The paper presents integral analysis of data obtained on carbonate reservoir rocks of Bashkir and Tournai formations (Republic of Tatarstan, Russia) under specially designed experimental studies for ...measuring rock permeability alteration under changes of pore pressure with constant triaxial outer (geostatic) stresses. Characteristic hysteretic effects of permeability alteration under cyclic changes of pore pressure are revealed and related to the reservoir and mechanical properties of rock samples, as well as different fluid saturation. It is shown that cyclic geomechanical treatment can promote significant improvements of flow characteristics of a carbonate rock material.
The results of experimental studies of emulsification processes in rotor-disk mixers having various designs of the working units that allow control of size-wise disperse particle distribution are ...reported. It is shown that the size of disperse particles decreases with increase of the area of perforations in the working units of rotor-disk mixers and with installation of additional components (teeth). Thereupon, the power consumption increases because, with the experimental parameters (rotation frequency, flow rate, ratio of mixer components, etc.) remaining identical, the average size of disperse particles decreases and, consequently, the interface area increases.
► We study an evasion differential game with several pursuers and one evader. ► The game is with integral constraint on control functions of the players. ► We assume that the total resource of the ...pursuers does not exceed that of the evader. ► We present an explicit strategy for the evader which guarantees evasion. ► Evasion is proved by estimating distances between evader and the pursuers.
We study a two dimensional evasion differential game with several pursuers and one evader with integral constraints on control functions of players. Assuming that the total resource of the pursuers does not exceed that of the evader, we solve the game by presenting explicit strategy for the evader which guarantees evasion.
We consider a linear pursuit game of one pursuer and one evader whose motions are described by different-type linear discrete systems. Controls of the players satisfy total constraints. Terminal set ...M is a subset of ℝn and it is assumed to have nonempty interior. Game is said to be completed if yk-xk∈M at some step k. To construct the control of the pursuer, at each step i, we use positions of the players from step 1 to step i and the value of the control parameter of the evader at the step i. We give sufficient conditions of completion of pursuit and construct the control for the pursuer in explicit form. This control forces the evader to expend some amount of his resources on a period consisting of finite steps. As a result, after several such periods the evader exhausted his energy and then pursuit will be completed.
This is the second paper in a series of reviews devoted to the scientific achievements of the Leningrad and St. Petersburg school of probability and mathematical statistics from 1947 to 2017. This ...paper is devoted to the works on limit theorems for dependent variables (in particular, Markov chains, sequences with mixing properties, and sequences admitting a martingale approximation) and to various aspects of the theory of random processes. We pay particular attention to Gaussian processes, including isoperimetric inequalities, estimates of the probabilities of small deviations in various norms, and the functional law of the iterated logarithm. We present a brief review and bibliography of the works on approximation of random fields with a parameter of growing dimension and probabilistic models of systems of sticky inelastic particles (including laws of large numbers and estimates for the probabilities of large deviations).
We consider pursuit-evasion differential game of countable number inertial players in Hilbert space with integral constraints on the control functions of players. Duration of the game is fixed. The ...payoff functional is the greatest lower bound of distances between the pursuers and evader when the game is terminated. The pursuers try to minimize the functional, and the evader tries to maximize it. In this paper, we find the value of the game and construct optimal strategies of the players.
The problems of weak and strong invariance of a constant multivalued mapping with respect to the heat conductivity equation with time lag are studied. Sufficient conditions of weak and strong ...invariance of a given multivalued mapping are obtained.
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