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We study the influence of fishery on a structured fish population under random changes of habitat conditions. The population parameters correspond to dominant pelagic fish species of Far-Eastern seas of the northwestern part of the Pacific Ocean (pollack, herring, sardine). Similar species inhabit various parts of the Word Ocean. The species body size distribution was chosen as a main population feature. This characteristic is easy to measure and adequately defines main specimen qualities such as age, maturity and other morphological and physiological peculiarities. Environmental fluctuations have a great influence on the individuals in early stages of development and have little influence on the vital activity of mature individuals. The fishery revenue was chosen as an optimality criterion. The main control characteristic is fishing effort. We have chosen quadratic dependence of fishing revenue on the fishing effort according to accepted economic ideas stating that the expenses grow with the production volume. The model study shows that the population structure ensures the increased population stability. The growth and drop out of the individuals’ due to natural mortality smoothens the oscillations of population density arising from the strong influence of the fluctuations of environment on young individuals. The smoothing part is played by diffusion component of the growth processes. The fishery in its turn smooths the fluctuations (including random fluctuations) of the environment and has a substantial impact upon the abundance of fry and the subsequent population dynamics. The optimal time-dependent fishing effort strategy was compared to stationary fishing effort strategy. It is shown that in the case of quickly changing habitat conditions and stochastic dynamics of population replenishment there exists a stationary fishing effort having approximately the same efficiency as an optimal time-dependent fishing effort. This means that a constant or weakly varying fishing effort can be very efficient strategy in terms of revenue.

This article is devoted to the study of self-propulsion of bodies in a fluid by the action of internal mechanisms, without changing the external shape of the body. The paper presents an overview of theoretical papers that justify the possibility of this displacement in ideal and viscous liquids.

A special case of self-propulsion of a rigid body along the surface of a liquid is considered due to the motion of two internal masses along the circles. The paper presents a mathematical model of the motion of a solid body with moving internal masses in a three-dimensional formulation. This model takes into account the three-dimensional vibrations of the body during motion, which arise under the action of external forces-gravity force, Archimedes force and forces acting on the body, from the side of a viscous fluid.

The body is a homogeneous elliptical cylinder with a keel located along the larger diagonal. Inside the cylinder there are two material point masses moving along the circles. The centers of the circles lie on the smallest diagonal of the ellipse at an equal distance from the center of mass.

Equations of motion of the system (a body with two material points, placed in a fluid) are represented as Kirchhoff equations with the addition of external forces and moments acting on the body. The phenomenological model of viscous friction is quadratic in velocity used to describe the forces of resistance to motion in a fluid. The coefficients of resistance to movement were determined experimentally. The forces acting on the keel were determined by numerical modeling of the keel oscillations in a viscous liquid using the Navier – Stokes equations.

In this paper, an experimental verification of the proposed mathematical model was carried out. Several series of experiments on self-propulsion of a body in a liquid by means of rotation of internal masses with different speeds of rotation are presented. The dependence of the average propagation velocity, the amplitude of the transverse oscillations as a function of the rotational speed of internal masses is investigated. The obtained experimental data are compared with the results obtained within the framework of the proposed mathematical model.

We study an appearance of gravitational convection in a porous medium saturated by the double-diffusive fluid. The rectangle heated from below is considered with anisotropy of media properties. We analyze Darcy – Boussinesq equations for a binary fluid with Soret effect.

Resulting system for the stream function, the deviation of temperature and concentration is cosymmetric under some additional conditions for the parameters of the problem. It means that the quiescent state (mechanical equilibrium) loses its stability and a continuous family of stationary regimes branches off. We derive explicit formulas for the critical values of the Rayleigh numbers both for temperature and concentration under these conditions of the cosymmetry. It allows to analyze monotonic instability of mechanical equilibrium, the results of corresponding computations are presented.

A finite-difference discretization of a second-order accuracy is developed with preserving of the cosymmetry of the underlying system. The derived numerical scheme is applied to analyze the stability of mechanical equilibrium.

The appearance of stationary and nonstationary convective regimes is studied. The neutral stability curves for the mechanical equilibrium are presented. The map for the plane of the Rayleigh numbers (temperature and concentration) are displayed. The impact of the parameters of thermal diffusion on the Rayleigh concentration number is established, at which the oscillating instability precedes the monotonic instability. In the general situation, when the conditions of cosymmetry are not satisfied, the derived formulas of the critical Rayleigh numbers can be used to estimate the thresholds for the convection onset.

