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In the last few years, significant progress has been observed in the field of rotating detonation engines for aircrafts. Scientific laboratories around the world conduct both fundamental researches related, for example, to the issues of effective mixing of fuel and oxidizer with the separate supply, and applied development of existing prototypes. The paper provides a brief overview of the main results of the most significant recent computational work on the study of propagation of a onedimensional pulsating gaseous detonation wave in a non-uniform medium. The general trends observed by the authors of these works are noted. In these works, it is shown that the presence of parameter perturbations in front of the wave front can lead to regularization and to resonant amplification of pulsations behind the detonation wave front. Thus, there is an appealing opportunity from a practical point of view to influence the stability of the detonation wave and control it. The aim of the present work is to create an instrument to study the gas-dynamic mechanisms of these effects.

The mathematical model is based on one-dimensional Euler equations supplemented by a one-stage model of the kinetics of chemical reactions. The defining system of equations is written in the shock-attached frame that leads to the need to add a shock-change equations. A method for integrating this equation is proposed, taking into account the change in the density of the medium in front of the wave front. So, the numerical algorithm for the simulation of detonation wave propagation in a non-uniform medium is proposed.

Using the developed algorithm, a numerical study of the propagation of stable detonation in a medium with variable density as carried out. A mode with a relatively small oscillation amplitude is investigated, in which the fluctuations of the parameters behind the detonation wave front occur with the frequency of fluctuations in the density of the medium. It is shown the relationship of the oscillation period with the passage time of the characteristics C₊ and C₀ over the region, which can be conditionally considered an induction zone. The phase shift between the oscillations of the velocity of the detonation wave and the density of the gas before the wave is estimated as the maximum time of passage of the characteristic C₊ through the induction zone.

In this paper, we consider two variants of the concept of sharp minimum for mathematical programming problems with quasiconvex objective function and inequality constraints. It investigated the problem of describing a variant of a simple subgradient method with switching along productive and non-productive steps, for which, on a class of problems with Lipschitz functions, it would be possible to guarantee convergence with the rate of geometric progression to the set of exact solutions or its vicinity. It is important that to implement the proposed method there is no need to know the sharp minimum parameter, which is usually difficult to estimate in practice. To overcome this problem, the authors propose to use a step adjustment procedure similar to that previously proposed by B. T. Polyak. However, in this case, in comparison with the class of problems without constraints, it arises the problem of knowing the exact minimal value of the objective function. The paper describes the conditions for the inexactness of this information, which make it possible to preserve convergence with the rate of geometric progression in the vicinity of the set of minimum points of the problem. Two analogs of the concept of a sharp minimum for problems with inequality constraints are considered. In the first one, the problem of approximation to the exact solution arises only to a pre-selected level of accuracy, for this, it is considered the case when the minimal value of the objective function is unknown; instead, it is given some approximation of this value. We describe conditions on the inexact minimal value of the objective function, under which convergence to the vicinity of the desired set of points with a rate of geometric progression is still preserved. The second considered variant of the sharp minimum does not depend on the desired accuracy of the problem. For this, we propose a slightly different way of checking whether the step is productive, which allows us to guarantee the convergence of the method to the exact solution with the rate of geometric progression in the case of exact information. Convergence estimates are proved under conditions of weak convexity of the constraints and some restrictions on the choice of the initial point, and a corollary is formulated for the convex case when the need for an additional assumption on the choice of the initial point disappears. For both approaches, it has been proven that the distance from the current point to the set of solutions decreases with increasing number of iterations. This, in particular, makes it possible to limit the requirements for the properties of the used functions (Lipschitz-continuous, sharp minimum) only for a bounded set. Some computational experiments are performed, including for the truss topology design problem.

The paper gives an overview of methods for estimating the parameters of random point fields with local interaction between points. It is shown that the conventional method of the maximum pseudo-likelihood is a special case of the family of estimation methods based on the use of the auxiliary Markov process, invariant measure of which is the Gibbs point field with parameters to be estimated. A generalization of this method, resulting in estimating equation that can not be obtained by the the universal Takacs–Fiksel method, is proposed. It is shown by computer simulations that the new method enables to obtain estimates which have better quality than those by a widely used method of the maximum pseudolikelihood.

