It is shown that the product of any number N of identical fourth-order matrices $\Lambda$ can always be represented as a linear combination of four independent powers of this matrix: $(\Lambda)^0 = I$ , $\Lambda$, $(\Lambda)^2$, and $(\Lambda)^3$. An analogous feature is established for the N-th degree of a second-rank tensor, i.e., a tensor constructed from N tensors $\phi_n{}^i(x)$ all of whose indices are sequentially convoluted, apart from the contravariant index to the first tensor and the covariant one for the last.
Show AbstractCalculations have been made on the probability of a massive neutrino decaying to a pair of W bosons and then electron in a steady external magnetic field. The exact wave functions for the electron and a W boson in a magnetic field are used. An expression is obtained for the decay probability as a function of the electron's polarization. The asymptotes of this expression are considered.
Show AbstractThe classical equations of motion are analyzed for a relativistic electron in the superposition of a standing wave and a steady magnetic field, which gives an integral of motion relating the energy to the radius of the cyclotron orbit. The cases of finite and infinite motion are examined. The quantum approach is based on solving the Klein-Gordon equation and is supplemented by analysis of the energy spectrum as affected by the type of boundary conditions.
Show AbstractThe spectral and angular intensity distribution have been obtained for the joint emission from a system of electrons moving over similar circles, and an approximate expression is derived for the total emission intensity.
Show AbstractTransitional scattering is considered for a dielectric-permittivity wave at a charged filament having the form of a spiral line or sinusoid. Perturbation methods give expressions for the spectrum and the angular distribution. The polarization of the radiated electromagnetic waves has been examined. The emission spectrum is analyzed.
Show AbstractCross sections have been calculated for neutrino (antineutrino) scattering at nuclei $\bar{\nu}(\nu)A_i\to \nu(\bar{\nu})A_f$ due to neutral-current interact ion. A study is made of the neutrino excitation of isoscalar transitions in $^{12}С(0^+0\to 1^+0)$ and $^{14}N (1^+0\to 2^+0)$, which is sensitively dependent on the isoscalar component of the weak neutral hadron axial current. When the latter is present, the total neutral hadron axial current. When the latter is present, the total cross sections for neutrino and antineutrino excitation of the isoscalar transition in $^{14}N$ show considerable differences in relation to the energy $E_{\nu}$ of the neutrino (antineutrino).
Show AbstractA method is proposed for calculating final-state interaction effects for deuteron electrodisintegration, which is based on the relativistic-diagram technique. Expressions are obtained for the vertex functions $\Gamma_{NN}$ and the nuclear electromagnetic current. The $\Gamma_{NN}$ аге determined from the invariant nucleon-scattering amplitude. The proposed formalism enables one to determine the final-state interaction in terms of partial N-N scattering amplitudes outside the energy surface.
Show AbstractIt is shown that allowance for the quark-parton baryon structure enables one to derive the Gell-Mann and Okubo mass formula for the quark model. The masses of the $\Lambda$ and $\Sigma$ hyperons are nondegenerate. It is notable that in this approach, there are relationships between the realization of F and D forms of coupling and the quark distributions in the baryons.
Show AbstractAn apparatus, is described for examining transient processes and for recording watt-ampere and quasi-resonant emission characteristics from injection lasers working under pulse conditions and with pulse-code modulation. The risetime of pumping current pulse does not exceed 1 nsec, while the interval between two pulses in a code sequence is set in the range 0-20 nsec, which enables one to examine the modulation characteristics at frequencies close to the limiting one.
Show AbstractThe excitation of ionization-diffusion waves (striations) is considered for the positive column of a direct-current discharge in a conical tube at high current levels. The condition for striation self-excitation is derived. It is found that the upper self-excitation limit for argon in tubes with small semivertex angles is lower than that in a cylindrical tube whose radius lies between the radii for the ends of the cone.
Show AbstractA study has been made of the effects of uniaxial mechanical pressure on the dielectric constant and dielectric loss of $KTaO_3$ crystals at 4.2 К over the range 0.5-1.28 GHz. As the pressure increases, the resonant frequency of the $H_{01\delta}$ mode in a cylindrical resonator decreases monotonically. There is a considerable increase in the dielectric loss in $KTaO_3$ when an inhomogeneous pressure is applied. This agrees with the view that charged line defects (dislocations) multiply in $KTaO_3$ crystals under pressure.
