More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

Замечание К теории по степенного возникновения подви жных слоев в плазме инертных газов

[1] t _B , t _B . , t _B , . .

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A note on the theory of the successive production of moving striations in the plasma of inert gases

Approximate expressions are derived on the basis of Pekárek's theoretical paper [1] for the period of the maximum t_B of a wave packet produced by the passage of a wave of stratification before the aperture of a photomultiplier, and for its time width in the half-height t_B. The relaxation time of a wave of stratification, following from the theory [1], can thus be calculated by means of the experimentally measured velocity of motion of the maximum of a wave packet u and its width t_B. The calculation is supplemented by numerical data on the magnitude of errors committed by using approximate expressions.

     

ПРОВОДИМОСТЬ СРЕДНЕ Й ЧАСТИ КАНАЛА КОНДЕНСИРОВАННЫХ РА ЗРНДОВ

. , . . - , 500 10 000 30 500 . - , .     

Inequalities for the Schattenp-norm. III

We present some inequalities for the Schattenp-norm of operators on a Hilbert space. It is shown, among other things, that ifA is an operator such that ReAa0, then for any operatorX, AX+XA* _p 2aX _p . Also, for any two operatorsA andB, A–B ₂ ² +A*B* ₂ ² 2A–B ₂ ² .     

Quantitative method for determination of fibre texture in wires I. Principle of method and analytical expression of absorption factor

An X-ray diffraction method is described for the quantitative determination of the fibre texture in cylindrical specimens (wires), which does not require specimen preparation. The integrated intensity of the diffracted radiation from a certain atomic plane is measured in the direction parallel to the plane determined by the axis of the wire and by the direct beam for different orientations of the axis of the wire. These measurements can be carried out in practice using an X-ray counter diffractometer or Weissenberg goniometer. The pole figure is determined from the dependence of the diffracted intensity on the orientation of the wire after correcting the intensities for the absorption of radiation in the specimen. The geometric arrangement enables the absorption factor to be calculated analytically. Its form was verified experimentally by measuring the dependence of the intensity of the 220 reflection on the orientation of the axis of a cylindrical specimen of Al containing randomly oriented crystals.

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I.

( ), . , , , . . , . . 220 .

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The author wishes to thank Z. iký for help in carrying out the measurements and calculations.     

The iteration method in multiple scattering: The transfer equation

Using the iteration method, the author obtains the transfer equation for the scattering of electromagnetic waves in a system comprising a large number of statistically independent particles spherical in shape under the condition c^–1 1 c is the density of the number of particles, the scattering cross section for a single particle, and the wave number. The method is easily extended to the scattering of scalar waves.In conclusion the author expresses his thanks to V. E. Zuev and S. D. Tvorogov for their guidance and observations on the study.     

Alfven-wave scattering in inhomogeneous media

Alfven-wave scattering by inhomogeneities of the permittivity tensor (r) is examined. The scattering index , phase velocity v*, and group velocity c* are calculated over the entire wavelength range. Asymptotic formulas for , v*, and c* are derived for long (as compared with scatterer size), short, and ultrashort wavelengths.Moscow Institute of Electronic Engineering. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, No. 5, pp. 421–432, May, 1992.     

TypeN vacuum space-times as special functions in ℂ2

The members of one explicit class of functions in ² are identified with the geodetic shear-free null congruences in Minkowski's space-time. Members of a second explicit class are identified with the type-N vacuum space-times with twist-free rays. These two classes are special subclasses from a larger class of functions associated with the type-N space-times. This larger class is characterized in the following way: If and are holomorphic variables in ², thenu (, , ), a function holomorphic in, belongs to the class provided the function u/ u satisfies the tangential Cauchy-Riemann equation for an antiholomorphic function on the 3-surface whereu (, , ) has real values.This work was supported in part by NSF grant No. MPS74-14191-A01.     

Double quantum transitions in paramagnetic resonance

The theory of double quantum transitions of the M=±2 type, with regard to inhomogeneously broadened spin systems is studied in this paper with the approximation ²T₂T₃ 1. We suppose that the inhomogeneous broadening is formed by an inhomogeneous crystal field. The obtained results describe the magnitude of absorption as a function of the h.f. power and also describe the shape of the absorption curve. It is demonstrated that in inhomogeneously broadened spin systems the absorption curve of double quantum transitions has the form of the difference of two different Lorentz's curves and that at the saturation ( ²T₂T₁ 1) the absorption increases with the cube of the h.f. field intensity. The shape of the curves is expressed by means of phenomenological relaxation constants of the system.

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M=±2 ²T₂T₃ 1. , - . . , ( ²T₂T₁ 1) . .

     

Power-law falloff in the kosterlitz-Thouless phase of a two-dimensional lattice Coulomb gas

We give a rigorous proof of power-law falloff in the Kosterlitz-Thouless phase of a two-dimensional Coulomb gas in the sense that there exists a critical inverse temperaturegb and a constant >0 such that for all> and all external charges R we have , whereG (x) is the two-point external charges correlation function,=dist(, Z), and for 0$$ " align="middle" border="0"> . In the case of a hard-core or standard Coulomb gas with activityz, we may choose=(z) such that(z)24 asz0.     

Amplitude-distortion factors for the inelastic scattering of an electron at a neon atom in an electric field

Inelastic electron scattering at a neon atom in the presence of an external electric field is considered. The distortion factors of the cross section _M (F) are calculated for a series of 4d and 5d levels. It is shown that the distortion factor in strong fields is a nonlinear and nonmonotonic function of the field. The distortion factors and transition probabilitiesA , are compared. The correlation between the behavior ofA , and _M (F) is explained by the dependence of the mean dipole moment of the Stark state on the field strength.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 97–110, January, 1996.     

