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The paper considers one of the numerical methods to solve problems of scattering electromagnetic waves on the systems formed by parallel-oriented cylindrical elements – two-dimensional photonic crystals. The method is based on the classical partition approach used for solving the wave equation. Тhe method principle is to represent the field as the sum of the primary field and the unknown secondary field scattered on the medium elements. The mathematical expression for the latter is written as the infinite series according to elementary wave functions with unknown coefficients. In particular, the N elements-scattered field is found as the sum of N diffraction series in which one of the series is composed of the wave functions of one body and the wave functions in the remaining series are expressed in terms of the eigenfunctions of the first body using addition theorems. Further, to meet the boundary conditions, on the surface of each element, we obtain systems of linear algebraic equations with the infinite number of unknowns – the required expansion coefficients, which are solved by standard methods. A feature of the method is the use of analytical expressions to describe diffraction on a single element of the system. In contrast to most numerical methods, this approach allows one to obtain information on the amplitude-phase or spectral characteristics of the field only at the local points of the structure. The high efficiency of this method stems from the fact that there is no need to determine the field parameters in the entire area of space occupied by the multi-element system under consideration. The paper compares the calculated results of the transmission spectra of two-dimensional photonic crystals using the considered method with the experimental data and numerical results, obtained by other approaches, and demonstrates their good agreement.

Рассмотрены специальные преобразования декартовых координат, позволяющие строить эффективные (экономичные) алгоритмы численного моделирования многомерных случайных величин. В качестве иллюстративных и практически значимых примеров таких преобразований рассмотрены переходы к полярным, сферическим, параболическим и цилиндрическим координатам., The purpose of the paper was to expand the range of efficient (economical) computer algorithms for simulation of multi-dimensional random variables. The authors noticed that in a number of applied problems (for example, when modelling twoor three-dimensional isotropic vectors), transitions from Cartesian to other coordinate systems (for example, to polar or spherical) are effective. In this regard, the new generalizing notation of the computable simulated transformation of Cartesian coordinates is introduced in the paper. Such transformations allow constructing effective (economical) algorithms for the numerical modelling (simulation) of multi-dimensional random variables. The problem of finding examples of constructive and practical applications for computer simulated transformations of Cartesian coordinates is formulated. Transitions to polar, spherical, parabolic and cylindrical coordinates are considered as illustrative examples of such transformations. The practical applications of computable simulated transformations of Cartesian coordinates found in the scientific literature are described in detail by the authors. These applications are associated with both computer modelling (simulation) of isotropic vectors and Gaussian distribution along with the numerical solution of boundary value problems and problems of radiation transfer. Thus, the introduced notion of the computable simulated transformations of Cartesian coordinates is quite constructive. It opens up prospects for the scientific search for new transformations of this type with the aim of using them in stochastic computer models for important processes and phenomena., Вычислительные технологии, Выпуск 6 2021, Pages 62-84

Публикация посвящена применению методов вычислительной геометрии, интервального анализа и линейного программирования к задачам физики управляемого термоядерного синтеза. Рассмотрены геометрические аспекты проблемы, получены проекции светимостей различных объемов сферического токамака на плоскость матричного детектора, изучены изображения предполагаемых макроскопических структур и микроскопических включений. Для набора модельных распределений светимости объема токамака поставлена задача восстановления сигнала. Решение получено с использованием задач линейного программирования., The problems of reconstruction of plasma luminosity are important for physics and technology of power plants-tokamaks. The Globus-M research tokamak obtained a large amount of data using a matrix detector in pinhole camera geometry. From the mathematical point of view, finding the luminosity for different regions of the plasma volume according to the matrix detector is an inverse problem related to the field of integral geometry. An essential feature of the particular task is the use of a single fixed camera with a small viewing angle. In this regard, application of methods of harmonic analysis of data is not enough. The paper investigates the geometric aspects of the problem. In the general view, a threedimensional object is projected onto a two-dimensional plane through a diaphragm. Under the assumption of azimuthal symmetry, there is a central projection of the luminosity of the body of rotation onto a flat matrix detector. The initial information for the calculation is the plasma boundary obtained from magnetic sensors. There is no reliable information about the internal structure of the plasma, so its division into regions of the equal luminosity is not unambiguous. The paper presents an algorithm for finding the projections of the luminosity of plasma volumes on the plane of the matrix detector. A set of model direct problems for the construction of algorithms for their recognition according to the detector data was investigated. Images of supposed macroscopic structures and microscopic inclusions were obtained. The methodological basis of the work is the use of interval analysis methods for solving geometric and algebraic problems. This approach allows obtaining qualitative and quantitative results that takes into account the uncertainty of the input data with the minimum amount of computational costs. Algebraic solvability is investigated in the interval formulation using response functionality. Solutions for a set of test problems are obtained, which demonstrate the availability of successful reconstruction for real data. An important result of the study is an information about the presence of uncertainties in geometric data and related calculations by obtaining results about the luminosity of the plasma by solving linear programming problems., №25 (2020)

Introduction: the paper considers the topical problem of teaching students – future engineers – by computational methods of mathematics. The focus is on developing students̓ necessary professional competencies. Competencies are described in accordance with the Russian Federal State Educational Standard and the international standard by the European Association for Engineering Education SEFI. In order for students to thoroughly study the subject and have a strong professional competence, it is proposed to use a computer-based tutor. The aim of this research is to develop the special methodology of creating the computer-based tutors for teaching mathematical and engineering disciplines to students of technical specialties within the framework of a competence-oriented approach, to compare the effectiveness of classical teaching computational methods by using manual calculations, and training with the involvement of computer-based tutors. The advantages of computer-based tutors were proved in this paper. Materials and Methods: the basis of the research was methods of system analysis and descriptive and analytical methods, primarily experimental. To identify advantages of the proposed approach the methods of empirical research were used (observation and comparison). To prove the efficiency, classical methods of measurement were used. Results: based on the competence approach, a methodology of creating a computer tutor has been developed. It covers most the professional competencies that need to be studied. Also, students are guaranteed to receive the necessary competencies in the right sequence. The research showed that the use of specially designed software, such as Computer-based tutors, in the process of mathematical methods studying connected with the computational procedures allows us to achieve: on the one hand, deep digestion by students (as in using manual calculations), on the other hand to accelerate learning process and increase students motivation. As a result of pedagogical experiment on the use the computer-based tutors the progress in studies has been recorded: the percentage of positive ratings increased from 65 to 88 %. Also, the motivation of students to study mathematics was increased by 12 percent on average. Discussion and Conclusions: the methodology of creation and use of computer-based tutors has high practical significance and allows increasing the effectiveness of teaching mathematics within the competence approach for students of technical specialties. The use of the interactive computer-based tutors focused on mastering professional competencies, is effective for studying mathematical and engineering disciplines by students of technical universities. In particular, a positive effect has been achieved with the introduction of computer-based tutors in the educational process of Kazan National Research Technical University named after A. N. Tupolev-KAI, Kazan, Russia (the University is aimed at training engineers-designers for aerospace industry), Saarland Technical University, Saarbrucken, Germany (the University is focused on training IT engineers), and a number of other Russian and foreign technical universities.

