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The choice of the optimal strategy for a significant number of applied problems can be formalized as a game theory problem, even in conditions of incomplete information. The article deals with a hierarchical game with a random second player, in which the first player chooses a deterministic solution, and the second player is represented by a set of decision makers. The strategies of the players that ensure the Stackelberg equilibrium are studied. The strategy of the second player is formalized as a probabilistic solution to an optimization problem with an objective function depending on a continuously distributed random parameter. In many cases, the choice of optimal strategies takes place in conditions when there are many decision makers, and each of them chooses a decision based on his (her) criterion. The mathematical formalization of such problems leads to the study of probabilistic solutions to problems with an objective function depending on a random parameter. In particular, probabilistic solutions are used for mathematical describing the passenger’s choice of a mode of transport. The problem of optimal fare choice for a new route based on a probabilistic model of passenger preferences is considered. In this formalization, the carrier that sets the fare is treated as the first player; the set of passengers is treated as the second player. The second player’s strategy is formalized as a probabilistic solution to an optimization problem with a random objective function. A model example is considered. © 2021 Udmurt State University. All rights reserved. Funding. The study was funded by federal budget of the Russian Federation within the framework of the state order, the project «Optimization of the transport and logistics system based on modeling the development of transport infrastructure and models of consumer preference».

Optimization problems with random parameters are studied. The traditional approach to their solution consists in finding a deterministic solution satisfying a certain criterion: optimization of the expected value of the objective function, optimization of the probability of attaining a certain level, or optimization of the quantile. In this review paper, we consider a solution of a stochastic optimization problem in the form of a random vector (or a random set). This is a relatively new class of problems, which is called "probabilistic optimization problems." It is noted that the application of probabilistic solutions in problems with random parameters is justified in the cases of multiple decision makers. Probabilistic optimization problems arise, for example, in the analysis of multicriteria problems; in this case, the weight coefficients of the importance of criteria are regarded as a random vector. We consider important examples of economic-mathematical models, which are optimization problems with a large number of decision makers: the problem of optimal choice based on the consumer's preference function, the route selection problem based on the optimization of the generalized cost of the trip, and the securities portfolio problem with a distribution of the investors' risk tolerance. Mathematical statements of these problems are given in the form of problems of probabilistic optimization. Some properties of the constructed models are studied; in particular, the expected value of the probabilistic solution of an optimization problem is analyzed. © 2020 Krasovskii Institute of Mathematics and Mechanics. All rights reserved.

To identify source water for trees growing on permafrost in Siberia, we applied mechanistic models that quantify physical and biochemical fractionation processes, leading to oxygen isotope variation (δ18O) in plant organic matter. These models allowed us to investigate the influence of a variety of climatic factors on tree-ring cellulose from two dominant species: Larix cajanderi Mayr. from northeastern Yakutia (69° 22′ N, 148° 25′ E, ~ 250 m a.s.l.) and Pinus sylvestris L. from Central Yakutia (62°14′ N, 129°37′ E, ~ 220 m a.s.l.). The climate of the region is highly continental with short growing seasons, low amount of precipitation and these forest ecosystems are growing on permafrost, which in turn impact the water cycle and climate variation in the δ18O of source water. We compared outputs of the Land surface Processes and eXchanges (LPX-Bern v. 1.3), and Roden-Lin-Ehleringer (RLE) models for the common period from 1945 to 2004. Based on our findings, trees from northeastern and central Yakutia may have access to additional thawed permafrost water during dry summer periods. Owing to differences in the soil structure, active thaw soil depth and root systems of trees at two Siberian sites, Larix cajanderi Mayr. trees can access water not more than from 50 cm depth, in contrast to Pinus sylvestris L. in Central Yakutia which can acquire water from up to 80 cm soil depth. The results enhance our understanding of the growth and survival of the trees in this extreme environment.

Перечислены конструкторские задачи построения высокочастотных трактов фазированных антенных решеток с заданным амплитудно-фазовым распределением СВЧ сигнала среднего уровня мощности. Предложены варианты реализации трактов на несимметричной полосковой линии. На примере описания конструкций двух СВЧ модулей показана возможность применения интегральной технологии к построению диаграммообразующих антенных систем метрового, дециметрового диапазонов длин волн для сокращения их массы, габаритов, стоимости изготовления и настройки. Предложены варианты комплектующих для построения интегральных фазированных антенных решеток. В качестве основного комплектующего элемента использован направленный ответвитель с нужной связью, обеспечивающий амплитудное и фазовое распределение сигнала по заданному закону. А в качестве подложки для полосковой линии предлагается использовать диэлектрический материал с диэлектрической проницаемостью более 10. Показаны возможности применения современного программного обеспечения для проектирования, точного численного моделирования и настройки антенных СВЧ модулей. В работе подробно описана методика расчета амплитуднофазовых характеристик делителей с помощью программы Microwave Office фирмы Applied Wave Research (AWR). Приведены расчетные и экспериментальные диаграммы направленности антенных систем, выполненных на базе разработанных и изготовленных описанных интегральных СВЧ модулей. The article specifies the design challenges associated with the construction of phased antenna array high-frequency paths with a given amplitude-phase distribution of an average power level microwave signal. The authors propose several variants of the microstrip-based implementation of these paths. The design description for two microwave modules shows the possibility of using the integrated technology to build VHF and UHF wavelength band beam-forming antenna systems in order to reduce their mass, dimensions, production and setup costs. The article proposes what component parts could be used to build integrated phased antenna arrays. As a basic set of components used directional coupler with the right connections, providing amplitude and phase distribution of the signal by a given law. And as the substrate for the stripline is proposed to use a dielectric material with a dielectric constant greater than 10. The authors demonstrate the possibilities for the usage of state-of-the-art software to design, conduct accurate numerical simulation for and setup microwave antenna modules. The paper described in detail the calculation method of amplitude – phase characteristics of subgroups using Microwave Office software company Applied Wave Research (AWR). The calculated and experimental radiation pattern of antenna systems performed based on the developed and manufactured by the described integrated microwave modules. Тимофеева Галина Александровна, инженер-исследователь Управления научной и инновационной деятельностью, Южно-Уральский государственный университет, г. Челябинск; vchtehno@mail.ru. Бигильдин Ильдар Мансурович, студент кафедры конструирования и производства радиоаппаратуры, Южно-Уральский государственный университет, г. Челябинск; bigildin93@mail.ru. G.A. Timofeeva, vchtehno@mail.ru, I.M. Bigildin, bigildin93@mail.ru South Ural State University, Chelyabinsk, Russian Federation

An efficient control problem for bilinear multistage system with random perturbations is considered. The efficient solutions are choosen by two criteria: the first is maximization of a mean value, the second is minimization of a variance of utility function. Such approach has been suggested by Markovitz H. [13] to solve one-stage problem of the portfolio selection in financial analysis. The existence conditions of the stationary efficient controls are obtained in case of incomplete information on the parameters of distributions. The randomization method for unknown parameters is used to construct a control problem solution. The concept of an adjoint stochastic optimization problem is introduced. The connection and separation problems of efficient control and observation are studied by means of adjoint problem solution., AMS subject classification: 90C31, 90A09, 49K15, 49L20.

Changes of intercellular pH in petunia germinating male gametophyte under exogenous phytohormones suggest a potential it role in the growth.