Faculty of Physics
M.V.Lomonosov Moscow State University

## On the quasioptimal interruption of iterative regularizatfon process

Moscow University Physics Bulletin 1982. 37. N 4. P. 1

The concept of quasi-optimal approximation is generalized to iteration solution of an operator equation. It is proved that the quasi-optimal choice of the number of iterations generates a stochastically regularizing(according to Tikhonov) algorithm.

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## On the differences of absorption and excitation spectra of dye-stuff solutions.

### L.V. Levshin, M.G. Reva, B.D. Ryzhikov, S.I. Stal'makhоvich

Moscow University Physics Bulletin 1982. 37. N 4. P. 6

We present a scheme for the formation of inhomogeneously broadened spectra which, by including the dependence of the quantum yield of luminescence on the fluctuations of frequency of the 0-0 transitions, makes it possible to explain the observed differences in the absorption and excitation spectra.

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## On the method of cancellation of the infrared divergences in quantum electrodynamics

### Воrue V.Yu., II'in V.A., Slavnov D.A.

Moscow University Physics Bulletin 1982. 37. N 4. P. 10

We obtain formulas for the scattering cross section in quantum electrodynamics, which are free from infrared divergencies. The cross section is expressed in terms of the number operators of the registered particles. This obviates the necessity for summation over soft photons in the final state, as it is effectively taken into account in the formula. We analyze the dependence of the inclusive scattering cross sections on small variations of the initial states.

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## Parametrical interaction of gravitational and electromagnetic radiation

### V.I. Grigoriev

Moscow University Physics Bulletin 1982. 37. N 4. P. 15

We discuss the generation of electromagnetic waves during the propagation of gravitational waves in matter, and estimate the parameters of the electromagnetic waves which are created during the propagation of gravitational radiation from far extraterrestrial sources.

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## Optimal control of wave front and time profile of optical irradiation spreading in nonlinear medium

### Yu.N. Karamzin, A.P. Sukhorukov, V.A. Trоfimоv

Moscow University Physics Bulletin 1982. 37. N 4. P. 19

We develop an algorithm for the optimization of parameters of optical radiation propagating in media with various nonlinearity mechanisms. The convergence of the algorithm is analyzed. We optimize the focusing of the beam and the shape of the pulse.

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## About secular variations of the nodes and apses in the system ξU. Ma. Ursae Majoris

### A.A. Оrlоv, N.A. Sоlоvауa

Moscow University Physics Bulletin 1982. 37. N 4. P. 23

The work is devoted to the application of the stellar three-body problem to the system ξU.Ma. We determine the secular variations of longitudes of the nodes and periastrons of the components of the system, and made a comparison with the results of Brownrs theory.

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## On the coastal circulation induced by surge and ebb of water

### N.K. Shelkovnikov, S.A. Arsenyev

Moscow University Physics Bulletin 1982. 37. N 4. P. 26

We study the effect of surge-ebb flows on the surface temperature of the ocean, thickness of the mixed layer, and on the temperature in the thermocline, in the region of the coastal shelf. The obtained solution of the problem is compared with observations. The model explains a mechanism for the formation of the cold deep waters.

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## On the one method of solution of Lyppman-Shvinger's equation for nonhermit operator of interaction

### A.I. Vasкin, G.A. Ivanоv, A.M. Pоpоva

Moscow University Physics Bulletin 1982. 37. N 4. P. 32

We present a method for the solution of the Lippmann-Schwinger equation for the quantum-mechanical two-body problem under the assumption that the interaction operator is complex. The essence of the method consists of reducing the equation to a system of two equations which can contain only a weak integrable singularity.

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## On the relaxation to equilibrium in quantum systems

### A.G. Shumovskaya, A.S. Shumovskii

Moscow University Physics Bulletin 1982. 37. N 4. P. 36

It is shown that the method which was applied in a previous work to classical spin systems, is also suitable for obtaining exact evolution equations in quantum quasi-spin systems with pairwise "infinite-radius" interaction, taking into account the precession character of the motion of quasi-s'pins.

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## On the nature of a random field in irradiated semiconductor

### V.L. Воnсh - Вrueviсh, P.S. Sul'zhenkо

Moscow University Physics Bulletin 1982. 37. N 4. P. 41

We study the random field in a semiconductor with semi-macroscopic radiation defects.

