About the singularity criterion in general relativity

The metric in vacuum is found for the case of a spherical charged dust source. It is shown that a dead zone occurs in the vacuum, impenetrable to light or test particles. All singularities resulting from theorems about geodesic lines, are located in the dead zone and do not represent a physical problem for the theory. The infinite-density type singularities may be absent inside matter-filled zone.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 94–99, 1987.     

Self-activated luminescence of zinc sulfide

The nature of the luminescence of zinc sulfide in the spectral range (360), 380–420 nm (SAL) at 80K is analyzed. It is shown that the appearance of SAL radiation is accompanied by additional absorption in the region (350) 365–370 nm at 80K. The low-temperature spectra of sphalerite, exposed to different radiation and subjected to different treatment, are studied. The multiband luminescence of the isoelectronic sulfur impurity in ZnO deposits in the region 383–640 nm is discussed. It is concluded that SAL luminescence is attributable to the localization of excitons in ZnS on clusters, whose formation precedes the precipitation of the ZnO·S phase. The formation of oxygen clusters and deposits on dislocations in ZnS is studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 60–66, February, 1987.     

Effect of uniaxial stresses on the character of the first-order antiferromagnetic phase transition in an Mn-8 at. % Ge alloy

The method of neutron diffraction is used to construct temperature dependences of the intensity of 110 antiferromagnetic reflection under the influence of compressive stresses = 0–150 MPa along [001]. Application of the stresses leads to an increase in the transition temperature, the transition being delayed in proportion to the increase in the load. On the other hand, the loading leads to a reduction in the magnetization jump for the antiferromagnetic sublattices. Thus, at > 100 MPa, the antiferromagnetic transformation takes on features of a second-order phase transformation. The transition which takes place in the stressed state is characterized by smoother rearrangment of short-order antiferromagnetic order into long-range order, as is evidenced by erosion of the transition boundary. The model proposed here — which does not ascribe the usual effect to uniaxial stresses on the antiferromagnetic transition in -Mn alloys — is based on the anomalous temperature dependence of the elastic constants.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 92–97, March, 1987.     

Lipschitz functions of self-adjoint operators in perturbation theory

Let A be a self-adjoint operator in a Hubert space. In order that for each differentiable function f and for each self-adjoint operator B one should have the estimate f(B)–f(A) c_f B–A it is necessary and sufficient that the spectrum. of the operator A be a finite set. If m is the number of points of the spectrum of the operator A, then for the constant cf one can take 8(log₂m+2)² [f], where [f] is the Lipschitz constant of the function f.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 141, pp. 176–182, 1985.     

Density of the set of attractive compacta

A compact set K in a smooth closed manifold M is said to be attractive, if on M there exists a system of differential equations, for which K is an asymptotically stable invariant set. It is proved that the set of attractive compacta is dense and its complement contains a dense set of type G in the space of all compacta of the manifold M endowed with two natural topologies.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 143, pp. 170–175, 1985.     

Some features of solar wind protons, α particles and heavy ions behaviour: The Prognoz 7 and Prognoz 8 experimental results

The paper describes the results of investigations of the solar wind ions, carried out on board the high apogee Prognoz 7 and Prognoz 8 Earth's satellites with the aid of an SKS instrument (USSR) and a Monitor instrument (USSR-SSR). Behaviour of proton and that of components on the front of Earth's bow and interplanetary shock waves were compared by means of the energoanalysis and energy-mass analysis techniques. In several long-term periods of observation the solar wind heavy ions — oxygen, silicon and iron were determined. It enabled us to estimate the solar corona chemical composition and electron temperature.Presented at the 5th General Assembly IAGA/IAMAP August 5–17, 1985, Prague, Czechoslovakia.     

Damping width of double resonances

Damping width of the double giant dipole resonance of ¹³⁶Xe excited in relativistic heavy ion collisions is calculated by diagonalizing a microscopic Hamiltonian in a basis containing one-, two- and three-phonon states. The coupling between these states is determined making use of the fermion structure of the phonons. The resulting width of the double giant dipole resonance is close to \(\left( {3_1^ + } \right)\) times the width of the single giant dipole resonance.