Show AbstractResults are presented on a UHF oscillator stabilized by a metal-dielectric resonator. Frequency-response curves and quality-factor data are given for the resonator modes and the stabilization coefficients at room temperature.
Show AbstractA theoretical study is made of the interaction between the director for a homeotropically oriented nematic liquid crystal and a light wave of ordinary type at inclined incidence. Various methods are employed to calculate the director-reorientation threshold in response to a plane wave and a bounded beam. An oscillatory state is detected from the numerical solution of the equations describing the director reorientation within the framework of a simple model.
Show AbstractA laser system is described that has an automated recording system and is used for examining processes in molecular gases under conditions of IR-IR and UV excitation.
Show AbstractExperimental studies have been performed on a $^{129}Хе$ stabilizer, with the nuclei polarized by exchange interaction with potically oriented $^{133}Cs$ atoms. This spin stabilizer based on oriented $^{129}Хе$ operates with magnetic fields of 5-500 nT.
Show AbstractA theoretical study is made of photoionization for excited states of the sodium atom $1s^22s^22p^23p^2P_J$ at energies up to 3 Rу. The energy dependence of the parameters completely describing the process has been derived. The photoabsorption cross section, the polarization, and the angular distributions of the photoelectrons are examined for conditions characteristic of current experiments.
Show AbstractStudies have been made on the effects of the magnitude and direction of an external magnetic fied in the frequency range 10-45 MHz on the polarization, damping, and velocity of magnetoelastic waves in hematite. It is found that the damping is strongly dependent on frequency for field strengths less than 2 kOe. When the field is reduced from 4 kOe to 0.05 kOe, the velocity is reduced by more than 40%. It has been shown by experiment that one can rotate the shear-wave's plane of polarization through 90° by altering the field strength and direction.
Show AbstractDetermining the three-particle distribution $g_3$ is considered for an equilibrium system in which the particles interact via a pair potential. The form of $g_3$ is determined from a variational principle for the free energy by the use of the second equation in the BBHCI chain to provide additional conditions in conjunction with the correlation-attenuation principle. A study is made of the behavior of $g_3$ in configurations near the most likely one; this agrees with published data from computer experiments and virial expansion.
Show AbstractIt is shown that one can use variables characterizing the distance of a point in the $\rho T$ diagram from the spinodal and the symmetry line to obtain a phase diagram that is the same for different substances. In this diagram, segments of straight lines represent the spinodal, binodal, critical isotherm, and symmetry line. These variables also enable one to formulate a simple equation of state for a wide region around the critical point.
Show AbstractOxygen has an effect on green-leaf thermoluminescence. The strengths of the peaks apart from the A one are dependent on the environment $O_2$ concentration. The sum of the B and С peaks falls to zero in the absence of $O_2$. To produce these peaks requires the presence of oxygen only during the heating. There is assumed to be negative feedback between the oxygen producing system and the $O_2$ concentration.
Show AbstractMittag-Loffler expansion has been used for the reciprocal of the distance as the potential of a planet in terms of spherical functions, with the series converging everywhere outside the surface; an estimate is made of the representativeness.
Show AbstractA study has been made of the effects of evacuation, transverse electric fields, illumination, and temperature change on acoustoelectronic storage in a layered piezoelectric-semiconductor structure. Some parameters have been determined for the surface states in the semiconductor, and information has been obtained on the trapping and recombination kinetics.
Show AbstractObservations have been made on the conductivity changes in a-Si:H films and in the activation energy after preliminary illumination, and also on the suppression of the temperature-dependent quenching of the band-band photoconductivity and superlinearity in the lux-ampere characteristics; explanations are given via the formation of an additional concentration of broken silicon bonds, which acquire a donor or acceptor character and correspondingly displace the Fermi level $E_F$ upwards or downwards in accordance with the equilibrium position of that level in the film. The recombination model is discussed.
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