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

## Ne'v relations in tensor algebra

### V.I. Grigor'ev and I.Р. Denisova

Moscow University Physics Bulletin 1996. 1996. N 2. P. 1

Expressions are obtained for the coefficients in the expansion ofthe Nth power of an arbitrary second-rank tensor in an N-dimensional pseudo-Riemannian space. These expressions are convenient for analytical investigations. Some new relations in tensor algebra are found.

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## Finslerian nonlinear invariance and Lorentz transformations

### G.S. Asanov

Moscow University Physics Bulletin 1996. 1996. N 2. P. 6

The special-relativistic Finslerian metric function is shown to bе invariant under а nonlinear realization of Lorentz transformations.

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## The Einstein-Podolsky-Rosen paradox and the bell inequality in а quantum system with memory

### D.А. Slavnov

Moscow University Physics Bulletin 1996. 1996. N 2. P. 11

The Einstein-Podolsky-Rosen paradox and the Bell inequality are considered in а quantum system with memory. It is shown that if several levels of memory are assumed to exist one can oЬtain the same results as in the standard quantum mechanics. The physical interpretation in this case will bе very simple and clear.

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## The renormgroup method for functions of many variaЫes

### V.V. Belokurov and V.V. Kamchatnyi

Moscow University Physics Bulletin 1996. 1996. N 2. P. 15

Solutions to the renormgroup equations depending on two or more dimensionless combinations of some dimensional variables are examined. It is shown that, generally, the form of the functional dependence on the ratio of dimensionless variaЫes cannot bе determined bу the renormgroup method. The structure of such solutions is found for some special cases.

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## On the theory of nonlinear plasma waves

### Р.А. Polyakov

Moscow University Physics Bulletin 1996. 1996. N 2. P. 21

А nonlinear theory of plasma waves in а cold one-dimensional plasma is elaborated using the Lagrange formalism to describe the plasma medium and subsequently pass to the Euler variables. А new representation for nonlinear running and standing waves is obtained, and а new analytical solution for а bounded plasma is found that satisfies the necessary boundary conditions.

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## Gas heating kinetics in pulse-periodic air discharge

### V.V. Lodinev, V.М. Shibkov, and L.V. Shibkova

Moscow University Physics Bulletin 1996. 1996. N 2. P. 26

Gas heating kinetics has Ьееп investigated under the conditions of а pulse-periodic discharge in air. Various mechanisms of energy supply to the translational degrees of freedom of the molecular gas have Ьееп studied. It is shown that in the active phase of pulsed discharge in air, at high values of the reduced electric field $(E/n>10^{15} V/cm^2)$, gas heating proceeds at the expense of quenching the electronically excited nitrogen molecules.

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## А setup for studying drifting ionospheric disturbances

### V.D. Gusev, N.V. Karabanov, and D.V. Kir'anov

Moscow University Physics Bulletin 1996. 1996. N 2. P. 32

The paper describes an experimental automated setup designed bу the authors (Department of Physics, Moscow University) for studying drifting ionospheric disturbances.

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## Diagnostics of plasma in а low-pressure surfatron from radial SHF field distribution

### S.Е. Bobkov, Р.S. Bulkin, G.S. Solntsev, and L.I. Tsvetkova

Moscow University Physics Bulletin 1996. 1996. N 2. P. 35

The possibility of determining electron concentration n from the radial distribution of the amplitudes of the field components $Е_{r}(r), E_{z}(r), H_\phi(r)$ of а surface electromagnetic wave in а surfatron is examined. U se is made of а plasma waveguide model taking into account tube walls. Of three types of electromagnetic probes, the one recording $Е_{r}(r)$ gives the best results. Nonlinear effects caused bу the influence of probes on the discharge are observed at small probe-tube distances.

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Optics and spectroscopy

## Mutual influence of diffraction-coupled lasers in а Talbot resonator

### V.Р. Kandidov and I.V. Pashkova

Moscow University Physics Bulletin 1996. 1996. N 2. P. 41

The amplitude and phase relationships between the fields which form а diffraction coupling are studied as functions of the filling factor of the waveguide array. It is shown that а periodic field is formed in а Talbot resonator as а result of interference of the fields of individual waveguides which sets in at certain amplitude and phase relationships in the plane of their apertures.

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Solid state physics

## The influence of cuЬic anisotropy on the domain structure of ferromagnetic films

### L.I. A.ntonov, Е.А. Mukhina, and Е.V. Lukasheva

Moscow University Physics Bulletin 1996. 1996. N 2. P. 49

The problem of the periodic structure of magnetization of а ferromagnetic singlecrystal film with cuЬic anisotropy has been numerically solved. The computation results are illustrated bу the magnetization distributions of two films with parameters chosen to demonstrate the special features of the film domain structures.

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## X-Ray and Mossbauer studies of the Mn2.75Fe0.25Al alloy isostructural to β-Мn

### А.S. Vinogradova, V.S. Zasimov, А.S. Ilyushin, I.А. Nikanorova, and I.S. Nikanorov

Moscow University Physics Bulletin 1996. 1996. N 2. P. 53

А combined X-ray and Mossbauer study revealed local dist1·ibutions of iron and aluminum atoms in $\beta —Mn_{2,75}Fe_{0,25}Al$ after various types of thermal treatment

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## The magnetic properties of $SmFe_{11-x}Co_{x}Ti$ single crystals

### S.А. Nikitin, I.S. Tereshina, Т.I. Ivanova, and Yu.F. Popov

Moscow University Physics Bulletin 1996. 1996. N 2. P. 56

The effect of substituting atoms of Со for Fe on the magnetic properties of $SmFe_{11-x}Co_{x}Ti (x=0, 1, 2, ..., 6)$ single crystals in pulsed magnetic fields up to 120 kOe at temperatures of 4.2 to 300 К was studied. The concentration dependences of the magnetic anisotropy constants $К_1$ and $К_2$ and anisotropy fields $H_a$ were de_termined. Magnetic phase transitions induced Ьу an applied field were observed.

