On asymptotic approximation of a solution of a boundary-value problem for a nonlinear nonautonomous equation

On the basis of periodic Ateb functions, in the resonance and nonresonance cases, we construct the asymptotic approximation of one-frequency solutions of a boundary-value problem for a nonlinear nonautonomous equation.     

Thickness and temperature dependence of subsidiary absorption thresholds in yttrium-iron-garnet thin films

The microwave subsidiary absorption threshold in tangentially magnetized yttrium-iron-garnet (YIG) films was measured as a function of the static magnetic field, film thickness and decrease in the 0.3–3 μm range is observed. The effect is explained quantitatively by using modified Damon-Eshbach dispersion relations which take into account exchange interactions.

The effect of temperature on h_crit, the smallest threshold field amplitude, in the 250<T< 450 K temperature range can be expressed by an empirical relationship h_crit M_s(T)^-1.6 where M_s is the saturation magnetization. This h_crit vs M_s relationship is similar to that obtained for the magnetization dependence of parallel pump thresholds in Li-Ti ferrite compounds.     

Pseudo-Strong Regularity Around a Set

A generalization of strong regularity around a vertex subset C of a graph Γ, which makes sense even if Γis non-regular, is studied. Such a structure appears, together with a kind of distance-regularity around C , when an spectral bound concerning the so-called predistance polynomial of C is attained. As a main consequence of these results, it is shown that a regular (connected) graph Γwith d + 1 distinct eigenvalues is distance-regular, and its distance- d graph Γ d is strongly regular with parameters a = c , if and only if the number of vertices at distance d from each vertex satisfies an expression which depends only on the order of Γand the different eigenvalues of Γ.     

Toughening of epoxies via craze-like damage

The fracture behavior of a core-shell rubber (CSR) modified epoxy is investigated using both fracture mechanics and microscopy tools. The CSR-modified epoxy is found to be toughened via numerous line-array cavitations of the CSR particles, followed by plastic flow of the epoxy matrix. The toughening effect via the above craze-like damage process is found to be as effective as that of the well-known widespread rubber cavitation/matrix shear yielding mechanisms. The conditions for triggering the craze-like damage appear to be both stress state and rubber concentration dependent. The type of rubber tougheners utilized also plays a critical role in triggering this rather unusual craze-like damage in epoxy systems. © 1993 John Wiley & Sons, Inc.     

Electron-transfer kinetics and activation barriers for the reductions of nitrosonium and nitronium ions in aprotic solvents

Using the cyclic voltammetry (CV), the electron-transfer kinetics for the reductions of NO⁺ and NO₂⁺ cations have been studied at the Pt electrode in nitromethane, sulfolane, and propylene carbonate. The heterogeneous rate constants have been determined by two independent procedures from the transfer coefficient α, the diffusion coefficient D, from a detailed examination of the CV-peak separations, and from an inspection of the values of the cathodic peak potentials at different scan rates. The results have been compared to those reported in the literature, and discussed. In the classical model, outer-sphere electron-transfer reactions are considered subject to an activation energy arising from solvent reorganization and bond reorganization processes. The solvent and molecular reorganizational barriers for these electroreductions have been assessed in aprotic media. The Marcus-Hush theory has been applied to the self-exchange reactions of the NO₂⁺/NO₂ and NO⁺/NO couples in an attempt to predict the rate of electron transfer. The findings indicate some improvement between theory and experiment. However, it should be noted that the experimental values of k_s found for the NO₂⁺ reduction in the solvents used are still too high in comparison with those determined theoretically. In view of the fairly strong coordination of the solvent molecule(s) as ligand(s) to NO₂⁺ and NO⁺ cations, we believe that such discrepancies should stem, to some extent, from the involvement of an inner-sphere pathway by generation of an activated complex on the surface of the Pt electrode. © 1993 John Wiley & Sons, Inc.     

Orbifolds, Sheaves and Groupoids

We characterize orbifolds in terms of their sheaves, and show that orbifolds correspond exactly to a specific class of smooth groupoids. As an application, we construct fibered products of orbifolds and prove a change-of-base formula for sheaf cohomology.     

Chemical composition and reaction analysis of single aerosol particles

In situ measurements of gas-liquid surface reactions of single aerosol microdroplets are presented. By means of optical levitation in combination with elastic (Mie) and inelastic (Raman) light scattering it is possible to get information on the chemistry of e.g. acid/base reactions as well as the physical behavior of single microparticles.     

Selective saturation and inversion of multiple resonances in high-resolution solid-state 13C experiments using slow spinning CP/MAS and tailored DANTE pulse sequences.

Taking advantage of the long 13C T1 values generally encountered in solids, selective saturation and inversion of more than one resonance in 13C CP/MAS experiments can be achieved by sequentially applying several DANTE pulse sequences centered at different transmitter frequency offsets. A new selective saturation pulse sequence is introduced composed of a series of 90 degrees DANTE sequences separated by interrupted decoupling periods during which the selected resonance is destroyed. Applications of this method, including the simplification of the measurement of the principal values of the 13C chemical shift tensor under slow MAS conditions, are described. The determination of the aromaticity of coal using a relatively slow MAS rate is also described.     

Gibbs random fields invariant under infinite-particle Hamiltonian dinamics

The Liouville operator for an infinite-particle Hamiltonian dynamics corresponding to interaction potentialU is used to introduce the concept of a locally weakly invariant measure on the phase space and to show that if a Gibbs measure with potential of general form is locally weakly invariant then its Hamiltonian is asymptotically an additive integral of the motion of the particles with the interactionU.Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 3, pp. 424–459, March, 1992.