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

## Foundations of possibility theory. Methods of optimal estimation and decision making. Estimation of fuzzy elements and their distribution parameters

### Yu.P. Pyt'ev

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

Methods for optimal estimation of fuzzy elements and their distribution parameters are considered. The methods are based on minimizing the possibility and/or necessity of estimation errors.

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## Error-perturbation and uncertainty relations

### Yu.I. Vorontsov

Moscow University Physics Bulletin 1998. 53. N 6. P. 8

The relation between the error of coordinate measurements and momentum perturbation has been studied. It has been shown that, with respect to the state of the system after measurement corresponding to the reduction postulate and accepted in quantum theory, this relation is similar to the uncertainty relation only for the initial system state with a minimum product of uncertainties. The obtained relation is shown to be similar to the uncertainty relation for arbitrary initial system states only with respect to a mixture of reduced states.

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## Generating equation for Ward identities and anomalies

### D.A. Slavnov

Moscow University Physics Bulletin 1998. 53. N 6. P. 13

An equation generating the Ward identities for renormalized Green functions is obtained within the framework of dimensional renormalization along lines with the use of integer dimensions only. The generating functional is developed for anomalies, and the anomaly absence condition is obtained.

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## Electron radiation in an electromagnetic axial trap

### A.I. Toropova

Moscow University Physics Bulletin 1998. 53. N 6. P. 17

A trap variant, where particles move in a homogeneous stationary magnetic field and in an electrostatic field produced by two equipotential planes and an axial surface of revolution, has been proposed. A solution of canonical equations has been found. It has been demonstrated that interaction of electrons with the radiation field leads to suppression of a parametric resonance. A model trap considering the finite conductivity of resonator walls and losses due to ollisions with gas has been studied.

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Optics and spectroscopy

## Dynamics of formation of fractal clusters from laser flare

Moscow University Physics Bulletin 1998. 53. N 6. P. 24

The formation of fractal clusters during laser-induced vaporization of (Ce$_2$O$_3$)$_x$(CeF$_3$)$_{1-x}$ and ((CeO$_2$)$_x$(CeF$_3$)$_{1-x}$ mixtures was studied by light scattering techniques. The scaling exponents of the cluster-size distribution function were determined. The obtained results were compared with the literature data, and the mechanism of fast formation of fractal clusters from percolation structures existing in laser flare was discussed.

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## Photosynthesis inhibitor and activator effects on the luminescence parameters of bean leaves

### V.A. Karavaev$^1$, I.B. Polyakova$^1$, M.K. Solntsev$^1$, T.P. Yurina$^1$, E.A. Kuznetsova$^2$, A.M. Kuznetsov$^1$

Moscow University Physics Bulletin 1998. 53. N 6. P. 29

Slow fluorescence induction and thermoluminescence of bean leaves treated with a photosynthesis inhibitor (diuron) and a photosynthesis activator were studied. A positive correlation between relative fluorescence quenching during slow induction and steady-state photosynthesis intensity was observed. Diuron and the activator were found to shift the maximum of thermoluminescence to lower and higher temperatures, respectively.

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Solid state physics

## On the theory of isotopic effects in high-temperature superconducting compounds

### A.V. Vedyaev, A.M. Savchenko, M.A. Savchenko, A.V. Stefanovich

Moscow University Physics Bulletin 1998. 53. N 6. P. 35

Isotopic effects in high-$T_{c}$ systems are considered. For strong spin-phonon coupling, the calculated isotopic effect index is substantially lower than the classical index for low-$T_{c}$: superconductors. The isotopic effect indices of high-$T_{c}$: systems such as $\rm{La}_{2-x}\rm{Sr}_x\rm{CuO}_4$ and $\rm{YBa}_2 \rm{Cu}_3 \rm{O}_{7-y}$ are calculated from the dependence of the inverse exchange correlation length on the ion mass. This dependence can be obtained in the limit of maximum amplification of effective electron-phonon coupling by spin fluctuations of exchange nature. The theoretical estimates are compared with the experimental data.

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Geophysics

## On the biogenic origin of magnetite and greigite in water basin sediments and soils

### V.F. Babanin$^1$, V.I. Trukhin$^2$, N.V. Verkhovtseva$^3$, A.M. Shipilin$^1$

Moscow University Physics Bulletin 1998. 53. N 6. P. 39

The results of long-term observations of the formation of magnetically ordered minerals in the cenosis of natural ooze microorganisms are presented. Using the magnetic measurements and the M$\stackrel{..}{o}$ssbauer spectroscopy, the composition of iron-containing minerals has been monitored. The X-Ray diffractometry and light microscopy were also applied to investigating the ooze magnetic fraction. The formation of magnetite and greigite has been established, leading to increased values of the ooze magnetic parameters. The residual magnetization exceeds the natural magnetization of soils by 4-5 orders of magnitude. The saturation magnetization and the initial magnetic susceptibility have respectively increased by 3 orders of magnitude and by a factor of 15.

