Faculty of Physics
M.V.Lomonosov Moscow State University
Theoretical and mathematical physics

## Foundations of possibility theory. Methods of optimal estimation and decision making. 4. Maximal extension of possibility

### Yu.P. Pyt'ev

Moscow University Physics Bulletin 1998. 53. N 1. P. 1

It is shown that a possibility $P(\cdot): \mathcal{A}\rightarrow[0,1]$ can always be extended from an arbitrary $\sigma$-algebra $\mathcal{A}$ of subsets of $X$ to the algebra $\mathcal{P}(X)$ of all subsets of $X$ with preservation of all properties of the possibility, and that a measure $p(\cdot): \mathcal{L}(X)\rightarrow[0,1]$ specifying a possibility of fuzzy events can be extended with preservation of its properties to the class of all functions $X\rightarrow[0,1]$.

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## Spectral problem for the radial Schr$\stackrel{..}{o}$dinger equation with confining-type potentials

### A.S. Vshivtsev$^1$, A.V. Prokopov$^2$, V.N. Sorokin$^1$, A.V. Tatarintsev$^1$

Moscow University Physics Bulletin 1998. 53. N 1. P. 6

A procedure based on the generalized integral transform method is applied to determining energy spectra for a large class of radial Schr$\stackrel{..}{o}$dinger-type equations. This procedure is shown to be usefully employed in a number of known potentials. Moreover, it yields essentially new analytical results for such significant potentials as the Cornell potential important for the hadron physics.

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## Account of metal structure periodicity in description of surface electron gas properties in terms of multiparticle density functionals

### O.S. Erkovich, A.M. Popova

Moscow University Physics Bulletin 1998. 53. N 1. P. 11

The electron gas spatial distribution near a metal surface is analyzed subject to the crystal lattice periodic structure. Within the formalism of multiparticle density functionals, an analytic expression for the two-particle density function of electron gas in a periodic potential is derived. These results can be used for calculating the electron gas characteristics in solids.

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## Particular solutions to nonlinear Schr$\stackrel{..}{o}$dinger-type equations of special form

### E.G. Barinova, A.G. Kornienko, A.R. Frenkin, G.A. Chizhov

Moscow University Physics Bulletin 1998. 53. N 1. P. 14

Nonexponential solutions to one-dimensional nonlinear Schr$\stackrel{..}{o}$dinger-type equations of special form derived by the quadrature method are studied. For the first time examples of analytic solutions to some types of these equations are given.

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## Dimensional renormalization without noninteger dimensions

### D.A. Slavnov

Moscow University Physics Bulletin 1998. 53. N 1. P. 19

A renormalization scheme for generating functionals of Green functions is obtained. The suggested scheme is a version of the dimensional renormalization, but it uses finite integer positive dimensions only.

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## Finslerian invariant and coordinate lengths in the inertial reference frame

### G.S. Asanov

Moscow University Physics Bulletin 1998. 53. N 1. P. 24

Basing on Finslerian invariances, temporal and spatial scales in inertial reference frames are defined. The respective Finslerian metric function is indicated, and the Finslerian deformation coefficients are calculated.

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## Regions of noise-immune data reception over ionospheric radio communication links with selective excitation of characteristic waves

### V.V. Balinov, Yu.V. Berezin, S.E. Polishchuk, D.E. Ryzhov

Moscow University Physics Bulletin 1998. 53. N 1. P. 30

Noise-immune reception regions for selective excitation of characteristic waves in an ionospheric communication link are investigated. It is shown that for ionospheric paths to 16 $Z_m$. long, the area of noise-immune reception is about $S\sim\:$50 Z$_m^2$ (at the ionospheric layer half-depth $Z_m=\:$100 km, $S\sim\:$500,000 sq. km). The area $S$ for different azimuthal angles and different radio path lengths is evaluated. It is shown that vertical wave incidence creates especially favorable conditions for implementing regional ionospheric radio communication networks with single-path propagation of radio waves and, consequently, highly reliable data transmission.

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Optics and spectroscopy

## Collinear diffraction of a light beam on consecutive acoustic trains

### V.N. Parygin, A.V. Vershubskii

Moscow University Physics Bulletin 1998. 53. N 1. P. 35

A system of equations for collinear diffraction of light on two consecutive acoustic trains of finite length with a Gaussian amplitude distribution is derived. Solving these equations yields the amplitude distribution patterns for transmitted and diffracted light under strong acousto-optical interaction. This allows us to calculate the shapes of diffracted light pulses for different train lengths, phase differences, and intertrain distances.

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## Influence of near-surface medium inhomogeneity on polarization effects in light reflection

### A.A. Golubkov, V.A. Makarov

Moscow University Physics Bulletin 1998. 53. N 1. P. 40

It was shown that, contrary to some authors opinion, the polarization effects observed recently in low-intensity light interaction with $\bar{4}3m$-class crystals (GaAs, InSb) did not point to any violation of the symmetry principle for kinetic coefficients in these crystals, since these effects are mainly caused by near-surface nonuniformity of their optical properties. Polarization effects were indicated which, if observed, would actually confirm the symmetry principle violation of these crystals kinetic coefficients.

