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The paper investigates the frequency response of the mutual coupling between multi-wire overhead lines with length comparable to the wavelengths of the highest power frequency harmonics. Deenergized overhead transmission lines are influenced by electromagnetic interference from neighboring in-service overhead lines, railway traction lines, as well as other extended conductors with currents. The voltages induced on the overhead lines are dangerous to life or health of maintenance personnel. The values of the induced voltages can be determined either by direct measurement or by calculation. The paper presents the results of experimental studies of double-circuit overhead lines of the Kola energy system. It has been shown that the frequency spectrum of the induced voltage is different from the spectrum of the source of interference, and this difference has a resonant nature. The amplitude of the voltage induced by higher harmonics can be comparable with the amplitude of the voltage induced by the power frequency. The similar results have been received in studies of influence of the AC railway traction line on adjacent overhead transmission lines. ATP-EMTP numerical analysis has been performed to receive the frequency characteristics that explain the experimental results. Preliminary estimates indicate that the cause of the phenomenon is most likely due to the resonant nature of the frequency response of the mutual coupling. The resonant nature is characterized by the interrelation of the length of overhead lines and the wavelength of the higher harmonics. A wave resonance of currents and voltages that appears in the lines lead to the "magnification" of the individual induced voltage harmonics falling in the maxima of the frequency characteristics of mutual coupling.

Представлен метод балансировки нагрузки вычислений с использованием кривых Гильберта применительно к параллельному алгоритму решения уравнений мелкой воды. Рассматриваемая система уравнений мелкой воды возникает в сигма-модели общей циркуляции океана INMOM (Institute of Numerical Mathematics Ocean Model) при разрешении гравитационных волн и является одним из основных блоков модели. Из-за наличия в океанах островов и берегов балансировка нагрузки вычислений на процессоры является особенно актуальной задачей. В качестве одного из таких методов был выбран метод балансировки нагрузки вычислений с использованием кривых Гильберта. Продемонстрирована большая эффективность этого метода по сравнению с равномерным разбиением без балансировки нагрузки и показано, что этот метод служит хорошей альтернативой библиотеке разбиений METIS. Оптимальность реализованного разбиения для мелкой воды точно соответствует оптимальности и для трехмерной сигма-модели INMOM в силу одинакового количества вертикальных уровней во всей расчетной области., This paper presents a method of load balancing using Hilbert space-filling curves applied to a parallel algorithm for solving shallow water equations. We consider the system of shallow water equations in the form presented in the ocean general circulation sigma-model INMOM (Institute of Numerical Mathematics Ocean Model). This system of equations is one of the basic blocks of the model. Due to land points in the computational grid, the load balancing is an especially urgent task. The method of load balancing using Hilbert space-filling curves is chosen as one of such methods. The paper demonstrates the greater efficiency of this method in comparison with the uniform partitioning without load balancing. It is shown that this method is a good alternative to the METIS standard library. Moreover, the optimality of the implemented partition for the shallow water equations exactly corresponds to the optimality for the INMOM three-dimensional sigma-model due to the same number of vertical levels in the entire computational domain., ВЫЧИСЛИТЕЛЬНЫЕ МЕТОДЫ И ПРОГРАММИРОВАНИЕ: НОВЫЕ ВЫЧИСЛИТЕЛЬНЫЕ ТЕХНОЛОГИИ, Выпуск 1 2019

This paper is dedicated to space-temporal radiation analysis of ultra-wideband (UWB) tapered slot antennas (TSA). This antenna type has gained its popularity owing to remarkable UWB performance, low-profile geometry, and essential integration with active RF modules on a common substrate. When TSA is considered as a radiator of UWB pulses, the traditional radiation patterns are no longer fully satisfactory for estimation of its radiation performance. Thus, an antenna should be described as a linear circuit with its pulse response or complex transfer function.Currently, a very few papers reveal such performance features of TSA. Moreover, usually, an antenna model is based on the full-wave CAD model (FDTD, FIT) and, thus, its straightforward evaluation is quite time consuming. However in previous works it was shown that radiation patterns of TSA could be calculated using an approximate two-step approach. Crucial ideas of this method are based on two core stages:aperture field distribution evaluation;radiation performance evaluation using a model of an elementary magnetic radiator in the neighborhood with semi-infinite conducting plane.The first step concerns the full-wave solution of two-dimensional problem on the eigenmode of a slot-line. Thus, unlike a three-dimensional full-wave CAD model, the two-step model enables to evaluate antenna performance in considerably shorter time retaining a high accuracy of results.A mathematical model of the improved two-step approach is comprehensively described in this paper, with special attention being paid to aperture field distribution. A developed calculation algorithm was successfully verified on benchmark models. Calculated results are compared with those of obtained via full-wave simulation. In all cases both methods have shown results of high identity.

