On Series of Ordinals and Combinatorics

This paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑_bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑_bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of all n-element subsets for each natural number n ≥ 2. Moreover, series ∑_β<αf(β) are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic.     

Temperature and frequency dependence of the spin-lattice relaxation times of E′1 centers in neutron-irradiated quartz glass

Results are reported for measurements of the spin-lattice relaxation times of E′₁ centers in quartz glass, produced by neutron irradiation, with the measurements made at two frequencies 9.25 and 24.0 GHz over a wide temperature interval 1.5–300 K. The experimental data are interpreted on the basis of interaction mechanisms of the spins with two-level systems with excitation energies ∼6, ∼26, and ∼420 cm⁻¹. A small modification of the existing theory allows us to explain a number of features of the observed temperature and frequency dependence of the relaxation rate. The results are compared with the data available in the literature on spin-lattice relaxation of irradiation centers in crystalline quartz and quartz glass. Fiz. Tverd. Tela (St. Petersburg) 39, 1335–1337 (August 1997)     

Pseudo-epitaxial C60 films prepared by a hot-wall method

We have used both reflection-geometry and grazing-incidence-geometry X-ray scattering to study thin films of C₆₀ evaporated onto mica substrates via a hot-wall technique. The growth mode yields close-packed C₆₀ planes, which are parallel to the substrate surface and which exhibit out-of-plane correlation lengths of 850 Å. In the film plane the C₆₀ is at best pseudo-epitaxial, with a 0.9° distribution of crystallite orientations, a 450 Å in-plane correlation length, and a 3.7% lattice mismatch, better than obtained by other thin film techniques but far from the accepted definition of single crystal thin film epitaxy.     

Donor-acceptor complexes of quinoline N-oxides with boron trifluoride

Molecular n-v complexes of quinoline N-oxides with BF₃ have been studied by electronic and IR spectroscopy. In most case the donor centre is the oxygen atom of the N-oxide group.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1087–1092, August, 1994.     

Influence of the chemical composition of plant oils on cytochrome P-450

The influence of sunflowerseed and cottonseed oils and also of fractions of normal and oxidized triacylglycerols isolated from them on cytochrome P-450 from rat liver microsomes has been investigated.     

Synthetic analogs of natural flavolignans. V. A new synthesis of 6-halogeno-1,3-benzodioxane analogs of silandrin and hydnocarpin

6-Halogeno-1,3-benzodioxane analogs of chalcones have been synthesized by various methods. Flavanone and flavone analogs of silandrin and hydnocarpin have been obtained from them. The structures of the new flavonoids have been shown by their PMR spectra.     

Luteolin glucosides fromFerula varia

Institute of the Chemistry of Plant Substances, Academy of Sciences of the Republic of Uzbekistan, Tashkent, fax (3712) 891475. Translated from Khimiya Prirodnykh Soedinenii, No. 5, pp. 679–680, September–October, 1994.