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Solid state physics

## Solution of one inverse problem of photothermal diagnostics with the use of the Tykhonoff regularization method

### V.V. Aleshin, V.A. Vysloukh

Moscow University Physics Bulletin 1998. 53. N 1. P. 44

The problem of nondestructive photothermal diagnostics of one-dimensional medium is considered. An algorithm based on numerical minimization of the objective function and spline approximation of the medium parameters is developed. The algorithm reproduces satisfactorily the shape of non.uniformities.

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## Effect of strong electric field and IR radiation on long-term relaxation of piezoresistance in $p$-GaAs/AlGaAs

### E.V. Bogdanov$^1$, K.I. Kolokolov$^1$, V.N. Kravchenko$^1$, N.Ya. Minina$^1$, A.M. Savin$^1$, O.P. Hansen$^2$

Moscow University Physics Bulletin 1998. 53. N 1. P. 48

Infrared radiation and strong electric field effects on uniaxial compression-induced long-term resistance relaxations of two-dimensional holes at the $p$-GaAs /Al$_{0,5}$Ga$_{0,5}$As heterointerface at 4.2 and 77 K were measured. A sharp decrease in relaxation times under charge carriers heating by illumination and, at 77 K, by electric field was observed. At 4.2 K, an electric field over 200 V/cm did by itself cause sample switching to a metastable high-resistance state.

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Geophysics

## Secular variation of the Earth's mean radius

### Yu.V. Barkin

Moscow University Physics Bulletin 1998. 53. N 1. P. 53

It is shown that the mechanism of subduction and accumulation of the masses of oceanic platforms leads to a slow decrease of the Earth's mean radius at a rate of $\sim\:$0.35 mm/year.

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## On nonlinear waves described by fifth-order evolution equations

### S.A. Arsen'ev, A.Yu. Gubar', N.K. Shelkovnikov

Moscow University Physics Bulletin 1998. 53. N 1. P. 57

The fifth-order quadratic-cubic nonlinear equation for long waves in the ocean is reduced to a nonlinear Schr$\stackrel{..}{o}$dinger equation. Solutions in the form ofbreezer long-wave trains modulated by evolvent kinks are derived and studied. Long waves on finite-depth water are proved to be stable.

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Astronomy

## Eccentricity variations of the external orbit of $\xi$ U.Ma.

### N.A. Solovaya

Moscow University Physics Bulletin 1998. 53. N 1. P. 62

An analytical solution for variations of the external orbit in ternary stellar systems of $\varepsilon$ Lyr type is obtained. An example of the $\xi$ U.Ma. system is considered.

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Theoretical and mathematical physics

## Casimir energy on a multistring space

### Yu.V. Grats

Moscow University Physics Bulletin 1998. 53. N 1. P. 68

The energy density of vacuum fluctuations on a multistring space is known to have nonintegrable singularities, hence the total vacuum energy per unit string length diverges. The Casimir effect study is shown to lead to necessary additional regularization corresponding to renormalization of bare values of angle deficits for strings.

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## The coupling constant value at the Grand Unification scale

### P.I. Pronin, K.V. Stepanyants

Moscow University Physics Bulletin 1998. 53. N 1. P. 70

Using the analogy between Bogomolny's inequality in the field theory and the harmonic oscillator Hamiltonian in quantum mechanics, a possible explanation of the coupling constant numerical value at the Grand Unification scale is proposed which proves to be equal to l/8$\pi$.

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## Magnetooptical investigation of the micromagnetic structure of Fe-enriched amorphous ribbons

### E.E. Shalygina, N.I. Tsidaeva, L.M. Bekoeva

Moscow University Physics Bulletin 1998. 53. N 1. P. 78

The results of magnetooptical investigation of the micromagnetic structure of amorphous Fe$_{73}$Co$_{12}$B$_{15}$ ribbons are presented. A strong dispersion of magnetic anisotropy on a macro- and microscale in the initial state of the ribbons is detected. As a result, their local magnetic properties are rather heterogeneous, an irregular ripple-structure forms on remagnetization of the ribbons, and blocking of magnetization processes, accompanying this structure is observed. The influence of thermomagnetic annealing on the micromagnetic structure of the ribbons is investigated.

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Solid state physics

## Electrophysical method of pore size determination in porous silicon

### V.M. Demidovich, G.B. Demidovich, S.N. Kozlov, A.A. Petrov

Moscow University Physics Bulletin 1998. 53. N 1. P. 74

A method of pore size determination in a porous system based on its conductivity measurement with pores filled with a liquid conducting adsorbate is proposed. To evaluate the method, the silicon pore size is estimated using the data on the system conductivity in vapors of water and alcohol. The obtained results are in good agreement with pore size estimates obtained by adsorption methods.

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