Математическое моделирование и программирование
Уважаемые коллеги! Мы рады приветствовать вас на нашем сайте! Серия «Математическое моделирование и программирование» Вестника ЮУрГУ была создана в 2008 году и в настоящее время представлена четырьмя выпусками в год. Основной целью редакционная коллегия и редакционный совет серии «Математическое моделирование и программирование» считают пропаганду исследований в области математического моделирования в естественных, технических и экономических науках. Приоритетное право на публикацию имеют: результаты качественных исследований математических моделей, выявляющие какие-либо неочевидные их свойства, результаты численных исследований, содержащие разработки новых вычислительных алгоритмов применительно к математическим моделям, комплексы программ, созданные для постановки вычислительных экспериментов. Эти результаты могут быть представлены в форме как обзорных, так и оригинальных статей, а также (для молодых ученых, магистрантов и аспирантов) в форме кратких сообщений. Кроме того, предусмотрены рубрики «Математическая деятельность» и «Персоналии». Приглашаем к сотрудничеству всех авторов, разделяющих цели и задачи «Вестника Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование». Редакционная коллегия, редакционный совет
FAST X-RAY SUM CALCULATION ALGORITHM FOR COMPUTED TOMOGRAPHY PROBLEM
In iterative methods of computed tomography, each iteration requires to calculate a multitude of sums over values for the current reconstruction approximation. Each summable set is an approximation of a straight line in the three-dimensional space. In a cone-beam tomography, the number of sums to be calculated on each iteration has a cubic dependence on the linear size of the reconstructed image. Direct calculation of these sums requires the number of summations in a quartic dependence on the linear image size, which limits the performance of the iterative methods. The novel algorithm proposed in this paper approximates the three-dimensional straight lines using dyadic patterns, and, using the adjustment of precalculation and inference complexity similar to the adjustment employed in the Method of Four Russians, provides the calculation of these sums with a sub-quartic dependence on the linear size of the reconstructed image.
Copyright (c) 2023 Mathematical Modelling, Programming & Computer Software
IMPLEMENTATION OF SURFACE-RELATED MULTIPLE PREDICTION PROBLEM ON RECONFIGURABLE COMPUTER SYSTEMS
The traditional methodology of computer-aided synthesis of parallel-pipeline programs for reconfigurable computer systems based on field programmable gate arrays (FPGAs) is aimed at the highest possible computer system performance, achieved on available hardware resource. Application of such an approach to real-time problems can lead to inefficient use of system hardware resource. Frequently, this fact leads to idle stand of occupied equipment and to higher requirements to power consumption, size and cost of the end product. We suggest a new methodology to synthesize of parallel-pipeline programs for solution of realtime computationally intensive problems. The methodology provides data processing having a specified rate which depends on a specified time interval. With the help of the developed methodology, it is possible to synthesize a problem computing structure, which requires the minimum hardware resource for the specified system performance. In order to illustrate the suggested methodology, we give the solution of the real-time surface-related multiple prediction problem. We evaluate various configurations of reconfigurable computer systems based on Xilinx Kintex UltraScale FPGAs.
ОБ ОДНОЙ ЗАДАЧЕ МАРШРУТИЗАЦИИ С НЕАДДИТИВНЫМ АГРЕГИРОВАНИЕМ ЗАТРАТ
Исследуется задача последовательного обхода мегаполисов (непустых конечных множеств) с условиями предшествования и неаддитивным агрегированием затрат. Предполагается, что на 'внешнем' уровне (при оценивании системы циклов, определяемых всякий раз этапами внешнего перемещения и внутренних работ) вариант агрегирования отвечает задаче 'на узкие места' с корректирующим параметром. На 'внутреннем' уровне (в пределах цикла) агрегирование затрат на внешнее перемещение и проведение работ может быть произвольным. Построен 'неаддитивный' вариант процедуры динамического программирования, включая экономичный вариант, использующий условия предшествования. Оптимальный алгоритм на основе ДП реализован в виде программы для ПЭВМ в случае постановки, ориентированной на задачу об управлении автономной системой, функционирующий в агрессивной среде и осуществляющей последовательно процесс демонтажа источников воздействий (данной среды) на систему. Эта постановка может отвечать инженерной задаче о демонтаже источников радиационного излучения при аварийных ситуациях на АЭС в случае применения роботизированной системы с электронным оборудованием, функционирование которого возможно лишь при соблюдении допусков на интенсивность радиационного воздействия в течении всего временного промежутка. Для данного варианта общей постановки проведен вычислительный эксперимент с применением ПЭВМ.
