Asymptotics of Dirichlet Spectrum on Some Class of Noncompact Domains

We investigate the asymptotic behaviour of the counting function of Dirichlet eigenvalues on some class of noncompact manifolds. We prove that in cases when the volume or the perimeter (the volume of the boundary) of the manifold is infinite, some additional (nonclassical) terms appear in the precise asymptotics. The coefficients at the classical terms in those are regularized in some special way volume (resp. perimeter) of the manifold.     

Hille and Nehari type criteria for third-order dynamic equations

In this paper, we extend the oscillation criteria that have been established by Hille [E. Hille, Non-oscillation theorems, Trans. Amer. Math. Soc. 64 (1948) 234-252] and Nehari [Z. Nehari, Oscillation criteria for second-order linear differential equations, Trans. Amer. Math. Soc. 85 (1957) 428-445] for second-order differential equations to third-order dynamic equations on an arbitrary time scale T, which is unbounded above. Our results are essentially new even for third-order differential and difference equations, i.e., when T=R and T=N. We consider several examples to illustrate our results.     

Special features of magnetic susceptibility dispersion in nanocrystalline magnets

It is demonstrated theoretically that the initial (both elastic and viscous) magnetic susceptibility components for nanocrystalline magnets caused by the processes of rotations (in the region of linear response) have resonant rather than relaxation character typical already for the susceptibility component caused by displacements of domain boundaries. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 88–92, June, 2007.     

Features of polystyrene synthesis in the presence of (diphenylbutadiene)tricarbonylchromium

Features of radical polymerization of styrene in the presence of (diphenylbutadiene)tricarbonylchromium were studied.     

Kinetics of Hydrogen Peroxide Decomposition in Guaiacol Solution, Catalyzed by Hexacyanoferrate(II)

The kinetics of hydrogen peroxide decomposition in a guaiacol solution, catalyzed by potassium hexacyanoferrate(II), were studied. The reaction mainly follows the pathway of guaiacol hydroxylation. The reaction order is 1 with respect to H₂O₂, 0.5 with respect to hexacyanoferrate, and from 0.4 to 0 with respect to guaiacol (the latter parameter decreases with increasing guaiacol concentration). The apparent activation energy is 105 kJ mol^{- 1}. A kinetic scheme of the process was proposed. An expression consistent with the experiment was obtained for the rate of hydrogen peroxide decomposition in the presence of guaiacol, catalyzed by hexacyanoferrate(II).     

Spin dynamics investigated by EPR in the paramagnetic regime of La2/3Ca1/3Mn1−x Me x O3 (Me = Al, In) manganites

We report an electron paramagnetic resonance (EPR) investigation of the spin dynamics in the paramagnetic regime of the colossal magnetoresistive manganites La_2/3Ca_1/3Mn_1?x Me _x O₃ (Me=Al, In;x≤0.05). The temperature dependences of the EPR linewidth and integral intensity have been analyzed in terms of the bottleneck spin relaxation and small-polaron hopping models. The exchange coupling integral between Mn³⁺ and Mn⁴⁺ ions and the polaron activation energy decrease with increasing doping level. A discussion is given concerning the factors which could explain the observed changes.     

Intermolecular interactions of p-nitrophenol with butyl acetate,according to IR spectroscopic data

Infrared difference spectroscopy has been used to study the association of p-nitrophenol (NP) with butyl acetate (BA) in CCl₄ and in undiluted BA. It has been shown that in CCl₄, an associate is formed, [NP·BA] ·BA (Ia), in which one molecule of BA is linked to the NP by a hydrogen bond, and the second BA molecule is linked to the H-complex NP·BA by outer-sphere (dipole-dipole) interaction. In undiluted BA with low concentrations of NP, (Ia) is formed; with high concentrations of NP, an associate [(NP)₂BA] ·mBA is formed, in which two molecules of NP are bonded successively to each other and with a BA molecule; and the number of outer-sphere BA molecules may depend on the concentration of free BA molecules in the solutions.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 3, pp. 593–599, March, 1991.