The paper provides an overview of the main events of the International Workshop–Conference on Function Theory dedicated to the Centenary of the birth of S. B. Stechkin, which was held in Yekaterinburg online from August 3 to August 12, 2020, for the 45th time since 1971. A description of the traditions and peculiarities of such workshops that have developed over the years as well as a list of reports by the conference participants are given. The paper also contains memoirs about Sergei Borisovich Stechkin, the initiator of such workshops–conferences, the founder and head of the scientific school on function theory. © 2020 Krasovskii Institute of Mathematics and Mechanics. All rights reserved.

Рассмотрена задача выявления аномальных наблюдений в данных больших размерностей на основе метода многомерного шкалирования с учетом возможности построения качественной визуализации данных. Предложен алгоритм модифицированного метода главных проекций Торгерсона, основанный на построении подпространства проектирования исходных данных путем изменения способа факторизации матрицы скалярных произведений при помощи метода анализа кумулятивных кривых. Построено и проанализировано эмпирическое распределение F -меры для разных вариантов проектирования исходных данных, Purpose. Purpose of the article. The paper aims at the development of methods for multidimensional data presentation for solving classification problems based on the cumulative curves analysis. The paper considers the outlier detection problem for high-dimensional data based on the multidimensional scaling, in order to construct high-quality data visualization. An abnormal observation (or outlier), according to D. Hawkins, is an observation that is so different from others that it may be assumed as appeared in the sample in a fundamentally different way. Methods. One of the conceptual approaches that allow providing the classification of sample observations is multidimensional scaling, representing by the classical Orlochi method, the Torgerson main projections and others. The Torgerson method assumes that when converting data to construct the most convenient classification, the origin must be placed at the gravity center of the analyzed data, after which the matrix of scalar products of vectors with the origin at the gravity center is calculated, the two largest eigenvalues and corresponding eigenvectors are chosen and projection matrix is evaluated. Moreover, the method assumes the linear partitioning of regular and anomalous observations, which arises rarely. Therefore, it is logical to choose among the possible axes for designing those that allow obtaining more effective results for solving the problem of detecting outlier observations. A procedure of modified CC-ABOD (Cumulative Curves for Angle Based Outlier Detection) to estimate the visualization quality has been applied. It is based on the estimation of the variances of angles assumed by particular observation and remaining observations in multidimensional space. Further the cumulative curves analysis is implemented, which allows partitioning out groups of closely localized observations (in accordance with the chosen metric) and form classes of regular, intermediate, and anomalous observations. Results. A proposed modification of the Torgerson method is developed. The F1-measure distribution is constructed and analyzed for different design options in the source data. An analysis of the empirical distribution showed that in a number of cases the best axes are corresponding to the second, third, or even fourth largest eigenvalues. Findings. The multidimensional scaling methods for constructing visualizations of multi-dimensional data and solving problems of outlier detection have been considered. It was found out that the determination of design is an ambiguous problem., Вычислительные технологии, Выпуск 3 2020

It is assumed that the socalled "One Tower" skyscraper with a height of 403.9 meters, considered in the distinctive paper, will be located in the Moscow International Business Center (MIBC) and will become one of the tallest buildings in Europe. The project of a unique object was developed in the architectural bureau "Sergey Skuratov Architects" and "GKTtechStroy" LLC (under the direction of M.I. Kelman). Generally the paper is devoted to computational studies of the stress-strain state, strength and stability ofload-bearing structures of this multifunctional residential complex with an underground parking lot. The paper provides a brief description of the natural conditions of the area of the location of the object, its load-bearing structures, characteristic and design loads, their combinations. Besides, formulation of objectives of computational research is presented. Then numerical methods, algorithms and software, which were used for computational static and dynamic analysis of skyscraper and analysis of corresponding stress-strain state are described. Further, the developed and verified advanced detailed finite element model of the coupled system "pile foundation - load­bearing structures of residential building" is considered. This model adequately reflects corresponding geometric, stiffness, inertial and load parameters and the resulting stress-strain state. Resulting parameters of the stress-strain state, strength and dynamics of load-bearing structures of "One Tower" sky­scraper with allowance for design (in accordance with design codes) combinations of vertical and wind loads and progressive collapse analysis are under consideration as well. As a result a reasonable conclusion is made about the reliability of the criterion parameters obtained by structural analysis including strength analysis, stability analysis and dynamic analysis of the loadbearing structures of the building. Computational structural analysis was performed with the use of licensed certified finite element software package ANSYS Mechanical, verified by the Russian Academy of Architecture and Construction Sciences (RAACS). Reinforcement of structures was designed in "OM SNiP Zhelezobeton" software after converting of resultant efforts from ANSYS Mechanical.

