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1.
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...  相似文献   
2.
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 P(Gn??) does not converge as n (here, the probability distribution is uniform over the set of all graphs on the labeled set of vertices {1,,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.  相似文献   
3.
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.  相似文献   
4.
This work continues the search for optimal preparation methods and studies of structural and transport characteristics of BICUTIVOX solid solutions of the general composition Bi4V2 − x Cu x/2Ti x/2O11 − δ (x = 0.0−0.35).  相似文献   
5.
The results of our studies of solid solutions of the general composition Bi4V2 − x Fe x/2Cr x/2O11 − 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.  相似文献   
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7.
The limit probabilities of the first-order properties of a random graph in the Erd?s–Rényi model G(n, n?α), α ∈ (0, 1), are studied. A random graph G(n, n?α) is said to obey the zero-one k-law if, given any property expressed by a formula of quantifier depth at most k, the probability of this property tends to either 0 or 1. As is known, for α = 1? 1/(2k?1 + a/b), where a > 2k?1, the zero-one k-law holds. Moreover, this law does not hold for b = 1 and a ≤ 2k?1 ? 2. It is proved that the k-law also fails for b > 1 and a ≤ 2k?1 ? (b + 1)2.  相似文献   
8.
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 Bi13Mo5 ? x Me x O34 ? 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.  相似文献   
9.
We propose a new general definition of Volterra operators. Several types of evolutionary operators, including Volterra ones in the sense of A.N. Tikhonov, satisfy this definition. For equations with generalized Volterra operators we introduce the notions of local, global, and maximally extended solutions. For solutions to nonlinear equations we formulate the existence, uniqueness, and extendability conditions. The theorems proved in this paper imply both known and new results on the solvability of concrete equations. We adduce an example of the application of obtained results to the study of the Cauchy problem for functional differential equations.  相似文献   
10.
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