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## On the origin of ocean synoptic variability

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

Moscow University Physics Bulletin 1998. 53. N 6. P. 45

It is shown that planetary waves in the ocean are generated by the Earth's nonuniform rotation. The theoretical estimating formulas are obtained.

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Astronomy

## Investigations of solar activity from the "Heliostationary" orbit

### N.N. Kontor, B.V. Somov

Moscow University Physics Bulletin 1998. 53. N 6. P. 50

The scientific potential of the "Heliostationary" space experiment with respect to the key problems of the solar activity is discussed.

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Theoretical and mathematical physics

## Asymptotic calculation of electromagnetic processes in highly inhomogeneous nonconducting media

### G.N. Medvedev, B.I. Morgunov

Moscow University Physics Bulletin 1998. 53. N 6. P. 54

Electromagnetic processes in nonconducting isotropic inhomogeneous media are considered. Characteristics of the medium are markedly varying in several directions. To determine the electric and magnetic fields, the asymptotic methods are employed.

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## On the root vectors of a waveguide with composite filling

### A.N. Bogolyubov, A.L. Delitsyn, A.G. Sveshnikov

Moscow University Physics Bulletin 1998. 53. N 6. P. 57

The problem of completeness of the system of root vectors of a waveguide is considered. A new approach that reduces the problem to studying a linear operator bunch is applied. Theorems of completeness of the bunch root vectors and of the spectrum discreteness are formulated.

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Atomic and nuclear physics

## Polarization bremsstrahlung of fast electrons in a weakly ordered medium

### V.S. Blazhevich, V.K. Grishin, B.S. Ishkhanov, N.N. Nasonov, V.P. Petukhov, A.S. Chepurnov, V.I. Shvedunov

Moscow University Physics Bulletin 1998. 53. N 6. P. 60

The results of experimental investigation of the polarization or atomic bremsstrahlung of electrons with the energy of 2.4 MeV in a weakly ordered medium of tinsel aluminum with a quasiamorphous structure are discussed. The measurements have been carried out on the linear accelerator at the Research Institute of Nuclear Physics, Moscow State University. The experimental data are in a satisfactory agreement with the theoretical estimates.

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## Energy distribution of electrons in near-electrode plasma of low-pressure HF capacity discharge

### A.F. Aleksandrov, V.P. Savinov, I.F. Singaevskii

Moscow University Physics Bulletin 1998. 53. N 6. P. 63

To study the electron energy spectrwn in the plasma of a low-pressure capacity HF discharge in Xe and He, a charged particle energy analyzer was used. The mechanisms of the plasma electron energy spectrum formation, which include the near-electrode electron beams, were analyzed. The anomalous heating of electrons in Xe plasma was shown to be induced by the beam-plasma instability. The sharp decrease of plasma electron heating with increasing HF voltage was revealed, as the Ramsauer effect manifestation.

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Geophysics

## Tsunami excitation by a moving bottom displacement in compressible water

### M.A. Nosov, K. Sammer

Moscow University Physics Bulletin 1998. 53. N 6. P. 67

Wave generation in a compressible fluid of constant depth due to a traveling bottom displacement is considered. An expression that describes the behavior of the free fluid surface has been derived using the method of integral transforms in the linear potential theory. The initial stage of wave motion development with and without regard for fluid compressibility is considered. It is shown that neglecting the compressibility for real tsunami sources gives rise to considerable errors in determining the displacement of water surface above the ource region.

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## Modeling the effect of turbulence on water suspension of solid particles

### I.N. lvanova, Yu.G. Pyrkin, V.P. Petrov, M.A. Silaev

Moscow University Physics Bulletin 1998. 53. N 6. P. 71

The effect of turbulence on some characteristics of a water suspension of solid particles was experimentally investigated. It was found that the variance value of the flow velocity magnitude pulsation is lower in the suspension of solid particles than in pure water.

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Astronomy

## Motion of poles of the structurally nonuniform Earth in the Earth-Moon-Sun system (problem's planar variant)

### I.A. Gerasimov, N.V. Rakitina, L.V. Rykhlova

Moscow University Physics Bulletin 1998. 53. N 6. P. 75

In the framework of the planar variant of the three-body problem, the formulas are derived for the tidal force projections onto the axes of the Cartesian coordinate system with the origin located at the Earth's center. The results confirm Avsyuk's conclusion [3] that the Chandler periodicity is not exclusive and that the latitude variability should be regarded as a process induced by forced motions of the internal core occurring against the background of forced nutation of the structurally nonuniform Earth.

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Solid state physics

## Peculiarities of light propagation in ZnAs$_2$

### V.A. Morozova, S.F. Marenkin, O.G. Koshelev, A.G. Mironov

Moscow University Physics Bulletin 1998. 53. N 6. P. 78

The transmission coefficient of ZnAs$_2$ single crystals in the region of their transparency was found to depend on light polarization, photon energy, and sample thickness. These dependences were shown to arise from the special features of light propagation in ZnAs$_2$ caused by inhomogeneities sensitive to light polarization.

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