The paper is aimed at determining the marginal distributions of the estimates of model parameters for a nonlinear dynamic model of the cell population dynamics. The cell population system evolves in the laboratory (in vitro) and comprises two types of cells.Basic estimates of model parameters are obtained on a single limited sample of experimental data. The value of the number of populations of each cell type is obtained from the experiment at equal intervals of time. This paper proposes a technique for determining the marginal distributions of the parameter estimates using numerical modeling.This technique includes the identification of parameters of nonlinear models and test of the obtained model adequacy with base parameter estimates, the identification of the initial data and finding the reference trajectory. The initial data for the trajectory are found using the least squares method, while minimizing the deviation from the experimental trajectory. Data sets on measured densities of the populations at specific points in time are generated using the reference trajectory and the normally distributed random numbers generator. The problem of obtaining estimates of system parameters is solved for each data set. Tests of hypotheses about the marginal distribution of each parameter are carried out based on the calculated set of estimated parameters. To prove hypothesis, the Kolmogorov test is used. The description of a numerical example is included. The obtained marginal distributions of the parameter estimates can be further used to evaluate the probabilities of different scenarios of the population system development.DOI: 10.7463/mathm.0415.0812686

Рассмотрена задача маршрутизации транспорта с ограничениями по временным окнам. Требовалось составить план доставки товара клиентам, построив маршруты движения идентичных транспортных средств так, чтобы общая длина пройденного пути была минимальной. Для решения задачи разработан гибридный алгоритм. Он состоит из методов построения исходных решений, муравьиного алгоритма и локального поиска. В муравьином алгоритме в процессе формирования маршрутов разрешается нарушение временных ограничений при условии добавления штрафа в целевую функцию. Предложенный метод показал высокую эффективность при решении задач кластерного типа и задач с долгосрочным горизонтом планирования., The purpose of this paper is to improve the performance of a hybrid method based on ant colony optimization (ACO) that finds approximate solutions of the vehicle routing problem with time windows (VRPTW). In order to solve this problem it is required to design a plan for goods delivery to the customers generating the routes of identical vehicles so that the total travelled distance is minimal. For the VRPTW solving, the hybrid method is developed in which a usage of trial solutions makes it possible to explore the most promising parts of the search space. The initial methods for solution construction, an ant colony optimization (ACO) algorithm and local search are proposed in the framework of the hybrid method. In the ACO algorithm, when generating the routes, it is allowed to violate the time window constraints. A method to restore the feasibility of solutions is implemented within the relaxation scheme under “returns in time” principle. Numerical results for solving all problems with 25, 50 and 100 customers from the Solomon test set are obtained. We provide the results on the time and deviation of the solution of these problems in comparison with the results of other authors. Some problems and their classes were solved much faster by the algorithm proposed in this paper. Relative deviations from optimal values of the objective function for the most complex tasks decrease with increasing decision time. The proposed approach can be considered to be an additional or an alternative algorithm for solving the cluster type and the long-term planning horizon problems of the VRPTW., №5(23) (2018)

Многопользовательские схемы цифровых водяных знаков (ЦВЗ) предназначены для защиты авторских прав на цифровую продукцию. В данной работе рассматриваются две схемы ЦВЗ Боне—Шоу: базовая и каскадная, проводятся исследование и сравнительный анализ этих схем с целью определения более эффективной схемы из двух по длине, а также указаны границы значений параметров схем, для которых одна схема эффективнее другой., Multiuser digital watermarking is a powerful tool for copyright protection of widely replicable digital products. This paper addresses Boneh—Shaw fingerprinting schemes. The algorithms proposed by D. Boneh and J. Shaw allow a distributor to detect any unauthorized copy and trace it back to user and they work correctly for any size of coalition. The main idea of this paper is a comparative analysis of two Boneh—Shaw digital watermarks schemes (cascade and basics), which makes clear which one of these schemes is more effective in terms of the length of the label. Using the comparative analysis and numerical experiments, we obtain the specific values of the boundaries for input parameters in which one scheme will be more efficient than another. From the results of the comparative analysis it can be concluded that for large number of users of the scheme and a small size of the coalition (in relation of users number) it is advisable to use the cascade scheme. In the case of a small number of users and a large size of the coalition (compared to the number of users) it is more expedient to use the basic scheme., №3(23) (2018)

Предложен теоретико-информационный подход к оценке производительности суперкомпьютеров. Этот подход основан на характеристике “вычислительная способность”, которую можно определить теоретически, опираясь исключительно на описание архитектуры исследуемой системы. Предложен метод определения вычислительной способности суперкомпьютеров с учетом влияния межпроцессорного взаимодействия. Метод применяется в работе для оценки производительности пяти суперкомпьютеров среди первых 50 позиций в списке TOP500 (ноябрь 2016). Полученные результаты сравниваются с аналогичными значениями бенчмарка LINPACK и характеристиками Theoretical peak, используемыми для формирования рейтинга TOP500. По результатам сравнения делаются выводы относительно применимости указанного подхода для оценки производительности суперкомпьютеров на этапе разработки., In this paper we present the informational-theoretical approach to the evaluation of performance for supercomputers. This approach is based on the computer capacity characteristic which can be estimated theoretically (without any experiments over the working model of the investigated computer) relying on the description of the architecture of the system under study. We describe the method for estimation of the supercomputers Computer capacity which takes into account the influence of the interprocess communication. The described method is used in this paper to estimate the performance of the five supercomputers among the first fifty positions in TOP500 list (according to November 2016 data). The obtained results are compared with the values of LINPACK benchmark and Theoretical peak characteristic which are used to form the TOP500 rating. Based on the comparison we draw conclusions about the applicability of the presented approach to the evaluation of supercomputers performance at the design stage., №1(23) (2018)

Numerical method examines the impact of the static output characteristics of two types of frequency dithering LG: combination dithering consisting of harmonic oscillations and additional frequency noisy and periodic stand without a special frequency noisy type. The paper considers the technique of numerical analysis of dynamic synchronization zones, designed to meet the need for a series of computational experiments for static output characteristics with an accuracy of not worse than 0.005º/hour. A comparison of the results with those of the previously conducted independent research based on the approximate analytical, experimental, and numerical methods has shown qualitative and quantitative differences in the results of some researches and a good agreement with the results of others. The paper provides more accurate assessments of the impact of types and frequency dither parameters on the output stand stationary characteristic of LG with frequency noisiness, which by the nature and to extent is close to the frequency noisiness in devices used in practice.

This paper will demonstrate the importance of numerical analysis utilization in wind loads calculations for complex shape buildings, and comparison with the standard calculation based on the Russian construction code SP­20.13330.2016, since some difficulties arise when engineers use the standards (codes) such as complexity of setting aerodynamic coefficients and considering the influence of the surrounding buildings (both positive and negative). В данной статье будет рассматриваться важность применения численного анализа при расчете ветровых нагрузок для зданий сложной формы, а также сравнение со стандартным расчетом на основе СП-20.13330.2016, поскольку при использовании инженерами таких норм (коды) возникают некоторые трудности, как сложность задания аэродинамических коэффициентов и учета влияния окружающих зданий (как положительного, так и отрицательного).