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## On the possibility of laboratory detection of long periodical gravitational waves

### M.V. Sazhin

Moscow University Physics Bulletin 1982. 37. N 4. P. 49

We develop a laboratory method for the detection of gravitational waves by using the cummulative effect of the gravitational radiation on the frequency shift of the photon.

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## Asymptotic expansions of the dielectric responce functions of relativistic plasma

### L.S. Kuz'menkov, P.A. Polyakov, M.I. Sitnov, О.O. Trubachev

Moscow University Physics Bulletin 1982. 37. N 4. P. 53

We carry out a detailed analytical investigation of the dielectric response function (longitudinal dielectric permeability) ε$_{1}$(k,ω) of a Maxwellian relativistic plasma. Correct expansions for this function are obtained in the regions ω « kc and ω ~ kc, which are used to obtain asymptotic expressions for ω$_{1}$(k,ω). We give the regions of ω and k for which these expressions are meaningful, and derive formulae for the dispersion and damping decrement of Langmuir waves.

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## On the coherent states of relativistic particles

### I.M. Ternоv, V.G. Вagrоv

Moscow University Physics Bulletin 1982. 37. N 4. P. 59

We discuss some general properties of the coherent states of particles in quantum mechanics, and construct examples of relativistic coherent states of an electron moving in a constant and uniform magnetic field, and in the field of a plane electromagnetic wave.

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## The behaviour of nonlinear parametric divider with external phase variation

### L.V. Balakin, V.I. Medvedev

Moscow University Physics Bulletin 1982. 37. N 4. P. 67

We consider transient processes in phase-sensitive nonlinear-parametric frequency dividers when the frequency of the starting oscillation (which can be regular or parasitic) is changed. Analytical expressions are obtained for the time dependence of the amplitude and phase (frequency) of the "divided" oscillations for various types of variation of the phase of the starting ("dividing") oscillation.

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## Correlation of particles in relativistic plasma

### N.D. Naumоv

Moscow University Physics Bulletin 1982. 37. N 4. P. 74

We find the equilibrium distribution functions of particles and field oscillators for spatially uniform plasma in the absence of external fields. A correction is obtained to the first approximation of the equilibrium two-particle distribution function for relativistic plasma.

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## The coherent Raman mixing spectrum of generation

### S.Yu. Nikitin

Moscow University Physics Bulletin 1982. 37. N 4. P. 78

We study theoretically the generation spectrum of coherent Raman mixing. It is shown that for coherent Raman mixing in hydrogen, the generation spectrum is determined by the spectrum of the test wave, and is independent of the pumping spectrum.

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## On the topology of cosmological models near critical points

### G.A. Sardanashvili, V.P. Yanchevskii

Moscow University Physics Bulletin 1982. 37. N 4. P. 81

We define the gravitational singularities as singularities of a spaceli time foliation on the manifold X$^{4}$, and this definition is used to study the topology of singularities in homogeneous cosmological models.

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## On the surface wave generation in solid state plasma

### L.S. Воgdankeviсh, V.К. Grishin, M.F. Кanevskii

Moscow University Physics Bulletin 1982. 37. N 4. P. 84

We consider the excitation of a generator, based on the surface wave in solid-state plasma, by a relativistic electron beam propagating in a gas plasma. In a real experiment, there is usually residual gas above the surface of the solid which is ionized by the beam and forms a gas plasma. The gas plasma can also be created independently by using an additional weak beam, laser ray, etc. This makes it possible to control the parameters of the gas plasma. We consider the effect of parameters of the beam on the characteristics of the generator. It is shown that a relatively dense gas plasma effects strongly the electrodynamic properties of the generator. The generation frequency is practically independent of the energy of the beam, and remains at a sufficiently high level. The magnitude of the starting current decreases.