The temperature vibrations of urea molecules

The structural and dynamic parameters of urea at 112°K and 295°K were determined by the least squares method. The characteristic temperature of the torsional optical vibrations of a molecule about a C-O bond was determined and is in good agreement with the value determined by Raman scattering. The fractional X-coordinate of the nitrogen atom corrected for torsional vibrations was determined and it was found that the magnitude of the projection of the C-N bond in the given temperature range changes only within the limits of observational errors. A new method, called temperature difference synthesis, is described and it is shown that it is suitable for rapid qualitative determination of the thermal anisotropy of the vibrations of atoms in a crystal lattice.

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112°K 295°K. C-O , , . X- , C-N . , , , .

     

К ВОПРОСУ O КРИТИЧЕСКО Й ЧАСТОТЕ ПРИ ПРЕРЫВИСТОМ ОСВЕ ЩЕНИИ

c , c n , n AgBr. .     

Rapid graphical determination of the radial intensity distribution of the small-angle scattering of X-rays from the measured data

The radially symmetrical small-angle scattering pattern (which would be obtained by the use of a direct beam having a point-like cross section) is in practice distorted, especially by the beam height. To eliminate this distortion the integration of a set of curves based on the derivative of the measured intensity distribution is required to derive the true radial intensity distribution. A rapid graphical method of plotting these curves is described and its accuracy is proved on an example. It is further shown that the radial intensity distribution can be determined in principle using the values of the measured curve instead of its derivative.

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( ) . , . . . , .

     

СЕРНИСТЫЙ ТЕЛЛУР — ПО ЛУПРОВОДИОЕ СОЕДИНЕ НИЕ

, , , , .     

The surface layer on a ferromagnetic. The energy of some periodic domain structures

Explicit solutions are found for a number of special cases of the potential problem of periodic charge distribution. The effect of uneven distribution of the charges of a Bloch wall on the magnetostatic energy is studied, the effective width of the Bloch wall is determined, an analytical expression is found for this distribution of poles and finally the effective height of the surface layer is also determined. An expression is derived for the orientation of the vectors of magnetization in the surface layer with respect to the easy directions of magnetization. The stability of the basic domain structure up to an inclination of 6°of the plane under observation to the direction of easy magnetization and the dimensions of the domains in periodic closure structures follow from the calculations.

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. , , , , . . , 6°,, , .

     

Quark model based relativistically invariant meson exchange forces for two-nucleon scattering

A momentum space OBEP for the two-nucleon scattering is constructed starting from a relativistically invariant quark model predictions of the meson-nucleon coupling constants. Taking a relativistic meson propagators and working in a quasipotential Blankenbecler-Sugar two-nucleon dynamics the relativistic invariance of the whole problem is maintained. The NN forces are generated by an exchange of the, , , ,(600),, , and mesons. Phenomenological form factors for all meson-nucleon vertices and effective (600) and meson-nucleon couplings are utilized. The calculated NN phase shifts are in good agreement with the empirical data and with the predictions of the conventional Bonn OBEP model.The authors are indebted to G. V. Efimov, M. A. Ivanov and J. Lanik for many fruitful discussions. This work was partially supported by the Grant Agency of the Slovak Academy of Sciences under Contract No. GA-SAV-141/1992 and Contract No. GA-SAV-517/1992.     

ИЗМЕРЕНИЕ ЦИКРУЛЯРН ОЙ ПОЛЯРИЗАЦИИ γ-КВАН ТОВ, ИСПУСКАЕМЫХ ЯДРАМИ П ОСЛЕ ЗАХВАТА ПОЛЯРИЗ ОВАННЫХ ТЕПЛОВЫХ НЕЙТРОНОВ

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Measurement of the circular polarization of gamma-quanta emitted from the nuclei after the capture of polarized thermal neutrons

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, .

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, -.     

Radiation losses in completely ionized plasma

The losses caused by bremsstahlung during electron-ion and electron-electron collisions in a completely ionized plasma (in Born's approximation) are calculated. The calculation can be carried out analytically for a sufficiently dilute plasma (plasma with infinitely large Debay-Hückel radius). This assumption is satisfied very well by the known classification to actual controlled thermonuclear reaction. A dependence of the formI=an ². (1+3/2), wherea=0·73×10^–16 MeV.cm³.sec^–1,n is the number of ions per cm³ and =kT/mc ², is determined for the amount of energy radiated from 1 cm³ of plasma per sec. In the relativistic temperature regionkTmc ² the influence of electron-electron collisions begins to predominate. A number of important results concerning radiation losses in relativistic plasma will be published in a later paper.

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, ( ). ( -). . , I=an ². (1+3/2), =0,73. 10^–16 MeVcm²s^–1,n — =kT/mc ². kTmc ² . , .

     

Changes in EPR spectrum of free radical species inγ-irradiated polyformaldehyde

We have found that gamma-irradiated polyformaldehyde does not exhibit the effect of the disappearance of the hyperfine structure of EPR spectrum as a function of the dose or the time passed since the end of irradiation, as was found earlier for a group of polymers having only C-C-C-C-atoms in the polymer chain. This difference in the change in the EPR of the polyformaldehyde (PFA) spectrum compared with the polymers with a -C-C-C-C- chain is explained by the impossibility of forming a conjugate double bond in the -C-O-C-O- chain in PFA.

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, , -, , , atom C-C-C-C-. ( ) C-C-C-C- , C-O-C-O- qu .

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The author thanks K. Vacek for many valuable discussions which helped this work.