При решении задач динамики жидкостей и газов в области малых скоростей потока и при изотермических условиях с успехом применяется метод решеточных уравнений Больцмана (LBM). Для решения дискретного уравнения Больцмана может быть использован новый метод Particles-on-Demand (PonD), в котором в каждой точке сетки дискретизация функции распределения в пространстве скоростей центрирована относительно текущей скорости потока. В отличие от классического LBM, метод PonD применим не только для задач с малыми скоростями потока и при изотермических условиях. В данной работе реализован метод PonD D1Q5 с итерационным расчетом скорости переноса и явным расчетом первых трех моментов, включая скорости переноса. Показано, что рассмотренная модификация метода PonD хоть и накладывает ограничения на параметры, позволяет проводить расчеты в большем диапазоне допустимых скоростей., The purpose of the paper is to demonstrate applicability of the Particle on Demand (PonD) D1Q5 method with the explicit calculation of the first three moments to problem with high speed of the flow. The standard LBM is applicable for small flow velocities. Thus to overcome this limitation we use PonD. In this work, we use conservative version of PonD - the D1Q5 method with the explicit calculation of the first three moments. Methodology. The Pond over LBM was applied to the Riemann problem in order to demonstrate the advantage of the method. In this work, we choose the case when contact discontinuities could propagate at variable speed. Findings. If the interpolation pattern is fixed relative to the point at which there is a current update of the discrete distribution function, then the transfer step can be written explicitly, thus the scheme is conservative. On the other hand, this imposes additional restrictions on the temperature and the flow rate. But even if the PonD scheme is limited to a fixed interpolation pattern, it is possible to simulate flows with larger values of the Mach number than in the case when the classical method of lattice Boltzmann equations is used. Originality/value. In the described particular case of the PonD method, it is possible to avoid iterations by calculating the temperature and velocity values directly at a new time layer. In this work, we have investigated the properties and the range of applicability (admissible values of temperature and velocity) of such modification of PonD., Вычислительные технологии, Выпуск 1 (26) 2021, Pages 62-71

Предложены две устойчивые к ошибкам машинного округления и к аномальным данным квадратно-корневые модификации непрерывно-дискретного кубатурного фильтра Калмана, основанные на вариационном байесовском и коррентропийном подходах. Апробация разработанных алгоритмов на модельной задаче со случайным характером расположения аномальных наблюдений показала их работоспособность при сопоставимом качестве фильтрации. Подтверждена алгебраическая эквивалентность представленных квадратно-корневых и стандартных версий, Rounding errors due to the finite length of machine word can significantly affect the quality of estimation and filtering when solving the corresponding problems in various subject areas. In this regard, to improve the reliability of the obtained results, it is advisable to develop and then apply square-root modifications of the used algorithms. Purpose: developing the square-root modifications of the continuous-discrete cubature Kalman filter on the basis of variational Bayesian and correntropy approaches. Methodology: matrix orthogonal QR decomposition. Findings: two robust (resistant to the possible presence of anomalous data and to machine rounding errors) modifications of the continuous-discrete cubature Kalman filter have been developed. The first (variational Bayesian) algorithm is obtained by extending the known discrete equations of the extrapolation stage to the continuous-discrete case. The second algorithm, based on the maximum correntropy criterion, is proposed in this paper for the first time. The developed square-root algorithms for nonlinear filtering are validated on the example of one stochastic dynamical system model with the random location of anomalous observations. In doing so, the filtering quality, estimated by the value of the accumulated mean square error, was quite comparable for both modifications during equivalent results obtained for the corresponding root-free analogues. Value: the proposed square-root versions of robust modifications of the continuous-discrete cubature Kalman filter are algebraically equivalent to their standard analogues. Meanwhile, positive definiteness and symmetry of covariance matrices of the state vector estimates at the extrapolation and the filtration stages are provided. The developed algorithms will be used to develop software and mathematical support for parametric identification of stochastic nonlinear continuous-discrete systems in the presence of anomalous observations in the measurement data, Вычислительные технологии, Выпуск 3 2020

Рассмотрена задача прогнозирования временных рядов в ее одно- и многомерной постановках. Описан метод прогнозирования, в основе которого лежат алгоритмы сжатия данных и искусственного интеллекта. В качестве примера практического применения этого метода приведены вычисления для некоторых социальных, демографических и экономических показателей Новосибирской области. Наряду с широко используемыми на практике программами для сжатия данных, использованы реализации относительно менее известных моделей на основе формальных грамматик, а также метода, основанного на конечных автоматах. Для прогнозных значений построены доверительные интервалы., This paper describes and experimentally investigates a time series forecasting method based on data compression and artificial intelligence techniques. Its basic idea is to combine various algorithms that can estimate the compressed size of a sequence of discrete values into a single method of forecasting. Generalizations of the method to continuous and multivariate cases are described. We use several popular data compression libraries (zlib, bzip2, ppmd), as well as applications of relatively lesser-known algorithms based on formal grammars (re-pair) along with our implementation of an algorithm based on finite automata with multiple heads. All these are employed to make forecasts for some social, economic and demographic indicators of the Novosibirsk region. The article elaborates both our methodology and the methods used for data preprocessing. Confidence intervals with a confidence level of 0.95 are plotted for all predicted values; the average relative errors calculated from the results of predicting the already fixed values are given. Cases in which multivariate forecasting turned out to be more accurate than univariate forecasting are: 1. Average annual population and natural population growth in the Novosibirsk region. Figure 1 shows their graphs along with multivariate predictions, while confidence intervals and mean relative errors are presented in tables 1, 2. 2. Life expectancy and number of deaths in the Novosibirsk region. Figure 2 shows their graphs along with multivariate predictions, confidence intervals and mean relative errors are presented in tables 3, 4. Table 5 gives univariate forecasts of some other indicators of the Novosibirsk region. We think that the results of computations show that the proposed method is capable of finding non-trivial patterns in the data and can be used in practice., Вычислительные технологии, Выпуск 5 (25) 2020, Pages 80-90

