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Greatest core wall settlement to 2021 was predicted using field study data for settlement of the rockfill dam and asphalt-concrete core wall of the Boguchany HPP from 2011 to 2015.

The results of experiments on gallium crystal growth under conditions of microturbulent flow in the melt in a nonuniform vibration field are discussed. The vibration field in the conducting melt is generated by superposing profiled constant and oscillating magnetic fields. Among the features of the flow is the onset of intense small-scale turbulent flow which homogenizes the heat and concentration fields in the melt in the neighborhood of the growing crystal. High values of the transport coefficients, in particular, the effective thermal conductivity and diffusion coefficients, which ensure a high degree of supercooling of the melt in the neighborhood of the crystallization front, and a kinetic mechanism of single-crystal growth are recorded.

CONTENTS Introduction Chapter I. The main notions and facts § 1.1. The notion of randomness depends on a given probability distribution § 1.2. Three faces of randomness: stochasticness, chaoticness, typicalness § 1.3. Typical, chaotic and stochastic sequences: ways to a mathematical definition 1.3.1. Typicalness 1.3.2. Chaoticness 1.3.3. Stochasticness 1.3.4. Comments § 1.4. Typical and chaotic sequences: basic definitions (for the case of the uniform Bernoulli distribution) 1.4.1. Typicalness 1.4.2. Chaoticness Chapter II. Effectively null sets, constructive support, and typical sequences § 2.1. Effectively null sets, computable distributions, and the statement of Martin-Lof's theorem § 2.2. Proof of Martin-Lof's theorem § 2.3. Different versions of the definition of the notion of typicalness 2.3.1. Schorr's definition of typicalness 2.3.2. Solovay's criterion for typicalness 2.3.3. The axiomatic approach to the definition of typicalness Chapter III. Complexity, entropy, and chaotic sequences § 3.1. Computable mappings § 3.2. Kolmogorov's theorem. Monotone entropy § 3.3. Chaotic sequences Chapter IV. What is a random sequence? § 4.1. The proof of the Levin-Schorr theorem for the uniform Bernoulli distribution § 4.2. The case of an arbitrary probability distribution § 4.3. The proofs of the lemmas Chapter V. Probabilistic machines, a priori probability, and randomness § 5.1. Probabilistic machines § 5.2. A priori probability § 5.3. A priori probability and entropy § 5.4. A priori probability and randomness Chapter VI. The frequency approach to the definition of a random sequence § 6.1. Von Mises' approach. The Church and Kolmogorov-Loveland definitions § 6.2. Relations between different definitions. Ville's construction. Muchnik's theorem. Lambalgen's example 6.2.1. Relations between different definitions 6.2.2. Ville's example 6.2.3. Muchnik's theorem 6.2.4. Lambalgen's example § 6.3. A game-theoretic criterion for typicalness Addendum. A timid criticism regarding probability theory References

Godel's incompleteness theorem states that there is no system of axioms and rules of inference such that the totality of all assertions deducible from the axioms is the same as the totality of all true assertions in arithmetic (indeed, for every consistent system one can construct effectively a true but unprovable assertion). The present article is devoted to a proof of this theorem, based on the concepts and methods of the theory of algorithms; the necessary information from the theory of algorithms is provided. The paper does not require specialized knowledge of any kind (in particular, none from mathematical logic), but assumes only a familiarity with elementary mathematical terminology and symbolism.

This paper is based on the author's lecture "N.N. Luzin and the descriptive theory of sets" delivered on 13 December 1983 at the meeting of the Moscow Mathematical Society dedicated to the centenary of Luzin's birth. The paper is aimed at a wide readership and is regarded by the author as one of the means of introducing a reader to the sphere of ideas of the descriptive theory.

This paper investigates the gas flow in an electromagnetic field when the conductivity, being a function of the thermodynamic gas parameters, vanishes during the flow (switching off of the conductivity). In the case of steady supersonic flows in an expanding nozzle it was first shown analytically [1] and then confirmed by numerical experiment [2] that stable steady flow is not possible for all the problem parameters (for example, the values of the magnetic field at the exit). Instead of a steady flow a periodic regime is realized when narrow regions of conducting gas with currents flowing through them detach from the conducting region and propagate down the channel. In these papers the conductivity was assumed to be a function of only the temperature, such that for T ≪ T* σ(T) = 0. In [3, 4] the flows of conducting gas in the channels were calculated both with the given dependence of the gas conductivity on the temperature and on the basis of a three-component model by means of the Saha equation. At the same time, the development of periodic regimes in the flow in the nozzle was observed in both cases, but the mechanism of the origin of the current layers was not explained. The self-similar problem of the withdrawal of a nonconducting piston from a half-space occupied by a conducting gas with a magnetic field was investigated in [5] in a linear formulation. At the same time, regions of the problem parameters (the velocity of the piston and the magnetic field on it) were found when, in spite of the self-similar formulation of the problem, there is no self-similar solution. At the same time, regions exist where several solutions are possible. The possibility of the formation of isothermal rarefaction zones with low electrical conductivity when the Joule heating is balanced by the cooling of the gas on expansion (Butler waves) [6] was not taken into account in this paper, since they are unstable with respect to superheating. However, in the case of flow in a nozzle it was shown [2] that precisely the development of instabilities in these zones leads to the formation of the periodic regime. In the present paper the solution of the self-similar problem is constructed in a nonlinear formulation. The reason for the occurrence of regions in which the solution is multiply valued, which is associated with the process of arrival at self-similar boundary conditions, is explained. It is shown that a quasiperiodic regime can arise in the solution, occurring, in particular, in the regions of the problem parameters where there is no self-similar solution.

Heat and mass transfer in a liquid-liquid and liquid-solid medium are investigated theoretically and experimentally in a jet heat- and mass-transfer apparatus.

Among the numerations of classes of countable sets there can be distinguished those in which the number contains information about the set having the number-these are computable and potentially computable numerations—and those in which the set contains information about its number-these are covering and fully covering numerations. The conditions are established which are necessary and sufficient in order that all numerations of the given class should be covering. As a corollary it is established that there exist covering numerations which are not fully covering.

The restoring torque provides by the weight of the balanced platform can be made arbitrarily small if the point of application of the load Q is placed above the instantaneous center of rotation by an amount defined by the geometrical parameter D.

The method [or the determination of the step for numerical integration by the Runge approach is considered for the system ot equations describing the dynamics of atomic energy apparatus (AEA). A test of the algorithm developed t or the AEA shows that the integration step for them can be selected close to the maximum. In addition, an increase in the step results in a loss of stability for the calculation. The connection between the maximum step and the roots of a system of equations linearized at a series of points is given and the graphical interpretation for a maximum step in the plane of the roots is determined. It is shown that for the execution of the AEA algorithm on an electronic computer, it is feasible to divide it into two parts." the equations for the kinetics and the heat equations. Each of the parts is solved with different steps: the first- with a small constant step, the second- with a variable step. Fulfillment of these requirements enables one to select a reasonable design for the AEA algorithm.