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.     

First-Order Complexity of Subgraph Isomorphism via Kneser Graphs

Mathematical Notes - The problem of finding the least number of variables of a first-order formula expressing the statement that an input-graph contains a subgraph isomorphic to a given...     

Some features of the preparation,structure, and properties of BICUTIVOX

This work continues the search for optimal preparation methods and studies of structural and transport characteristics of BICUTIVOX solid solutions of the general composition Bi₄V_{2 − x} Cu _x/2Ti _x/2O_{11 − δ} (x = 0.0−0.35).     

Synthesis,region of existence,structural characteristics,and conductivity of BI(CR,FE)VOX solid solutions

The results of our studies of solid solutions of the general composition Bi₄V_{2 − x} Fe _x/2Cr _x/2O_{11 − δ} are presented. The crystal-chemical parameters of different polymorphic modifications of BIMEVOX were determined. The particle size distribution was determined by laser diffraction and optical microscopy. The surface of sintered preforms was studied by scanning electron microscopy. The conductivity of sintered poly-crystalline samples as a function of temperature and composition was studied by impedance spectroscopy. The conductivity was depends on the procedure for the synthesis of solid solutions. The most promising compositions were revealed.     

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.     

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.     

The Stability Criterion of a Semiconductor Superlattice in the Drift–Diffusion Approximation

A criterion for the electric stability of a semiconductor superlttice placed in a longitudinal electric field has been obtained using the drift–diffusion approximation. It is demonstrated that the account for the contact ohmicity yields a stability criterion that is different from that related to the negative differential conductivity.     

Polarization effects in the process of W+w−pair generation by a photon in a magnetic field

Standard Weinberg-Salam-Gleshow theory is used to calculate the probability of W⁺W^–-pair photogeneration in a magnetic field. The dependence of this probability on polarization of the particle pair and initial photon is studied, together with the dependence on magnetic field intensity and photon energy. The unitary relationship in the boson sector of the model is verified in the lowest order of perturbation theory with respect to the fine structure constant.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 13–17, May, 1990.