Отмечена роль ведущих отечественных ученых В.И. Денисова и В.Г. Горского в становлении и развитии теории планирования эксперимента и прикладных статистических методов анализа данных. На основе математической теории планирования эксперимента исследовано влияние параметров воздушной среды рабочих помещений на интенсивность испарения опасных химических веществ с поверхности пролива. Создана математическая модель, описывающая этот процесс. Данные исследования необходимы для оценки профессионального риска на химических производствах, The article addresses the important problem of assessing the professional risk of workers in industries where the chemical factor is possible, as well as the role of the mathematical theory of experimental design in conducting of experimental research. The role of leading Russian scientists Denisov Vladimir Ivanovich and Gorsky Vladimir Grigoryevich in the establishment and development of experimental design theory and applied statistical data analysis methods is noted in the work. It is noted that in order to successfully solve scientific, industrial, and technological problems, modern research engineer must have competencies in the field of the theory of mathematical statistics, practical skills in planning an experiment, and methods for statistical processing of experimental data. The aim of the studies presented in this paper is to assess the influence of the air environment of the working room (temperature, humidity) on the rate of evaporation of a hazardous chemical from the spill. The experiment was carried out on a facility that allowed varying over a wide range the temperature and humidity. The experiment was carried out in accordance with the plan developed on the basis of the mathematical theory of experimental design. The obtained mathematical model allows estimating the level of air pollution by hazardous chemicals in the temperature and humidity range typical of workrooms. A comparison of the concentrations calculated according to the model with the permissible level of air pollution (MPC of the working zone air) will allow assessing the risk of inhalation exposure to hazardous chemicals on working personnel in local emergency situations. Conducted research is necessary to assess occupational risk in chemical industries, Вычислительные технологии, Выпуск 3 2020

Математические модели многих технических систем имеют вид интегрального уравнения Вольтерра I рода с разностным ядром. Для таких систем задача идентификации заключается в построении оценки для импульсной переходной функции системы по измеренным (с шумами) значениям входного и выходного сигналов и является некорректно поставленной. В недавней работе авторов предложен устойчивый алгоритм идентификации, использующий аппарат сглаживающих кубических сплайнов для вычисления первых производных входного и выходного сигналов. К сожалению, сглаживающие кубические сплайны неудовлетворительно фильтруют аномальные измерения. Поэтому предложен двухшаговый алгоритм идентификации, на первом шаге которого аномальные измерения удаляются с использованием пространственно-локального фильтра, а затем строятся сглаживающие сплайны, Volterra integral equation of the first kind often represents stationary dynamic systems. For such a model, the non-parametric identification problem reduces to the estimation of pulse transition characteristics (that is the kernel of integral equation) from the registered noise-contaminated values of input and output signals. To formulate stable solution for identification problem authors propose algorithm that estimates pulse transition characteristics by solving Volterra integral equation of the second kind and involving first derivatives of input and output signals application that corresponds to non-stable problem. Smoothing cubic splines employed in robust calculation of first derivatives allow finding a stable solution of identification problem even when input and output signals of system identified are essentially noise-contaminated. Unfortunately, measured values of input and output signals also contain anomalous measurements such as pulse noises, glitches, etc. Such measurements are poorly smoothable by splines that cause high levels of first derivatives errors and, conversely, significant pulse transition characteristics identification errors of dynamic system. For all the reasons aforementioned, in this paper authors present the new stable two-step identification algorithm in case of anomalous measurements. The first step of the algorithm is for non-linear local-spatial combined filtration procedure of input and output signals that helps to effectively remove anomalous measurements. At the second step, smoothing cubic splines are used to calculate stable first derivatives of previously filtered signals. An extensive computational experiment showed the effectiveness of the proposed algorithm, which allows solving the identification problem with acceptable accuracy in practice even at high intensity of anomalous measurements. The experimental results give reason to recommend this algorithm for solving practical problems of identifying stationary systems, the mathematical model of which is the Voltaire integral equation of the first kind with a difference kernel, Вычислительные технологии, Выпуск 3 2020

Рассматривается проблема оценки относительной активности мономеров на основе дифференциального уравнения сополимеризации. Обосновано включение в модель погрешности измерения входного признака в виде ошибки Берксона. Предложен алгоритм одновременного оценивания констант сополимеризации и дисперсий ошибок с помощью метода максимального правдоподобия. На примере сополимеризации виниловых эфиров произведено сравнение разных методов оценивания констант сополимеризации. Показано, что метод на основе симметричных уравнений дает некорректные результаты. Результаты оценивания с помощью предложенного алгоритма наиболее близки к оценкам, полученным по нелинейному методу наименьших квадратов, Purpose. The purpose of this paper is to study methods for estimating copolymerization reactivity ratios based on the differential composition equation. Methodology. Most estimation methods reduce the differential composition equation to a linear form. They are based on the least squares method and do not take into account the measurement error in the input variable. Therefore they lead to statistically incorrect results. When analyzing the problem on the basis of the error-in-variables model in the classical case, additional information is required to determine the magnitude of the errors in measuring the concentration of monomers in the mixture and in the copolymer. Inclusion of the measurement error in the input variable into the model as the Berkson error is more consistent with the actual conditions of the experiments. It allows simultaneous estimating both the reactivity ratios and the variances of measurement errors using the maximum likelihood method. Results. The algorithm have been developed for estimating reactivity ratios with no additional information. The empirical study of estimation methods has been carried out using the example of copolymerization of vinyl esters. Findings. It is shown that the method based on symmetric equations gives incorrect results. Estimation results using the proposed algorithm are closest to the estimates obtained by the nonlinear least squares method, Вычислительные технологии, Выпуск 3 2020

Представлены две адаптивные модификации сигма-точечного фильтра Калмана с рекуррентным оцениванием ковариационных матриц шумов системы и измерений, на основе которых выполняется процедура параметрической идентификации нелинейных непрерывно-дискретных систем. Применение процедуры адаптивной параметрической идентификации позволило вычислить с достаточной точностью оценки параметров нескольких моделей радиационного давления солнечного излучения. Полученные результаты повысили качество прогнозирования траектории движения навигационного спутника, Purpose. The paper considers the problem of estimation of unknown parameters for various models of solar radiation based on adaptive modifications of the unscented Kalman filter. The estimations of the obtained parameters are used both in solar radiation models and in construction of trajectory of a navigation satellite. Methodology. To solve the problem of parametric identification of stochastic nonlinear continuous-discrete systems, several adaptive modifications of the unscented Kalman filter are considered. The algorithms assume recurrent estimation of covariance matrices of system noise and measurements. The maximum likelihood method is used for parametric identification of stochastic nonlinear continuous-discrete systems. Adaptive modifications of the unscented Kalman filter are used in the construction of the identification criterion. Estimates of unknown parameters of various solar radiation models are found for the movement for the navigation satellite model as an example. The satellite orbital movement forecast is made. Finding and value. The application of the adaptive parametric identification procedure allows calculating the estimates for the parameters of several models of the solar radiation with sufficient accuracy. The obtained results lead to significant improvement of quality of the prediction for satellite trajectory, Вычислительные технологии, Выпуск 3 2020

