Motion of a particle in the field of a rotating body in the post-Newtonian approximation. Alternative solutions

The components of the gravitational field are compared in the post-Newtonian approximation in the geometric (Einstein tensor) and field (Maxwellian vector form) theories of gravitation. The fundamental difference of these fields in the motion of a test particle is shown. The feasibility of qualitative detection of the vortex component of the gravitational field is found experimentally. The scheme for an alternate experiment is given.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 15–18, May, 1990.The author thanks A. S. Lantsev for the experimental part of the article presented here.     

Quantum diffusion of muonium in GaAs

The diffusion rate of muonium in the III–V compound semiconductor GaAs has been determined from measurements of muon spinT ₁ relaxation induced by motion in the presence of nuclear hyperfine interactions. It is shown for the first time in a semiconductor that (a) there is a crossover of the transport mechanism at about 90 K from stochastic to zero-phonon hopping, as evidenced by a steep rise in the hop rate at lower temperatures, and that (b) the muonium diffuses at the hop rate of 10¹⁰ s⁻¹ (corresponding diffusion constantD≈10⁻⁶ cm²s⁻¹) at lower temperatures as well as at room temperature.     

Low temperature synthesis, structure and bioactivity of xCaO· (1−x)SiO2 glasses

Glasses of composition expressed by the following general formula xCaO·(1?x)SiO₂ (0.30≤x≤0.50) can be prepared by means of the sol-gel route starting from tetramethylorthosilicate and calcium nitrate tetrahydrate They are all difficult to prepare by means of the traditional technique of quenching the melt, because of the high liquidus temperature,T ₁ t that in the case ofx=0.3 glass isT ₁ =1650°C. The DTA apparatus appears a valuable tool for defining the procedure necessary to obtain the glass through the sol-gel route. The glassx=0.3 is bioactive. The experimental results suggest that the gel structures, such as obtained at room temperature, are very similar; only at high temperature do the reactions of hydrolysis and polycondensation go to completion and the structural units characteristic of each glass are obtained.     

Superconvergence of recovered gradients of discrete time/piecewise linear Galerkin approximations for linear and nonlinear parabolic problems

Superconvergent error estimates in l₂(H¹) and l∞(H¹) norms are derived for recovered gradients of finite difference in time/piecewise linear Galerkin approximations in space for linear and quasinonlinear parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the parabolic context, and covers problems in regions with nonsmooth boundaries under certain assumptions on the regularity of the solutions. © 1994 John Wiley & Sons, Inc.     

Structural Transformations in Fe/Zr Bi- and Multilayers Induced by Ion-Beam Mixing

The Ar-ion-beam mixing of Fe/Zr bi- and multilayers is studied by conversion electron Mössbauer spectroscopy as a function of ion dose ranging from 1×10¹⁴ to 1×10¹⁷ at./cm². The mixing leads to amorphization of the Fe/Zr system. It was shown that the mixing process in bilayers depends strongly on the thickness of the Zr substrate. The amorphization is much more effective and occurs at lower ion doses in multilayers as compared to corresponding bilayers.     

Luminescence of self-trapped excitons in calcium fluoride under pulsed electron irradiation

Time-resolved pulsed spectroscopy was used to measure the luminescence spectra of calcium fluoride. Characteristic features of the luminescence of self-trapped excitons are discussed. It is shown that various configurations of self-trapped excitons incorporating hole nuclei of a more complex structure, may be formed in CaF₂ crystals. Fiz. Tverd. Tela (St. Petersburg) 40, 1226–1227 (July 1998)     

On the optimization of approximate integration by Monte Carlo methods

We solve the problem of optimization of monte Carlo methods for approximate integration over an arbitrary absolutely continuous measure. We propose a convenient model of Monte Carlo methods which uses the notion of transition probability.     

Migration of molecules in p-bromochlorobenzene with vacancies in its structure

Based on polarization measurements of the low-frequency Raman spectra of p-bromochlorobenzene and calculations of the frequency spectra of lattice vibrations by the Dean method it is shown that the structure may contain vacancies. Their presence affects the appearance of additional lines in the low-frequency spectrum, particularly in the vicinity of 70 cm⁻¹, and their positions depend weakly on the orientational disorder of the molecules with respect to the para substituents. The activation energies for diffusion in a randomly disordered p-bromochlorobenzene crystal with vacancies in the structure is calculated from atom-atom potentials. It is shown that the value of the activation energy varies along a selected direction and depends on the arrangement of the p-bromochlorobenzene molecules with respect to the para substituents, in contrast to the results for ordered p-dibromobenzene and p-dichlorobenzene. Fiz. Tverd. Tela (St. Petersburg) 40, 1835–1838 (October 1998)     

Multicriteria Goal Games

In this paper, we deal with multicriteria matrix games. Different solution concepts have been proposed to cope with these games. Recently, the concept of Pareto-optimal security strategy which assures the property of security in the individual criteria against an opponent's deviation in strategy has been introduced. However, the idea of security behind this concept is based on expected values, so that this security might be violated by mixed strategies when replications are not allowed. To avoid this inconvenience, we propose in this paper a new concept of solution for these games: the G-goal security strategy, which includes as part of the solution the probability of obtaining prespecified values in the payoff functions. Thus, attitude toward risk together with payoff values are considered jointly in the solution analysis.