Mössbauer study of Martian regolith analogues

Terrestrial basalt rocks considered to be a good analogues of the Martian regolith were studied by using the Mössbauer spectroscopy and X-ray diffraction. The weathering of basalts was followed by the changes of the Fe²⁺/Fe³⁺ ratio. The basalt rock undergoes alteration from primary mineral composition (olivine+pyroxene+plagioclase) through smectite to kaolinite clay with oxides and hydroxides with the increase of the Fe²⁺/Fe³⁺ ratio.     

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.     

The signature theorem and some related questions

Some corollaries of the Hirzebruch-Thom signature theorem are discussed. The multiplicativity of the signature and the naturalness of the Pontryagin classes for coverings in the case of ℚ-homology manifolds is proved. A geometric proof of Hirzebruch’s well-known “functional equation” for the virtual signature is outlined. Bibliography: 25 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 197–209. Translated by N. Yu. Netsvetaev.     

Formation of a two-dimensional periodic structure of local melting regions on a silicon surface upon pulsed light irradiation

The first results regarding the formation of a two-dimensional periodic structure of local melting regions on a silicon surface upon pulsed light irradiation are presented. The conditions are established, and the mechanism of the formation of such structures is discussed. Zh. Tekh. Fiz. 67, 97–99 (December 1997)     

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)     

Asymptotics of the necessary sample size under small error probabilities

The asymptotics of the necessary sample size is considered in testing close hypotheses when the error probabilities vanish. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part III.