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## Peculiarities of working regimes of electron detector of two millimiter range with open resonance system with periodic structure

### D.G. Afоnin, A.I. Коstienkо

Moscow University Physics Bulletin 1982. 37. N 4. P. 88

We discuss the characteristic features of operation regimes of an electron detector, operating in the two-millimeter range, with a virtual cathode, and an open resonant system with a period structure. We describe the construction, and give the dimensions, of the individual units. The device operation is based on the interaction of an electron beam with the forward and backward spatial harmonics; the device also operating in the diffraction regime. The current sensitivity of the detector varied across the range, and decreased significantly when going over from the diffraction regime to the travelling-wave and backward- wave regimes.

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## Solvation influence on the Brown's rotation of benzocarbolyn in alcoholic solutions

### L.V. Levshin, Yu.R. Pavlenko, E.K. Ruuge, B.D. Ryzhikov, N.R. Senatorova, A.N. Tikhonov

Moscow University Physics Bulletin 1982. 37. N 4. P. 92

The methods of optical and EPR spectroscopy, are used to show that the deviations from linear dependence of 1/P and T/ɳ in the Levshin-Perrin formula for ethanol solutions of benzocarboline are due to the temperature dependences of the lifetime of the excited state, and of the solvated volume of molecules of the dissolved substance. It is proved that it is justified to use a spherical model for the discussion of Brownian rotation of benzocarboline molecules.

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## The model of formation of temperature inversion in a thin near-water atmospheric layer

### A.A. Budnikov

Moscow University Physics Bulletin 1982. 37. N 4. P. 96

We consider an approximate mathematical model which takes into account the main factors in the interaction of the ocean and the atmosphere It is found that, in the framework of the present model, a temperature inversion layer Is formed by the action of volume heat sources in the atmosphere.

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## Device for perfoming of multifrequency selective experiments by the regenerative NMR method

### K.L. Zakharov, Yu.S. Konstantinov, A.M. Smirnov

Moscow University Physics Bulletin 1982. 37. N 4. P. 99

We developed an apparatus for multifrequency.experiments by using the regenerative NMR methods. The apparatus makes it possible to excite spin generation at individual lines in the NMR spectrum if the difference of resonance frequencies between the lines exceeds 4 Hz. We give an example of application of this apparatus in the experimental observation of nuclear magnetic double resonance.

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### G.P. Boyakhchyan, V.A. Vanke, S.K. Lesota

Moscow University Physics Bulletin 1982. 37. N 4. P. 103

We study the physical features of systems which consist of independently loaded dipoles. An example of such a system is rectenna (rectifying antenna). It is shown that the characteristics of these systems coincide with the transmitting characteristics of a system of the same dipoles with mutually incoherent excitation. The system of dipoles with independent loads has a relatively low directionality because of the absence of coherent amplification or reduction of the field in the appropriate directions, which is typical for systems with coherent excitation of the dipoles.

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## On the shock wave propagation law in the point explosion theory

### D.V. Skripkin

Moscow University Physics Bulletin 1982. 37. N 4. P. 106

The method of dimensionality theory is used to obtain a formula for the velocity of a shock wave which makes it possible to reduce the problem of explosion at the center of a gas sphere, to a problem with initial Cauchy data at the front of the shock wave.

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## Mutual diffusion coefficient of nitrobenzene— n-heptane system

### S.V. Kazakov, N.I. Chernova

Moscow University Physics Bulletin 1982. 37. N 4. P. 109

We study the temperature and concentration dependence of interdiffusion coefficient in the nitrobenzene-heptane system. We obtain numerical values for the exponent which determines the singular behavior of the diffusion coefficient as one approaches the critical point of mixing.

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## The study of threshold and intensity of SRS in the rubidium vapour at the various spectral ranges of pump radiation

### V.A. Mikhaylov, V.I. Odintsov

Moscow University Physics Bulletin 1982. 37. N 4. P. 112

We study experimentally the frequency dependence of the excitation threshold and the intensity of induced Raman scattering in rubidium vapor near the resonant transitions Rb 5$^{2}$S$_{1/2}—5^{2}Р_{1/2,3/2}$, while varying the pumping line-width between 0.2 and 20 cm$^{-1}$. In the immediate vicinity of resonance, we observe a sharp increase of the threshold and a decrease of intensity of the induced Raman scattering. In contrast with the backward scattering, under excitation of the forward induced Raman scattering the maximum of the scattered radiation is reached at large deviations from resonance of the order of several tens of cm$^{-1}$.

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