When recognizing workers on images of a construction site obtained from surveillance cameras, a situation is typical in which the objects of detection have a very different spatial scale relative to each other and other objects. An increase in the accuracy of detection of small objects can be achieved by using the Feature-Fused modification of the SSD detector. Together with the use of overlapping image slicing on the inference, this model copes well with the detection of small objects. However, the practical use of this approach requires manual adjustment of the slicing parameters. This reduces the accuracy of object detection on scenes that differ from the scenes used in training, as well as large objects. In this paper, we propose an algorithm for automatic selection of image slicing parameters depending on the ratio of the characteristic geometric dimensions of objects in the image. We have developed a two-pass version of the Feature-Fused SSD detector for automatic determination of optimal image slicing parameters. On the first pass, a fast truncated version of the detector is used, which makes it possible to determine the characteristic sizes of objects of interest. On the second pass, the final detection of objects with slicing parameters selected after the first pass is performed. A dataset was collected with images of workers on a construction site. The dataset includes large, small and diverse images of workers. To compare the detection results for a one-pass algorithm without splitting the input image, a one-pass algorithm with uniform splitting, and a two-pass algorithm with the selection of the optimal splitting, we considered tests for the detection of separately large objects, very small objects, with a high density of objects both in the foreground and in the background, only in the background. In the range of cases we have considered, our approach is superior to the approaches taken in comparison, allows us to deal well with the problem of double detections and demonstrates a quality of 0.82–0.91 according to the mAP (mean Average Precision) metric.

The effectiveness of communication and data transmission systems (CSiPS), which are an integral part of modern systems in almost any field of science and technology, largely depends on the stability of the frequency of the generated signals. The signals generated in the CSiPD can be considered as processes, the frequency of which changes under the influence of a combination of external influences. Changing the frequency of the signals leads to a decrease in the signal-tonoise ratio (SNR) and, consequently, a deterioration in the characteristics of the signal-to-noise ratio, such as the probability of a bit error and bandwidth. It is most convenient to consider the description of such changes in the frequency of signals as random processes, the apparatus of which is widely used in the construction of mathematical models describing the functioning of systems and devices in various fields of science and technology. Moreover, in many cases, the characteristics of a random process, such as the distribution law, mathematical expectation, and variance, may be unknown or known with errors that do not allow us to obtain estimates of the signal parameters that are acceptable in accuracy. The article proposes an algorithm for solving the problem of determining the characteristics of a random process (signal frequency) based on a set of samples of its frequency, allowing to determine the sample mean, sample variance and the distribution law of frequency deviations in the general population. The basis of this algorithm is the comparison of the values of the observed random process measured over a certain time interval with a set of the same number of random values formed on the basis of model distribution laws. Distribution laws based on mathematical models of these systems and devices or corresponding to similar systems and devices can be considered as model distribution laws. When forming a set of random values for the accepted model distribution law, the sample mean value and variance obtained from the measurement results of the observed random process are used as mathematical expectation and variance. The feature of the algorithm is to compare the measured values of the observed random process ordered in ascending or descending order and the generated sets of values in accordance with the accepted models of distribution laws. The results of mathematical modeling illustrating the application of this algorithm are presented.

Numerical analysis of the effects of the local heat source shape on transient natural convection in a square enclosure has been carried out. The local heat source has rectangular, triangular and trapezoidal shape. The boundary value problem formulated in the dimensionless variables such as stream function, vorticity and temperature by using the Boussinesq approximation has been solved by means of finite difference method. Distributions of streamlines and isotherms and time dependences for the average Nusselt number along the heat source surface in a wide range of governing parameters have been obtained.

Dynamic game theoretic models of the corporative innovative development are investigated. The proposed models are based on concordance of private and public interests of agents. It is supposed that the structure of interests of each agent includes both private (personal interests) and public (interests of the whole company connected with its innovative development first) components. The agents allocate their personal resources between these two directions. The system dynamics is described by a difference (not differential) equation. The proposed model of innovative development is studied by simulation and the method of enumeration of the domains of feasible controls with a constant step. The main contribution of the paper consists in comparative analysis of efficiency of the methods of hierarchical control (compulsion or impulsion) for information structures of Stackelberg or Germeier (four structures) by means of the indices of system compatibility. The proposed model is a universal one and can be used for a scientifically grounded support of the programs of innovative development of any economic firm. The features of a specific company are considered in the process of model identification (a determination of the specific classes of model functions and numerical values of its parameters) which forms a separate complex problem and requires an analysis of the statistical data and expert estimations. The following assumptions about information rules of the hierarchical game are accepted: all players use open-loop strategies; the leader chooses and reports to the followers some values of administrative (compulsion) or economic (impulsion) control variables which can be only functions of time (Stackelberg games) or depend also on the followers’ controls (Germeier games); given the leader’s strategies all followers simultaneously and independently choose their strategies that gives a Nash equilibrium in the followers’ game. For a finite number of iterations the proposed algorithm of simulation modeling allows to build an approximate solution of the model or to conclude that it doesn’t exist. A reliability and efficiency of the proposed algorithm follow from the properties of the scenario method and the method of a direct ordered enumeration with a constant step. Some comprehensive conclusions about the comparative efficiency of methods of hierarchical control of innovations are received.