Numerical investigation of mixing non-isothermal streams of sodium coolant in a T-branch is carried out in the FlowVision CFD software. This study is aimed at argumentation of applicability of different approaches to prediction of oscillating behavior of the flow in the mixing zone and simulation of temperature pulsations. The following approaches are considered: URANS (Unsteady Reynolds Averaged Navier Stokers), LES (Large Eddy Simulation) and quasi-DNS (Direct Numerical Simulation). One of the main tasks of the work is detection of the advantages and drawbacks of the aforementioned approaches.

Numerical investigation of temperature pulsations, arising in the liquid and T-branch walls from the mixing of non-isothermal streams of sodium coolant was carried out within a mathematical model assuming that the flow is turbulent, the fluid density does not depend on pressure, and that heat exchange proceeds between the coolant and T-branch walls. Model LMS designed for modeling turbulent heat transfer was used in the calculations within URANS approach. The model allows calculation of the Prandtl number distribution over the computational domain.

Preliminary study was dedicated to estimation of the influence of computational grid on the development of oscillating flow and character of temperature pulsation within the aforementioned approaches. The study resulted in formulation of criteria for grid generation for each approach.

Then, calculations of three flow regimes have been carried out. The regimes differ by the ratios of the sodium mass flow rates and temperatures at the T-branch inlets. Each regime was calculated with use of the URANS, LES and quasi-DNS approaches.

At the final stage of the work analytical comparison of numerical and experimental data was performed. Advantages and drawbacks of each approach to simulation of mixing non-isothermal streams of sodium coolant in the T-branch are revealed and formulated.

It is shown that the URANS approach predicts the mean temperature distribution with a reasonable accuracy. It requires essentially less computational and time resources compared to the LES and DNS approaches. The drawback of this approach is that it does not reproduce pulsations of velocity, pressure and temperature.

The LES and DNS approaches also predict the mean temperature with a reasonable accuracy. They provide oscillating solutions. The obtained amplitudes of the temperature pulsations exceed the experimental ones. The spectral power densities in the check points inside the sodium flow agree well with the experimental data. However, the expenses of the computational and time resources essentially exceed those for the URANS approach in the performed numerical experiments: 350 times for LES and 1500 times for ·DNS.

The article shows the relevance of research work in the field of creating control systems for unmanned vehicles based on computer vision technologies. Computer vision tools are used to solve a large number of different tasks, including to determine the location of the car, detect obstacles, determine a suitable parking space. These tasks are resource intensive and have to be performed in real time. Therefore, it is important to develop effective models, methods and tools that ensure the achievement of the required time and accuracy for use in unmanned vehicle control systems. In this case, the choice of the image representation model is important. In this paper, we consider a model based on the wavelet transform, which makes it possible to form features characterizing the energy estimates of the image points and reflecting their significance from the point of view of the contribution to the overall image energy. To form a model of energy characteristics, a procedure is performed based on taking into account the dependencies between the wavelet coefficients of various levels and the application of heuristic adjustment factors for strengthening or weakening the influence of boundary and interior points. On the basis of the proposed model, it is possible to construct descriptions of images their characteristic features for isolating and analyzing, including for isolating contours, regions, and singular points. The effectiveness of the proposed approach to image analysis is due to the fact that the objects in question, such as road signs, road markings or car numbers that need to be detected and identified, are characterized by the relevant features. In addition, the use of wavelet transforms allows to perform the same basic operations to solve a set of tasks in onboard unmanned vehicle systems, including for tasks of primary processing, segmentation, description, recognition and compression of images. The such unified approach application will allow to reduce the time for performing all procedures and to reduce the requirements for computing resources of the on-board system of an unmanned vehicle.