Исследуется зондирование снежного покрова методом радарной интерферометрии. Предложена приближенная модель интерферометрического зондирования, основанная на методе малых возмущений. Поле обратного рассеяния рассматривается как когерентная сумма волн, рассеянных на неровностях границ раздела “воздух - снег” и “снег - почва”. Представлены результаты определения водного эквивалента снега с помощью радарной интерферометрии на ровной земной поверхности (равнина) и поверхности с уклонами рельефа (холмисто-гористая местность). Проведена оценка вклада рассеяния от поверхности снега в значения амплитуды и интерферометрической фазы. Выполнен анализ влияния уклонов рельефа на оценку параметров снежного покрова. Приведены результаты численных оценок. Показано, что для местности с уклоном рельефа около 45изменения в интерферометрической фазе относительно ровной поверхности достигают 40%. Однако если склоны сравнительно ровные (менее 10), эти изменения не превышают 10%, The main characteristics of the snow cover determining its impact on the environment are its thickness and the snow water equivalent (SWE). SWE assesses the water content in the snow cover. Radar interferometry is one of the methods for determining SWE. The paper presents the results of snow cover sensing by radar interferometry on both flat Earth’s surface and terrain with relief. A backscattering model taking into account backscattering from the snow surface is proposed in contrast to the existing methods. The backscattering field is considered as a coherent sum of waves scattered on the irregularities of the air - snow and snow - soil interfaces. These interfaces are statistically rough surfaces with random irregularities, whose heights are described by uncorrelated stationary random functions with their mean values, standard deviations, and correlation radii. It is assumed that the irregularities are small compared to the wavelength, their slopes are small, and the conditions for the applicability of the method of small perturbations are satisfied. It is also supposed that roughness does not affect the coherent field according to the Born approximation. The incident and scattered waves are assumed to follow Snell’s law. The coherent waves reflection and transmission coefficients are determined by Fresnel formulas for a flat interface. The contribution of backscattering from the snow surface to the values of the amplitude and interferometric phase is estimated using small perturbation method. It is shown that the relative error of interferometric phase determination due to the influence of the wave scattered by the air - snow boundary does not exceed 8% for the angles of incidence of 20-45and the density of snow 0.2-0.3 g/cm. The approximate relations show the linear dependence between the interferometric phase and SWE. The model is extended to the general case of backscattering from snow cover on the Earth’s surface with relief. The influence of terrain slopes on the interferometric phase is estimated. It is shown that for hilly terrain with slopes of about 45, the relative changes in the interferometric phase could reach 40%. However, if the slopes are relatively flat (less than 10), these changes do not exceed 10%., Вычислительные технологии, Выпуск 4 (25) 2020

Системы уравнений с запаздываниями широко применяются в различных областях современного математического моделирования. В ходе разработки структуры математической модели и идентификации ее параметров приходится многократно решать задачу Коши для подобных систем. В случае высокой размерности системы, а также при условии жесткости задачи численное решение уравнений с запаздываниями может требовать значительных вычислительных и временных затрат. Таким образом, разработка и реализация эффективных алгоритмов численного решения различных классов уравнений с запаздывающими аргументами является актуальной задачей. В настоящей статье представлена модифицированная версия программного комплекса DIFSUBDEL, в которой реализованы методы численного решения дифференциальных уравнений с запаздываниями на основе линейных многошаговых методов. Переработанная версия разработана с применением принципов структурного программирования и является значительно более удобной в эксплуатации, чем исходная, а также обладает свойством потокобезопасности, что позволяет использовать комплекс в качестве блока в системах, основанных на технологиях параллельного программирования с общей памятью. Был проведен сравнительный анализ производительности переработанной системы DIFSUBDEL c другими существующими программными реализациями численных методов решения дифференциальных уравнений с запаздыванием и показана ее эффективность., The systems of delay differential equation are widely used in modern mathematical modeling. The process of mathematical model development and identification requires the repeated solution of initial value problems for such systems. The numerical solution of delay differential equations may be computationally expensive, especially when the problem is stiff and high-dimensional. Therefore, it is important to develop and implement the efficient algorithms for the numerical solution of different classes of delay differential equations. In this paper, a new implementation of DIFSUBDEL program package for the numerical solution of delay differential equations based on linear multistep methods is discussed. The modified version is based on structured programming principles to make the program thread safe and user-friendly. The modified program performance is compared with the existing implementations of numerical methods for the solution of delay differential equations., ВЫЧИСЛИТЕЛЬНЫЕ МЕТОДЫ И ПРОГРАММИРОВАНИЕ: НОВЫЕ ВЫЧИСЛИТЕЛЬНЫЕ ТЕХНОЛОГИИ, Выпуск 1 2020

Проведено сравнение качества решений модельного уравнения второго порядка с малым параметром, полученных по трем различным разностным схемам на специальных адаптивных сетках, явно задаваемых координатным преобразованием, а также на равномерных сетках в новых переменных, соответствующих этому преобразованию. Исследуются схемы второго порядка точности с диагональным преобладанием и без него и простейшая противопотоковая схема. На основе оценок погрешностей сделаны прогнозы относительно свойств решений, подтвержденные анализом и численными экспериментами. Показано, что схема второго порядка аппроксимации с диагональным преобладанием сходится равномерно по малому параметру со вторым порядком лишь в частном случае, когда коэффициент при старшей производной мал только в слое; если же он мал также и вне слоя, порядок сходимости первый. Установлено также, что схема без диагонального преобладания имеет существенно более качественные решения без осцилляций в новых переменных на равномерной сетке, чем в соответствующих им исходных физических координатах. В противоположность ей схемы с диагональным преобладанием не чувствительны к выбору системы координат., The paper compares solution quality to some model second- order equation with a small parameter obtained through three different schemes both on special adaptive grids specified explicitly by coordinate transformations eliminating layers and on uniform grids in a new coordinate related to the transformations. The schemes up to second order in physical and transformation variables both with a diagonal and not diagonal dominance and the simplest counter-flow scheme are analyzed. Predictions of a solution behavior based on estimates of solution errors are described, which are confirmed by numerical experiments and proofs. It is established, in particular, that the scheme of the second order with a diagonal dominance converges uniformly if the coefficient before the second derivative is small at the points of the boundary layer only. It was also demonstrated for the schemes without a diagonal dominance, mach better solutions without oscillations are obtained on uniform grids in new variables than on corresponding adaptive grids in the original physical coordinates., Вычислительные технологии, Выпуск 5 (25) 2020, Pages 66-79