Рассматривается применение плоских отсеков как модулей моделей инструментальных поверхностей. Выполнен морфологический выбор элементарных представителей, образуемых действием оператора параллельного переноса, результаты которого визуализированы, математически описаны и поддержаны примером проектного использования. Представленный комплекс геометрических модулей и их математических описаний предлагается к многоотраслевому использованию в системах автоматизированного проектирования с инструментальной составляющей, ориентированных на обслуживание формообразующих машиностроительных и других технологий. The application of the flat compartments as modules of the models of tool surfaces for machine-building and other purpose in industries with the shape-generating technologies has been considered. The main purpose of the study is allocation and systematization the basic typical elementary flat compartments of tool surfaces, the use of which by means of the operator of parallel transport allows to reproduce virtually any of them. The application of the theory of multi-parameter affine mappings of the space and some of the results of our research in the direction of its applied unification have been discussed in this paper. A systematic morphological selection of elementary flat compartments of tool surfaces formed by the action of the operator of parallel transport, the results of which are visualized and mathematically described, was made in this paper. The methodical example of the practical application of development is being shown. The presented complex of geometric modules and their mathematical descriptions is being offered for a diversified use in computer-aided design to development with tool component, service-oriented to shape-generating machine-building and other technologies. The proposed system of flat compartments formed by the action of the operator of parallel transport allows to perform modeling of tool production objects of any complexity, from a flat in planning application to a complex profile shape-generating edge in manufacture of turbine blade.

The wide spread of various radio systems with phase shift keying, including multi-position (MPSK), is due to their high noise immunity and ease of construction of the transmitting and receiving parts of the equipment. In real equipment, additional differential (relative) encoding is used when implementing transmitter and receiver circuits and, accordingly, DMPSK signals are used. One of the ways to receive such signals is to use an autocorrelation demodulator built on a quadrature scheme. The paper studies the noise immunity of an autocorrelation demodulator of signals with differential phase shift keying in the presence of Gaussian noise, Rayleigh fades and harmonic interference in the radio channel. The statistical parameters of signals and interference in the inphase and quadrature channels of the autocorrelation demodulator are determined. For M = 2 and 4, analytical formulas are obtained for the probability of a symbolic error, conditional on the random phase of harmonic. It is verified that the formula at M = 2 without harmonic interference reduces to an expression known from the literature. The values of the unconditional probabilities of symbolic errors are obtained by numerical averaging. It is shown that at a low level of harmonic interference, Rayleigh fading has a dominant effect. With a large level of interference, the additional energy loss can be several decibels, and at M = 4 these losses are significantly greater than at M = 2.

We consider an application of the Message Passing Interface (MPI) technology for parallelization of the program code which solves equation of the linear elasticity theory. The solution of this equation describes the propagation of elastic waves in demormable rigid bodies. The solution of such direct problem of seismic wave propagation is of interest in seismics and geophysics. Our implementation of solver uses grid-characteristic method to make simulations. We consider technique to reduce time of communication between MPI processes during the simulation. This is important when it is necessary to conduct modeling in complex problem formulations, and still maintain the high level of parallelism effectiveness, even when thousands of processes are used. A solution of the problem of effective communication is extremely important when several computational grids with arbirtrary geometry of contacts between them are used in the calculation. The complexity of this task increases if an independent distribution of the grid nodes between processes is allowed. In this paper, a generalized approach is developed for processing contact conditions in terms of nodes reinterpolation from a given section of one grid to a certain area of the second grid. An efficient way of parallelization and establishing effective interprocess communications is proposed. For provided example problems we provide wave fileds and seismograms for both 2D and 3D formulations. It is shown that the algorithm can be realized both on Cartesian and on structured (curvilinear) computational grids. The considered statements demonstrate the possibility of carrying out calculations taking into account the surface topographies and curvilinear geometry of curvilinear contacts between the geological layers. Application of curvilinear grids allows to obtain more accurate results than when calculating only using Cartesian grids. The resulting parallelization efficiency is almost 100% up to 4096 processes (we used 128 processes as a basis to find efficiency). With number of processes larger than 4096, an expected gradual decrease in efficiency is observed. The rate of decline is not great, so at 16384 processes the parallelization efficiency remains at 80%.