This study proposes and analyzes a discrete-time mathematical model of population dynamics with seasonal reproduction, taking into account the density-dependent regulation and sex structure. In the model, population birth rate depends on the number of females, while density is regulated through juvenile survival, which decreases exponentially with increasing total population size. Analytical and numerical investigations of the model demonstrate that when more than half of both females and males survive, the population exhibits stable dynamics even at relatively high birth rates. Oscillations arise when the limitation of female survival exceeds that of male survival. Increasing the intensity of male survival limitation can stabilize population dynamics, an effect particularly evident when the proportion of female offspring is low. Depending on parameter values, the model exhibits stable, periodic, or irregular dynamics, including multistability, where changes in current population size driven by external factors can shift the system between coexisting dynamic modes. To apply the model to real populations, we propose an approach for estimating demographic parameters based on total abundance data. The key idea is to reduce the two-component discrete model with sex structure to a delay equation dependent only on total population size. In this formulation, the initial sex structure is expressed through total abundance and depends on demographic parameters. The resulting one-dimensional equation was applied to describe and estimate demographic characteristics of ungulate populations in the Jewish Autonomous Region. The delay equation provides a good fit to the observed dynamics of ungulate populations, capturing long-term trends in abundance. Point estimates of parameters fall within biologically meaningful ranges and produce population dynamics consistent with field observations. For moose, roe deer, and musk deer, the model suggests predominantly stable dynamics, while annual fluctuations are primarily driven by external factors and represent deviations from equilibrium. Overall, these estimates enable the analysis of structured population dynamics alongside short-term forecasting based on total abundance data.

The work is devoted to the study of subgradient methods with different variations of the Polyak stepsize for minimization functions from the class of weakly convex and relatively weakly convex functions that have the corresponding analogue of a sharp minimum. It turns out that, under certain assumptions about the starting point, such an approach can make it possible to justify the convergence of the subgradient method with the speed of a geometric progression. For the subgradient method with the Polyak stepsize, a refined estimate for the rate of convergence is proved for minimization problems for weakly convex functions with a sharp minimum. The feature of this estimate is an additional consideration of the decrease of the distance from the current point of the method to the set of solutions with the increase in the number of iterations. The results of numerical experiments for the phase reconstruction problem (which is weakly convex and has a sharp minimum) are presented, demonstrating the effectiveness of the proposed approach to estimating the rate of convergence compared to the known one. Next, we propose a variation of the subgradient method with switching over productive and non-productive steps for weakly convex problems with inequality constraints and obtain the corresponding analog of the result on convergence with the rate of geometric progression. For the subgradient method with the corresponding variation of the Polyak stepsize on the class of relatively Lipschitz and relatively weakly convex functions with a relative analogue of a sharp minimum, it was obtained conditions that guarantee the convergence of such a subgradient method at the rate of a geometric progression. Finally, a theoretical result is obtained that describes the influence of the error of the information about the (sub)gradient available by the subgradient method and the objective function on the estimation of the quality of the obtained approximate solution. It is proved that for a sufficiently small error $\delta > 0$, one can guarantee that the accuracy of the solution is comparable to $\delta$.