Рассмотрена задача планирования эксперимента в условиях появления ошибок в объясняющих переменных. Сформулировано и доказано утверждение о способе вычисления элементов информационной матрицы Фишера с использованием обобщенного лямбда-распределения, доказано следствие о способе вычисления функции эффективности плана эксперимента. Сравнение результатов вычисления функции эффективности с использованием выведенного в следствии соотношения и с помощью известного соотношения для нормального распределения ошибок показало, что результаты совпадают. Построены оптимальные планы эксперимента для различных распределений случайных компонент., The problem of experimental design under conditions of errors in the explanatory variables is considered. The proposition of the method for calculating the Fisher information matrix elements using the Generalized Lambda-distribution is formulated and proved, the consequence of the method for calculating the efficiency function of the experimental design is proved. This method of calculating the Fisher information matrix takes into account the heterogeneity of the errors in random distribution throughout the planning area. In this paper, studies of the synthesis of optimal experimental designs using proven proposition and consequence under various conditions of computational experiments are presented. The results of calculating the efficiency function using the obtained relation and using the known relation for the normal distribution of errors are compared, it is found that the results coincide. Optimal experimental designs are constructed for various distributions of random components. The results of the synthesis of optimal experimental design showed that when function of efficiency is constant throughout the planning area then the optimal experimental design is equilibrium plan. When there are differences in the values of the efficiency function in the planning area, the optimal plan ceases to be equilibrium, Вычислительные технологии, Выпуск 3 2020

Рассмотрены вопросы автоматизированного мониторинга состояния сетчатых ограждающих конструкций, которые используются на предприятиях, производящих морские биоресурсы. Предложен алгоритм выделения порывов сетчатых ограждений в подводных условиях с применением методов компьютерного зрения, который реализован в виде комплекса программ на языке Python. Приведены результаты работы программного комплекса. Показано, что методы компьютерного зрения эффективно справляются с определением целостности ячеек сети на слабои среднезашумленных изображениях. Для работы в более сложных оптических условиях в состав программного комплекса предложено включить нейросетевой модуль., Purpose. The paper addresses image processing algorithms for the computer vision system of an autonomous uninhabited underwater vehicle, which automatically monitors the state of the mesh fence and thereby exclude the presence of a person in an aggressive underwater environment. Methodology. The MultiScale Retinex with Color Restoration algorithm and the Otsu method were implemented using the Python programming language to preprocess and filter the image. Methods from OpenCV computer vision library were used to detect damage to the mesh fence. Results. An algorithm is proposed for highlighting the impulses of mesh fencing in underwater conditions using computer vision methods implemented by the Python software. The software implementation results are provided. It is shown that computer vision methods effectively cope with determining the integrity of network cells in weakly and medium-noisy images. To work in more complex optical conditions, it is proposed to include a neural network module in the software package. Findings. The analysis of the results of the software package showed that it successfully copes with the classification of network cells in clean images. However, the transformations carried out at the pre-processing stage are not enough to complete noise elimination. In this regard, this study will continue to improve and expand the functionality of the software package. The result of the study will be a software package with a neural network module for full filtering of the external background and efficient detection of the mesh fence problem areas., №24 (2019)

Предложена математическая модель задачи о движении двумерного турбулентного потока жидкости в напорном канале с волнистым дном. Математическая модель включает уравнения Рейнольдса, уравнения переноса кинетической энергии и диссипации турбулентности, приведенные к квазигидродинамическому виду. Предложен алгоритм решения задачи с помощью метода контрольных объемов и метода конечных элементов. Численно решена задача о движении турбулентного потока над неподвижными пологими песчаными дюнами. Выполнено сравнение полученных расчетов с экспериментальными данными., Purpose. The aim of the paper is the development of mathematical models describing a turbulent river flow along gently sloping dunes and allowing estimation of the contribution of gently sloping dunes on the flow hydraulic resistance. Methodology. A quasi-hydrodynamic form of the classical RANS equations are used for describing the hydrodynamic flow. The standard k model is used for the turbulence viscosity while the equations have been transformed to the quasi-hydrodynamic form. A wall functions method is used for describing the flow near solid channel wall. Results. A new mathematical model for the problem of turbulent flow in a pressure channel with low-angle dunes is proposed. An algorithm for solving the problem is proposed. It is based on the control volume method and the finite element method. The problem of the turbulent flow over 6 fixed low-angle sand dunes is solved numerically. Numerical solutions are obtained with four different wall functions. A comparative analysis of the obtained solutions with the experimental data is carried out. Findings. It is shown that the proposed mathematical model describes the turbulent flow over low-angle dunes qualitatively and quantitatively. The solution obtained with the Volkov wall function provides the best agreement with the experiment. It is found out that the bed shear stress obtained in the near-wall computational cell by the wall functions method does not qualitatively agree with the experimental data for all considered wall functions. At the same time, the shear stress obtained in the next calculation cell agrees with the experimental data qualitatively and quantitatively. The average relative error of the shear stress obtained with the Volkov wall function is 6.84., №24 (2019)