This paper is concerned with ultrafilters and maximal linked systems of widely understood measurable spaces (nonempty sets with π-systems of its subsets are meant). The sets of ultrafilters and maximal linked systems are transformed to bitopological spaces by applying constructions that (in idea) meet the Wallman and Stone schemes. The focus is on ultrafilter space with topology of Wallman type. Conditions on the initial π-system for which the given space is supercompact are specified. Concrete classes of (widely understood) measurable spaces are listed for which the above-mentioned conditions are realized. Special attention is also given to one abstract problem of attainability under conditions when the choice of a concrete solution may have the following uncertainty: the set defining constraints can be an arbitrary element of a given nonempty family. The question of the existence of universally realized (in limit) elements in the space of values of the goal operator in our problem is considered. To obtain sufficient solutions, the supercompactness property of the ultrafilter space for special measurable structure is used; this structure is sufficient (under corresponding suppositions) for realization of all variants of constraints on the choice of a usual solution (control). © 2019 А. Г. Ченцов. Russian Foundation for Basic Research, RFBR: 18–01–00410 Funding. The research was funded by the Russian Foundation for Basic Research, project number 18–01–00410.

The sequences are an important part of the cryptography and analysis of their properties is of great interest. In this paper, the following characteristics of combined generator are analyzed: period of output sequences and the distribution of elements in the output sequences over finite field.

При исследовании механизмов генерации электромагнитного излучения, наблюдаемого в лабораторных экспериментах по взаимодействию релятивистских электронных пучков с плазмой, возникает проблема определения структуры, спектральных характеристик и мощности излучаемых электромагнитных волн. Так, при численном решении уравнений Максвелла возникает потребность в разработке точных, эффективных и надежных методов реализации открытых граничных условий, позволяющих электромагнитным волнам выходить из расчетной области без отражения. Распространение волн в вакууме описывается линейными уравнениям Максвелла, и, следовательно, можно легко найти частоты и амплитуды проходящих и отраженных волн с помощью анализа Фурье и определить их структуру. Для изучения этого вопроса достаточно рассмотреть задачу в двумерном случае. Целью настоящей работы является разработка методики определения направлений и амплитуд всех электромагнитных волн в вакууме, которые находятся в вычислительной области в определенный момент времени., In the study of generation mechanisms of electromagnetic radiation observed in laboratory experiments on the interaction of relativistic electron beams with plasma, the problem of determining the structure, spectral characteristics, and power of the emitted electromagnetic waves arises. So, in the numerical solution of Maxwell's equations, there is a need to develop accurate, efficient, and reliable methods for implementing open boundary conditions that allow electromagnetic waves to exit the computational domain without reflection. The linear Maxwell's equations describe the propagation of electromagnetic waves in vacuum and, therefore, it ispossible to easily find the frequencies and amplitudes of passing and reflected waves using the Fourier analysis and to determine their structure. In order to study this question, it is sufficient to consider the problem in the two-dimensional case. The aim of this paper is to develop a method of determining the directions and amplitudes of all electromagnetic waves in a vacuum that are in the computational domain at a certain instant of time., ВЫЧИСЛИТЕЛЬНЫЕ МЕТОДЫ И ПРОГРАММИРОВАНИЕ: НОВЫЕ ВЫЧИСЛИТЕЛЬНЫЕ ТЕХНОЛОГИИ, Выпуск 1 2019