The numerical methods developed by the author recently for calculating the molecular system based on the direct solution of the Schrodinger equation by the Monte Carlo method have shown a huge uncertainty in the choice of solutions. On the one hand, it turned out to be possible to build many new solutions; on the other hand, the problem of their connection with reality has become sharply aggravated. In ab initio quantum mechanical calculations, the problem of choosing solutions is not so acute after the transition to the classical format of describing a molecular system in terms of potential energy, the method of molecular dynamics, etc. In this paper, we investigate the problem of choosing solutions in the classical format of describing a molecular system without taking into account quantum mechanical prerequisites. As it turned out, the problem of choosing solutions in the classical format of describing a molecular system is reduced to a specific marking of the configuration space in the form of a set of stationary points and reconstruction of the corresponding potential energy function. In this formulation, the solution of the choice problem is reduced to two possible physical and mathematical problems: to find all its stationary points for a given potential energy function (the direct problem of the choice problem), to reconstruct the potential energy function for a given set of stationary points (the inverse problem of the choice problem). In this paper, using a computational experiment, the direct problem of the choice problem is discussed using the example of a description of a monoatomic cluster. The number and shape of the locally equilibrium (saddle) configurations of the binary potential are numerically estimated. An appropriate measure is introduced to distinguish configurations in space. The format of constructing the entire chain of multiparticle contributions to the potential energy function is proposed: binary, threeparticle, etc., multiparticle potential of maximum partiality. An infinite number of locally equilibrium (saddle) configurations for the maximum multiparticle potential is discussed and illustrated. A method of variation of the number of stationary points by combining multiparticle contributions to the potential energy function is proposed. The results of the work listed above are aimed at reducing the huge arbitrariness of the choice of the form of potential that is currently taking place. Reducing the arbitrariness of choice is expressed in the fact that the available knowledge about the set of a very specific set of stationary points is consistent with the corresponding form of the potential energy function.

We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and dual variables. First, we consider such problems with smooth composite terms, one of which has finite-sum structure. For this setting we propose a variance reduction algorithm with complexity estimates superior to the existing bounds in the literature. Second, we consider finite-sum saddle-point problems with composite terms and propose several algorithms depending on the properties of the composite terms. When the composite terms are smooth we obtain better complexity bounds than the ones in the literature, including the bounds of a recently proposed nearly-optimal algorithms which do not consider the composite structure of the problem. If the composite terms are prox-friendly, we propose a variance reduction algorithm that, on the one hand, is accelerated compared to existing variance reduction algorithms and, on the other hand, provides in the composite setting similar complexity bounds to the nearly-optimal algorithm which is designed for noncomposite setting. Besides, our algorithms allow one to separate the complexity bounds, i. e. estimate, for each part of the objective separately, the number of oracle calls that is sufficient to achieve a given accuracy. This is important since different parts can have different arithmetic complexity of the oracle, and it is desired to call expensive oracles less often than cheap oracles. The key thing to all these results is our general framework for saddle-point problems, which may be of independent interest. This framework, in turn is based on our proposed Accelerated Meta-Algorithm for composite optimization with probabilistic inexact oracles and probabilistic inexactness in the proximal mapping, which may be of independent interest as well.

The paper is devoted to one approach to constructing subgradient methods for strongly convex programming problems with several functional constraints. More precisely, the strongly convex minimization problem with several strongly convex (inequality-type) constraints is considered, and first-order optimization methods for this class of problems are proposed. The special feature of the proposed methods is the possibility of using the strong convexity parameters of the violated functional constraints at nonproductive iterations, in theoretical estimates of the quality of the produced solution by the methods. The main task, to solve the considered problem, is to propose a subgradient method with adaptive rules for selecting steps and stopping rule of the method. The key idea of the proposed methods in this paper is to combine two approaches: a scheme with switching on productive and nonproductive steps and recently proposed modifications of mirror descent for convex programming problems, allowing to ignore some of the functional constraints on nonproductive steps of the algorithms. In the paper, it was described a subgradient method with switching by productive and nonproductive steps for strongly convex programming problems in the case where the objective function and functional constraints satisfy the Lipschitz condition. An analog of the proposed subgradient method, a mirror descent scheme for problems with relatively Lipschitz and relatively strongly convex objective functions and constraints is also considered. For the proposed methods, it obtained theoretical estimates of the quality of the solution, they indicate the optimality of these methods from the point of view of lower oracle estimates. In addition, since in many problems, the operation of finding the exact subgradient vector is quite expensive, then for the class of problems under consideration, analogs of the mentioned above methods with the replacement of the usual subgradient of the objective function or functional constraints by the $\delta$-subgradient were investigated. The noted approach can save computational costs of the method by refusing to require the availability of the exact value of the subgradient at the current point. It is shown that the quality estimates of the solution change by $O(\delta)$. The results of numerical experiments illustrating the advantages of the proposed methods in comparison with some previously known ones are also presented.