In this paper we consider the controlled motion of a helical body with three blades in an ideal fluid, which is executed by rotating three internal rotors. We set the problem of selecting control actions, which ensure the motion of the body near the predetermined trajectory. To determine controls that guarantee motion near the given curve, we propose methods based on the application of hybrid genetic algorithms (genetic algorithms with real encoding and with additional learning of the leader of the population by a gradient method) and artificial neural networks. The correctness of the operation of the proposed numerical methods is estimated using previously obtained differential equations, which define the law of changing the control actions for the predetermined trajectory.

In the approach based on hybrid genetic algorithms, the initial problem of minimizing the integral functional reduces to minimizing the function of many variables. The given time interval is broken up into small elements, on each of which the control actions are approximated by Lagrangian polynomials of order 2 and 3. When appropriately adjusted, the hybrid genetic algorithms reproduce a solution close to exact. However, the cost of calculation of 1 second of the physical process is about 300 seconds of processor time.

To increase the speed of calculation of control actions, we propose an algorithm based on artificial neural networks. As the input signal the neural network takes the components of the required displacement vector. The node values of the Lagrangian polynomials which approximately describe the control actions return as output signals . The neural network is taught by the well-known back-propagation method. The learning sample is generated using the approach based on hybrid genetic algorithms. The calculation of 1 second of the physical process by means of the neural network requires about 0.004 seconds of processor time, that is, 6 orders faster than the hybrid genetic algorithm. The control calculated by means of the artificial neural network differs from exact control. However, in spite of this difference, it ensures that the predetermined trajectory is followed exactly.

The study tested correctness of three interatomic potentials available in the scientific literature in reproducing a vacancy diffusion in concentrated Fe–Cr alloys by molecular dynamic simulations. It was necessary for further detailed study of vacancy diffusion mechanism in these alloys with Cr content 5–25 at.% at temperatures in the range of 600–1000 K. The analysis of the potentials was performed on alloys models with Cr content 10, 20, 50 at.%. The consideration of the model with chromium content 50 at.% was necessary for further study of diffusion processes in chromium-rich precipitates in these alloys. The formation energies and the atomic mobilities of iron and chromium atoms were calculated and analyzed in the alloys via an artificially created vacancy for all used potentials. A time dependence of mean squared displacement of atoms was chosen as а main characteristic for the analysis of atomic mobilities. The simulation of vacancy formation energies didn’t show qualitative differences between the investigated potentials. The study of atomic mobilities showed a poor reproduction of vacancy diffusion in the simulated alloys by the concentration-dependent model (CDM), which strongly underestimated the mobility of chromium atoms via vacancy in the investigated range of temperature and chromium content. Also it was established, that the two-band model (2BM) of potentials in its original and modified version doesn’t have such drawbacks. This allows one to use these potentials in simulations of vacancy diffusion mechanism in Fe–Cr alloys. Both potentials show a significant dependence of the ratio of chromium and iron atomic mobilities on temperature and Cr content in simulated alloys. The quantitative data of the diffusion coefficients of atoms obtained by these potentials also differ significantly.

The effect of the nonlinear supratransmission in crystal of A₃B stoichiometry is studied by molecular dynamics on the example of Pt₃Al alloy. This effect is the transfer of energy at frequencies outside the phonon spectrum of the crystal. Research of the mechanisms of energy transport from the material surface to the interior is the important task, both from the theoretical point of view and from the prospects for practical application in the modification of near-surface layers by treatment with intense external influence of various types. The model was a three-dimensional face-centered cubic crystal whose atoms interact by means of the multiparticle potential obtained by the embedded atom method, which provides greater realism of the model in comparison with the use of pair potentials. Various forms of oscillation of the external influence region are considered. The possibility of energy transport from the crystal surface to the interior is shown by excitation of quasi-breathers near the region of influence and their subsequent destruction in the crystal and scattering of the energy stored on them. The quasibreathers are high-amplitude nonlinear atoms' oscillations of the alloy lightweight component at frequencies outside the phonon spectrum of the crystal. This effect was observed not with every oscillation's form of the region of influence. Quasi-breathers appeared most intensely near the region of influence with sinusoidal form oscillations. The results obtained indicate that the contribution of quasi-breathers to the energy transfer through the crystal increases with increasing amplitude of the influence. The range of amplitudes from 0.05 to 0.5 Å is considered. The frequency of the influence varied from 0.2 to 15 THz, which ensured the coverage of the entire spectrum of lowamplitude oscillations for this crystal's model. The minimum magnitude of the external effect amplitude at which this effect was observed was found to be 0.15 Å. At amplitudes greater than 0.5 Å, the cell rapidly decays for frequencies close to the optical branch of the phonon spectrum. The results of the study can be useful for laser processing of materials, surface treatment by low-energy plasma, and also in radiation materials science.