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Geophysics

## Observations of the Earth's deformation spectrum bу means of а laser interferometer-deformograph

### V.К. Milyukov and V.К. Kravchuk

Moscow University Physics Bulletin 1996. 1996. N 2. P. 60

Long-term observations of lithospheric deformations were car1·ied out in the frequency range of $5\cdot 10^{-6}$ to 103 Hz in the Northern Caucasus at the Baksan Geophysical Observatory (Shternberg Institute of Astronomy). Observations were made Ьу means of an underground laser interferometer-deformograph with а baseline of 75 m. The obtained estimate of the spectral density of deformations determines the background level of seismic noise over а wide frequency range.

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Astronomy

## The secular drift of the Earth's center of mass caused Ьу movements of lithospheric plates

### Yu.V. Barkin

Moscow University Physics Bulletin 1996. 1996. N 2. P. 65

The paper is concerned with the study of а subtle geodynamic phenomenonthe secular movement of the Earth's center of mass caused Ьу movements of lithospheric plates. Based on the plate model adopted, it is shown that in this epoch the Earth's center of mass is being displaced relative to the mantle in the direction of а point with the geographic coordinates ip = 42.3° N .L. and $\lambda=131,2°$ E.L. (toward the Sea of Japan) at а rate vc· = 4.45 cm/century. The phenomenon is primarily due to the underthrust effect of oceanic plates.

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Theoretical and mathematical physics

## On the problem of calculating dielectric waveguides

### А.N. Bogolyubov and А.V. Krasil'nikova

Moscow University Physics Bulletin 1996. 1996. N 2. P. 71

We propose а modification of an algorithm for а self-regulating net that enaЬles one to calculate efficiently the spectral characteristics of dieiectric waveguides with complex filling, and also а new method of calculating the cutoff frequencies for these waveguides.

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## Calculation of oscillations of nonuniform plates under local influences

### G.N. Medvedev, В.I. Morgunov

Moscow University Physics Bulletin 1996. 1996. N 2. P. 75

Steady-state oscillatory modes of nonuniform plate~ are considered in the presence of external perturbations. The perturbations are periodic in time and localized in а small circular region. The averaging procedure is used to asymptotically determine the displacement vector.

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## The effect of absorption on radio wave reflection bу the ionosphere for slant proЬing

### V.D. Gusev, Е.G. Mikhailova, and L.I. Prikhod'ko

Moscow University Physics Bulletin 1996. 1996. N 2. P. 78

The rigorous solution to the problem of radio wave propagation in а nonuniform ionospheric layer with а linear profile of permittivity and absorption is considered. The exact solution is oЬtained for the complex reflectivity of the layer. It is shown that, even for а low absorption, the attenuation of radio waves in the layer can Ье quite strong, while reflection is virtually absent.

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## А voltage-controlled precision high-frequency oscillator for а laser gyroscope

### V.А. Krainov and V.Е. Zharov

Moscow University Physics Bulletin 1996. 1996. N 2. P. 82

А voltage-controlled oscillator is described, which is one of the important units of the laser gyroscope used for the study of the Earth's rotation nonuniformity. The existing circuits of high-frequency oscillators do not еnаblе one to measure small variations of the angular speed of rotation. The oscillator proposed in this work is based on the principle of frequency synthesis: the generation of а lowfrequency signal and the mixing of this signal with а reference high-frequency signal.

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Solid state physics

## Effect of electron irradiation on the structure of Pr-Fe alloys

### А.S. Ilyushin, N.А. Khatanova, and Е.А. Rykova

Moscow University Physics Bulletin 1996. 1996. N 2. P. 85

The method of electron diffraction in powders revealed that in the alloy Pr- 77 at. % Fe after annealing for 10 h at 800°С two intermetallides are formed, Pr2Fe1т and PrFe2, in two Laves phase modifications, С14 and С15. It was shown that the PrFe2 С14 structure in powder grains is unstaЫe with respect to electron itradiation in the tube of an electron microscope, which results in а radiation-induced phase transition of the PrFe2 С14 intermetallide with а hexagonal lattice into an fcc structure with the space group FmЗm and the parameter а= 9.lA.

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## Diffraction of Mossbauer radiation in а perfect silicon crystal irradiated bу ultrasound

### А.А. Opalenko, А.А. Kornilova, and О.G. Koshelev

Moscow University Physics Bulletin 1996. 1996. N 2. P. 88

The effect of ultrasound on dynamic diffraction of Mossbauer gamma quanta in а silicon single crystal was investigated. Using Bragg's geometry, the total intensity and its elastic part were measured for the {111), (333), {444) and {220), (440) reflections under the action of high-frequency ultrasound {transverse waves). There is а decrease and oscillation of the elastic scattering intensity as the ultrasound amplitude increases, which contradicts to previously obtained data [1, 2].

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