The approach to classification of point sets based on dimensionality reduction and splitting space into regular grid is proposed. In paper we introduce concept of hypercube as the representation of point sets. The approach to reduce dimensionality based on point set signature as characteristic of spatial distribution of the set is proposed. The method described provides to exclude set of coordinate axis from classification with the increasing of classification precision and decreasing of computational cost. The experiments done show efficiency of our approach for multi-dimensional data. The advantage of proposed approach is fast determination of redundant coordinate axis for arbitrary set of input classes. Figs.: 1. Refs.: 17.Keywords: hypercube; regular grid; signature; point set; set spatial distribution; classification., В работе предлагается подход к решению задачи классификации точечных множеств на основе снижения размерности данных и разбиения пространства на регулярную сетку. Вводится понятие гиперкуба как способ представления точечных множеств. Предложен подход к снижению размерности на основе сигнатуры точечного множества как характеристики пространственного распределения множества. Разработанный метод даёт возможность исключить из дальнейшей классификации множество координатных осей при повышении точности классификации и уменьшении количества необходимых вычислений. Проведённые эксперименты показали работоспособность подхода на данных больших размерностей. Преимуществом предложенного подхода является быстрое определение избыточных координатных осей для произвольного набора исходных классов. Ил.: 1. Библиогр.: 17.Ключевые слова: гиперкуб; регулярная сетка; сигнатура; точечное множество; пространственное распределение множества; классификация., Запропоновано підхід до розв’язання задачі класифікації точкових множин на основі зниження розмірності даних і розбиття простору на регулярну сітку. Вводиться поняття гіперкубу як способу представлення точкових множин. Запропоновано підхід до зниження розмірності на основі сигнатурі точкової множини. Метод, що розроблено дозволяє виключити з подальшої класифікації множину координатних осей при підвищенні точності класифікації і зниженні кількості необхідних обчислень. Проведені експерименти показали придатність підходу на даних великих розмірностей. Перевагою підходу є швидке визначення надлишкових координатних осей для довільного набору вихідних класів. Іл.: 1. Бібліогр.: 17 назв.Ключові слова: гіперкуб; регулярна сітка; сигнатура; точкова множина; дані великих розмірностей; класифікація.

The article is devoted to the analysis of the topology of cellular communication networks using new methods of fractal geometry. In this paper is given the numerical modelling of the fractal dimension of the base stations of the Kurmanzhan–Datka micro-district of city Osh. It is shown that for effective analysis of cellular network properties used GIS system. The fractal dimension of the service area of the base stations of the above-mentioned district of Osh is investigated and determined., {"references":["Abdyrayeva, N. R. (2016). Analysis of existing base stations of Osh city with application of GIS technologies. Science. Education. Equipment, (1). 10-16.","Evdokimov, Yu. K., & Shakhturin, D. V. (2007). Fractal character of the topology of complex networks. Proceedings IV Intern. Conf. \"Methods and means of control of technological processes\". Saransk: Publishing house of the Mordovian University, 244-251.","Evdokimov, Yu. K., Potapov, A. A., & Shakhturin, D. V. (2008). Fractal modeling of message delays in large networks. The nonlinear world, 6 (8), 42-50."]}

The attainability problem with asymptotic constraints is considered. Such constraints can arise under weakening of constraints that are standard in control theory: phase constraints, boundary and intermediate conditions; trajectories of a system must satisfy these constraints. But asymptotic constraints can arise from the beginning as a characterization of trends in the implementation of desired behavior. For example, one can speak of implementation of powerful control impulses with vanishingly small duration. In this case, it is hard to tell whether any standard constraints are weakened. So, we have a set of complicating conditions with each of which we can juxtapose some analog of the attainability domain in control theory and (more precisely) the image of a subset of the usual solution space under the action of a given operator. In this paper, we investigate questions concerning the structure of an attraction set arising as an analog of the attainability domain. The investigation scheme is based on the application of a special way of extending solution space which admits a natural analogy with Wallman extension used in general topology. Then it is natural to suppose that the space of usual solutions is endowed with a topology (usually, it is a T1-space that is explored in this case). In this connection, questions concerning the replacement of sets forming asymptotic constraints by closures and interiors are addressed. Partially, questions associated with representation of the interior of the set of admissible generalized elements that form an auxiliary attraction set are discussed. © 2018 Udmurt State University. All rights reserved.

