/aug-cc-pVDZ method. All three systems have stationary points similar in geometry, but very different in energy, especially on going from M = Si, Ge on the one hand to M = Sn on the other. In addition to previously found isomers of (CH₃)₃Si⁺ which have their analogs in the two other systems, “side-on” complexes with ethane and propane were revealed for all cations studied. Predicted changes in transition state and dissociation energies on going from M = Si to M = Sn allowed us to rationalize the trends for the relative decomposition product yields observed in mass-spectrometry studies of these cations.     

Magnetization reversal of Nd-Fe-B sintered magnets at low temperatures

Barkhausen-like magnetization jumps at temperatures T < 9.5 K and the behaviour of the coercive field at low temperatures are studied in sintered Nd-Fe-B magnets with different chemical and phase compositions. The nonlinear temperature dependence of the coercive field H_c is well described in the thermal activation model at T > 10 K. The low temperature anomalies of H_c are discussed in terms of the quantum tunneling of the domain wall through the intergrain boundaries.     

Ab initio study of trimethyloxonium and disilylmethyloxonium cations as intermediates in reactions of CH3 cations with ethers and disiloxanes

The study of the gas-phase reactions ofCH₃⁺ cations generated from tert-butyl ether and hexamethyldisiloxane by the nuclear chemical method shows that these cations are produced via oxonium cations as intermediates. Trimethyloxonium and disilylmethyloxonium cations were taken as model structures for these intermediates, and their ab initio equilibrium geometries were refined at the HF/4-21 (O^*)G level of theory. The relative yields of the products of these reactions under competitive conditions found experimentally are in keeping with the theoretical relative stability of the (CH₃)₃O⁺ and (SiH₃)₂CH₃O⁺ cations. The geometry of the latter was also used for the discussion of the surface structures that arise when methanol chemisorbs onto silica. Some previously unassigned bands in the IR spectra of these surface species, the frequencies of which coincide with calculated CH stretching frequencies of the disilylmethyloxonium cation, were attributed to surface oxonium methoxy groups.