Описаны особенности реализации, структура и возможности информационных веб-систем, созданных в Институте вулканологии и сейсмологии ДВО РАН, цель которых обеспечить доступ к большому объему распределенных вулканологических данных для комплексного использования в научных исследованиях. Информационная система VOKKIA предназначена для интеграции и систематизации данных по наземным и подводным вулканам Курило-Камчатского региона и их извержениям, KVERT для сбора и интеграции данных оперативного мониторинга активности вулканов. Реализованные в информационных системах сервисы поиска и визуализации данных помогают обнаруживать взаимосвязи, закономерности и тенденции изменения вулканогенных процессов во времени., A large amount of unique scientific data has been collected in the Institute of Volcanology and Seismology (IVS) FEB RAS over the past years of investigations of the Kamchatka and the Kurile Island Arc volcanoes. The distributed nature of information storage makes it difficult to search and effectively use data in scientific research. Actual tasks include the integration of data into thematic information resources, organization of data access on the Internet, as well as the designing of tools for their comprehensive analysis. VOKKIA (Volcanoes of Kurile-Kamchatka Island Arc) and KVERT (Kamchatkan Volcanic Eruption Response Team) information web-systems have been developed in the IVS FEB RAS to solve these tasks. VOKKIA is designed to integrate and systematize the heterogeneous scientific data for the terrestrial volcanoes of Kamchatka, the Kurile Islands and submarine volcanoes of the surrounding seas including data on historical eruptions of active volcanoes. The KVERT system contains brief information about active volcanoes of Kamchatka and the Nothern Kuriles including their hazard. It provides collection and storage of operational data of visual, video, and satellite monitoring of volcanoes as well as automated preparation and sending KVERT releases on volcanic activity. The paper describes the development technology, structure and content of VOKKIA and KVERT. Besides, it describes data search and visualization services and statistical data analysis. The created services allow detecting the relationship, patterns and trends in volcanic processes over time., №24 (2019)

Одни из наиболее важных вычислительных задач разработка и адаптация итерационных методов для решения сверхбольших разреженных систем алгебраических уравнений. К таким вычислительным задачам приводит задача итерационной параллельной реконструкции трехмерных изображений промышленных изделий. Важно, что итерационные методы решения вычислительных задач большой размерности реализуются на параллельных структурах намного эффективнее, чем прямые методы их решения. В этой работе описан синхронный параллельный алгоритм, основанный на использовании системы MPI для решения задачи реконструкции трехмерных изображений промышленных изделий., Purpose. Currently, one of the most important tasks is the development and adaptation of iterative methods for solving ultra-large sparse systems of algebraic equations. Such computational problems are caused by the iterative parallel reconstruction of three-dimensional images of industrial products. It is important that iterative methods for solving computational problems of large size are implemented on parallel structures much more efficiently than direct methods for solving them. This paper describes a synchronous parallel algorithm based on the MPI system for solving the problem of reconstruction of three-dimensional images of industrial products. Methodology. It is important that iterative methods for solving computational problems of larger dimensionality on parallel structures are implemented more efficiently than the direct ones. Most algorithms based on direct solving methods have a significant hereditary sequential structure and require a large number of processors interactions which cannot be executed in parallel mode. Iterative methods, for the most part, require a significantly smaller number of interactions of this type and are relatively easily mapped onto parallel computational structures. Equally important, in most cases parallel implementations of classical iterative methods are more effective in terms of computational speed. The parallel execution of the algorithm is based on the distribution of the process in some way between various groups of processors. Depending on the interaction method between local processors, two different types of parallel iterative algorithms execution are distinguished: synchronous and asynchronous. In the former case, it is assumed that the processors complete the calculations and exchange all the necessary results before the start of a new iteration. The main disadvantage of synchronous parallel algorithms is that they require synchronization of iterations. This is a very difficult task, especially with large number of processors. In addition, the overall calculation speed is limited by the speed of the slowest processor. At the same time, faster processors spend most of their time in the waiting mode. But, nevertheless, the implementation of these parallel algorithms can be effectively achieved using the MPI standard. Findings. Synchronous parallel computing algorithms and program codes for threedimensional tomographic reconstruction in a conical beam were developed. Program code debugging and numerical calculations were performed on a hybrid cluster based on the OpenPOWER architecture using the MPI system. For designing a parallel threedimensional tomographic reconstruction, a voxel form of parallelism was used. Originality. Implemented parallel iterative technology of three-dimensional images reconstruction has undeniable advantages over traditional sequential iterative tomographic reconstruction. It allows reducing the time of tomographic reconstruction as many as tens of times, provides the ability to reconstruct products with sizes of 5123 to 10243 voxels with simultaneous storage of the submatrix node of the projection matrix in RAM, which eliminates the need for recalculation of matrix coefficients for each new iteration., №24 (2019)

Представлены результаты исследований, связанных с автоматическим формированием архитектур нейронных сетей, состоящих из набора модулей. Реализован алгоритмический подход, основанный на формировании матриц активных модулей. Предложены способы процедурной генерации архитектур нейронных сетей для решения задач классификации. Дается описание процесса автоматического формирования архитектуры PathNet, реализованной на основе новых подходов, а также рассматриваются примеры генерации трех новых архитектур глубоких нейронных сетей (3DNN, GraphNet и BraidNet). Архитектура BraidNet включает в себя построение графа связей сети на основе теории кос. Исследование на примере задачи классификации изображений MNIST показало применимость всех четырех предложенных нейронных сетей к распознаванию образов., There are various approaches to the algorithmic specification of the network structure in the deep learning problems, which are successfully used in applications. These methods can be generalized by the concept of procedural generation of neural network architectures. Methodology. In the work, we use binary matrix filters. The filters are obtained with the help of the Hadamard product. Such filters define active network modules, thereby changing the way information is transmitted between layers. To build various architectures, the theory of braids is used in the work. The article reproduces the wellknown PathNet architecture. Examples of generating three new deep neural network architectures (3DNN, GraphNet, and BraidNet) are examined. Findings. The paper shows how the procedural generation of neural network architectures allows avoiding manually setting the network structure and automatically forming it. The use of matrix filters simplifies the process of generating network architecture due to a large number of possible combinations of modules and connections between them. Using the MNIST classification problem as an example, it is shown how the architectures presented in the article solve real-world pattern recognition problems. The results of application of neural networks indicate their diminishing tendency to retraining due to the subsequent convergence and the presence of stochastic dynamics in the learning process. Originality/value. Learning methods with dynamic adaptive changes in the network architecture allows achieving satisfactory accuracy faster and should also be less prone to retraining. The BraidNet algorithm presented in the article is applicable for ICT SB RAS, 2019 a convenient brief record of the structure of a neural network in genetic algorithms. Such features make BraidNet a promising algorithm for further application and research in complex problems of pattern recognition, including using neuroevolutionary approaches., №24 (2019)