Гоббс считал, что естественное состояние это состояние войны, поскольку оно определяется фундаментальным и обобщенным недоверием. Выход из естественного состояния и конфликтов, которые оно неизбежно влечет, предполагает установление доверия. Однако обсуждение «доверия» в философии чаще всего фокусируется либо на изолированных диадах индивидов, доверяющих друг другу, либо на доверии в больших безликих институтах. Задача данной статьи заполнить пробел между этими двумя крайностями путем анализа «топологии сообществ доверия». Такие сообщества можно лучше всего представить как взаимосвязанные диадические отношения, которые приближены к идеалу поскольку они симметричны, рефлексивны и транзитивны. Немногие сообщества доверия соответствуют этому описанию, и те, что приближаются к нему, это, как правило, небольшие сообщества (от 3 до 15 индивидов). Именно в таких сообществах доверия возможно появление различных важных рациональных, познавательных, культурных благ и душевного спокойствия. Однако в сообществах доверия становятся возможными также многие сомнительные феномены. Сообщества могут изолироваться от окружающего общества, и тем самым стать источником недоверия со стороны окружения. Они могут вынудить своих членов отказаться от общественных благ в пользу родовых или частных благ. Этими недостатками сообщества доверия обязаны тем же самым механизмам, которые придают им положительную, рациональную, эпистемическую, культурную и психическую ценность, поэтому последствия работы этих механизмов можно только смягчить, но не исключить целиком.Hobbes emphasized that the state of nature is a state of war because it is characterized by a fundamental and generalized distrust. Exiting the state of nature and the conflicts it inevitably fosters is therefore a matter of establishing trust. Extant discussions of trust in the philosophical literature, however, focus either on isolated dyads of trusting individuals or trust in large, faceless institutions. In this paper, I begin to fill the gap between these extremes by analyzing what I call the topology of communities of trust. Such communities are best understood in terms of interlocking dyadic relationships that approximate the ideal of being symmetric, Euclidean, reflexive, and transitive. Few communities of trust live up to this demanding ideal, and those that do tend to be small (between three and fifteen individuals). Nevertheless, such communities of trust serve as the conditions for the possibility of various important prudential epistemic, cultural, and mental health goods. However, communities of trust also make various problematic phenomena possible. They can become insular and walled-off from the surrounding community, leading to a distrust of out-groups. They can lead their members to abandon public goods for tribal or parochial goods. These drawbacks of communities of trust arise from some of the same mechanisms that give them positive prudential, epistemic, cultural, and mental health value, and so can, at most, be mitigated, not eliminated.

Purpose. The models of electrical machines in the phase coordinates, the universal algorithm for the simulation of separate elements in a d-q coordinates system and in a phase-coordinates system are proposed. Methodology. Computer methods of investigation of transients in electrical systems are based on a compilation of systems of differential equations and their numerical integration solution methods. To solve differential equations an implicit method of numerical integration was chosen. Because it provides to complete structural simulation possibility: firstly developing models of separate elements and then forming a model of the complex system. For the mathematical simulation of electromagnetic transients in the elements of the electrical systems has been accepted the implicit Euler-Cauchy method, because it provides a higher precision and stability of the computing processes. Results. In developing the model elements identified two groups of elements: - Static elements and electrical machines in the d-q coordinates; - Rotating electrical machines in phase coordinates. As an example, the paper provides a model of synchronous and asynchronous electric machines in the d-q coordinates system and the phase coordinate system. The generalization algorithm and the unified notation form of equations of elements of an electrical system are obtained. It provides the possibility of using structural methods to develop a mathematical model of power systems under transient conditions. Practical value. In addition, the using of a computer model allows to implement multivariant calculations for research and study of factors affecting the quantitative characteristics of the transients., В статье рассматриваются методы математического моделирования элементов электрических систем, которые основаны на составлении систем дифференциальных уравнений и их решении методами численного интегрирования. Представлены дискретные уравнения электрических машин в системе координат d-q-0 и в системе фазных координат. Предложен алгоритм моделирования отдельных элементов электрических систем для разработки математической модели систем электроснабжения в переходных режимах., У статті розглядаються методи математичного моделювання елементів електричних систем, що засновані на складанні систем диференціальних рівнянь та їх розв'язанні методами чисельного інтегрування. Представлені дискретні рівняння електричних машин в системі координат d-q-0 і в системі фазних координат. Запропоновано алгоритм моделювання окремих елементів електричних систем для розробки математичної моделі систем електропостачання в перехідних режимах.

В работе предлагается математическая модель изображения отпечатка пальца на основе топологических векторов для линий, которая сохраняется в шаблоне изображения. Шаблоны содержат наборы признаков, по которым выполняется идентификация изображений. This paper presents a mathematical model of fingerprint based on the topological vectors for lines. The topological vectors and the list of minutiae are stored in the template. Templates are used to identify the fingerprint.