Green's temperature functions of massive scalar particles for finite matter density

An explicit expression is obtained for the Green's functions of a massive scalar field for nonnull temperatures and density in the form of a series in powers of m/T. The equivalence of the spectral-geometric approach and the temperature technique of Matsubara and Bernard is demonstrated. Corrections to the Stefan-Boltzmann law are obtained on the basis of the calculated Green's functions. The energy density is calculated in regions of high and low temperatures. The formulas obtained can prove to be useful in the discussion of the phase transition hadrons-quark-gluon plasma.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 32–40, July, 1991.     

Nonrelativistic polarization operator of a photon in an external nonabelian field of magnetic type

The photon polarization operator is computed in the presence of a constant external chromomagnetic field in nonrelativistic approximation. The found branching points of the polarization operator are compared with the minimal energy necessary for creation of scalar colored particles. The absence of confinement for such quarks in the field under consideration is noted.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 23–26, October, 1990.     

Emission of neutrino pairs by an electron in an ultrastrong magnetic field

The transitions of relativistic electrons in a magnetic field with the emission of an antineutrino-neutrino pair are considered. Probabilities are obtained for electron transitions to the ground state and weakly excited states. It is shown that in the case of an ultrastrong magnetic field (HH_o=m²c³/e=4.41·10¹³ G) such transitions made a considerable contribution to the total probability of the process.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 110–114, March, 1978.In conclusion, the authors express their profound gratitude to A. A. Sokolov for his attention to our work.     

Existential monadic second order logic of undirected graphs: The Le Bars conjecture is false

In 2001, J.-M. Le Bars disproved the zero-one law (that says that every sentence from a certain logic is either true asymptotically almost surely (a.a.s.), or false a.a.s.) for existential monadic second order sentences (EMSO) on undirected graphs. He proved that there exists an EMSO sentence ? such that $\mathsf{P}(G_n??)$ does not converge as $n\to \infty$ (here, the probability distribution is uniform over the set of all graphs on the labeled set of vertices $\{1,\dots ,n\}$). In the same paper, he conjectured that, for EMSO sentences with 2 first order variables, the zero-one law holds. In this paper, we disprove this conjecture.     

On the probability of the occurrence of a copy of a fixed graph in a random distance graph

The threshold probability of the occurrence of a copy of a balanced graph in a random distance graph is obtained. The technique used by P. Erd?s and A. Rényi for determining the threshold probability for the classical random graph could not be applied in the model under consideration. In this connection, a new method for deriving estimates of the number of copies of a balanced graph in a complete distance graph is developed.     

Oxygen-ionic conductors based on substituted bismuth molybdates with column-type structural fragments

The possibility of synthesizing oxygen-ionic conductors from substituted bismuth molybdates containing [Bi₁₂O₁₄] _n ⁸ⁿ⁺ columns, MoO₄ tetrahedra, and isolated Bi ions in their structure was studied. The specifics of their structure and electric conductivity were investigated. The general formula of the solid solutions can be recorded as Bi₁₃Mo_{5 ? x} Me _x O_{34 ? δ}, where Me is the fouror five-valent d metal (Ti, Zr, V, Nb). The electric conductivity of doped bismuth molybdates considerably increased compared with that of the matrix compound. The electric conductivity reached 5.5 × 10^?3 S cm^?1 at 700°C and 1.8 × 10^?4 S cm^?1 at 350°C for the zirconium-doped compound with x = 0.4. The porosity of the ceramics was less than 5%; the thermal expansion coefficient was of the order of 14 × 10^?6 K^?1. Based on the set of their characteristics, these compounds are recommended as materials for membranes of electrochemical devices.     

Photoproduction of neutrino pairs on an electron in a magnetic field

The spectral-angular and spectral distributions of the probability of photoproduction of neutrino pairs on an electron in a magnetic field are calculated. The dependence of the probability of this process on the magnetic-field strength, the orientation of the electron spin in the initial and final states, and also on the direction of the circular polarization of the wave is investigated.