Bounded sets in topological groups and embeddings

We show that the existence of a non-metrizable compact subspace of a topological group G often implies that G contains an uncountable supersequence (a copy of the one-point compactification of an uncountable discrete space). The existence of uncountable supersequences in a topological group has a strong impact on bounded subsets of the group. For example, if a topological group G contains an uncountable supersequence and K is a closed bounded subset of G which does not contain uncountable supersequences, then any subset A of K is bounded in G?(K?A). We also show that every precompact Abelian topological group H can be embedded as a closed subgroup into a precompact Abelian topological group G such that H is bounded in G and all bounded subsets of the quotient group G/H are finite. This complements Ursul's result on closed embeddings of precompact groups to pseudocompact groups.     

Onset of detonation in polydispersed fuel–air mixtures

Investigations of detonation onset in pulverized fuel–air mixtures were carried out. Combustion and detonation processes in sprays differ greatly from that in homogeneous mixtures, because not only chemical reactions, but physical processes of combustible mixture formation take place within the combustion zone (droplets atomization and evaporation). The polydispersed character of mixture and non-uniformity of droplet spatial distribution strongly affects spray combustion and detonation onset. The present paper contains the results of theoretical and experimental investigations of detonation onset peculiarities in polydispersed non-uniform hydrocarbon–air mixtures.     

Asymptotic behavior of neutron small-angle multiple scattering spectra

The asymptotic behavior of the spectra for large values of the scattering vector for the case of elastic multiple small-angle neutron scattering (SANS) is investigated theoretically and experimentally. An expansion of the spectrum in terms of the reciprocal of the magnitude of the momentum transfer is obtained taking account of the influence of the instrumental line. It is shown that, to within some factor, the leading term of the expansion is identical to the differential single-scattering cross section averaged over a statistical ensemble of particles; several subsequent terms in the expansion are calculated and the range of applicability of the resulting expressions is determined. The asymptotic behavior of the multiple SANS spectrum is measured, using a two-crystal neutron spectrometer, for samples of an HTSC ceramic, the alloy Fe-Ni, and Al powder. The agreement between the experimental results and the theoretical predictions is analyzed. Zh. éksp. Teor. Fiz. 114, 2194–2203 (December 1998)     

Low-mode tomography of inhomogeneities in a shallow sea

Potentialities of observing spatially localized inhomogeneities by the low-frequency low-mode pulsed diffraction tomography in a shallow sea are analyzed. A numerically simulated model is used to study the procedure of reconstructing the parameters of inhomogeneities by coprocessing the signals of the tomographic projections formed at the multistatic excitation and reception of low-frequency low-mode acoustic pulses.     

Spin wave spectrum and exchange interactions in the antiferromagnetic garnet Ca3Cr2Ge3O12 by inelastic neutron scattering

We have measured the spin wave spectrum for the garnet Ca₃Cr₂Ge₃O₁₂ by means of inelastic neutron scattering. The data can be well described in the framework of linear spin wave theory if we assume a Heisenberg model with two exchange parameters up to the next nearest neighbours (J ₁ andJ ₂) and a staggered anisotropy field (A). A least squares fit to the observed dispersion relations yield the following values for these parameters: J ₁=–0.582(8)K,J ₂=0.416(4)K,A=0.25(8)K. Although symmetry requires that two nearest neighbour exchange constantsJ ₁ andJ ₁ ^' must be distinguished, only the average J ₁=(J ₁+3J ₁ ^' )/4 and the condition –0.35 K <J ₁=J ₁-J ₁ ^' <0.50 K could be deduced from the experiment. The most striking result is the positive value ofJ ₂. We discuss the implications for an understanding of superexchange mediated by more than one oxygen atom. In an extension of the conventional analysis we have calculated the integrated intensities in order to check the eigenvectors directly. Good agreement between observed and calculated intensities was obtained.     

First example of the formation of bipolar spiro σ-complexes from 6-bromo-5,7-dinitrobenzo[e]-1,2,3,4-tetrazine 1,3-di-N-oxide

The reactions of 3,5,7-trimethyltropolone and 2-(N-benzylamino)tropone with 6-bromo-5,7-dinitrobenzo[e]-1,2,3,4-tetrazine 1,3-di-N-oxide afforded novel bipolar spiro -complexes. The kinetic and activation parameters of the R,S-enantiotopomerization of a chiral spiro -complex of 2-(N-benzylamino)tropone were determined using dynamic ¹H NMR spectroscopy.     

NO adsorption on unreconstructed and reconstructed Pt(100) surface at 300 K: HREELS studies

Dissociative adsorption at 300 K is shown to proceed only on unreconstructed Pt(100)–(1×1) surface. When heated, NO (ad) layers behave in a similar way on both surfaces. Dissociation products are N₂ and O(ad). Adsorption on the (hex) surface is supported to occur in islands. The island size in the saturation layer appears to be 40 Å.