THE BLOW-UP SOLUTIONS TO NONLINEAR FRACTIONAL DIFFERENTIAL CAPUTO-SYSTEM
In this paper, we establish the finite time blow-up of solutions to nonlinear differential systems governed by Caputo fractional differential equation. Then, we derive sufficient conditions on parameters with positive given data. Moreover, for this purpose under some assumptions, we prove the non existence of global solutions to the considered class of nonlinear fractional differential Caputo-system subject to the initial condition. To prove our main result, we apply the test function method, Riemann–Liouville integral, Caputo derivative operator and some general analysis tools. Our result is new and generalizes the existing one.
MODELLING OF THE AXISYMMETRIC PRECISION ELECTROCHEMICAL SHAPING
Проблема моделирования прецизионного формообразования и граничные условия сформулированы согласно закону Фарадея со ступенчатой зависимостью выхода по току от плотности тока. Задача сводится к решению краевой задачи для определения двух аналитических функций комплексного переменного. Первая функция производит конформное отображение области параметрического переменного на физическую плоскость. Для этого используется интеграл Шварца и интерполяция сплайном. В отличие от плоской задачи, для определения потенциала и функции тока осесимметричной задачи используются интегральные преобразования второй аналитической функции. Аналитическая функция определена в форме суммы двух слагаемых. Первое слагаемое учитывает особенности функции так, чтобы у второго слагаемого не было особенностей. Вторая функция определяется с помощью интеграла Шварца. Проводится интерполяция функций сплайнами третьей степени, при этом коэффициенты сплайнов равны производным этих функций, посредством которых вычисляются компоненты векторов напряженности. Предложен метод решения осесимметричных стационарных задач, который отличается от известных методов своей точностью. С помощью предложенного метода получены численные результаты, описывающие форму обрабатываемой поверхности. Выполнена оценка погрешности полученных результатов. Проведено сравнение с результатами решения плоской задачи, которое показало их качественное совпадение.
ACOUSTIC WAVES PROPAGATION IN HEATED WATER WITH VAPOR BUBBLES
Проблемы распространения волн в пузырьковых средах представляют большой интерес для исследователей на протяжении почти полувека в связи с широким распространением этих систем в природе и их интенсивным использованием в современных технологиях. Из литературы известно, что интенсивность затухания звуковых возмущений в рассматриваемых газожидкостных средах в основном определяется теплофизическими характеристиками газа, находящегося в пузырьках. Оказывается, что эти эффекты значительно усиливаются с ростом концентрации пара, обусловленного повышением температуры системы. В работе рассмотрено в плоскоодномерном и односкоростном приближении распространение малых возмущений в жидкости с пузырьками, заполненными паром, и не растворимым в жидкой фазе газом. Для учета межфазного тепломассообмена использовались уравнения теплопроводности и диффузии внутри пузырька и уравнение теплопроводности в жидкости вокруг пузырька. Из условия существования решения в виде затухающей бегущей волны с учетом эффектов акустической разгрузки пузырьков выписано дисперсионное уравнение, проведены численные расчеты для воды с парогазовыми пузырьками. Исследованы особенности отражения гармонических волн от границы раздела ≪чистой≫ жидкости и жидкости с парогазовыми пузырьками. Проведен численный анализ влияния начального объемного газосодержания αg0 с двумя начальными размерами пузырьков a0 = 10−6 м и 10−3 м. Изучено влияние частот возмущений и температуры среды на коэффициент затухания акустической волны.
Optimal Control in Linear Sobolev Type Mathematical Models
The article presents a review of the work of the Chelyabinsk mathematical school on Sobolev type equations in studying the optimal control problems for linear Sobolev type models with initial Cauchy (Showalter–Sidorov) conditions or initial-final conditions. To identify the nonemptiness of the set of feasible solutions to the control problem we use the phase space method, which has already proved itself in solving Sobolev type equations. The method reduces the singular equation to a regular one defined on some subspace of the original space and applies the theory of degenerate (semi)groups of operators to the case of relatively bounded, sectorial and radial operators. Here mathematical models are reduced to initial (initial-final) problems for an abstract Sobolev type equation. Abstract results are applied to the study of control problems for the Barenblatt–Zheltov–Kochina mathematical model, which describes fluid filtration in a fractured-porous medium, the Hoff model on a graph simulating the dynamics of I-beam bulging in a construction, and the Boussinesq– L¨ove model describing longitudinal vibrations in a thin elastic rod, taking into account inertia and under external load, or the propagation of waves in shallow water.
Tamara Balabekovna Chistyakova (to Anniversary Since Birth)
Copyright (c) 2020 Mathematical Modelling, Programming & Computer Software
Synthesis of Surface H-Polarized Currents on an Unclosed Cylindrical Surface
The article describes the inverse problem of diffraction of electromagnetic waves, finding surface H-polarized currents on an unclosed cylindrical surface according to a given radiation pattern. The work is based on modelling an operator equation with a small parameter. The operator is represented as the sum of a positive-definite, continuously invertible operator and a compact positive operator. The positive-definite operator exactly coincides with the main operator of the corresponding direct problem of diffraction of electromagnetic waves. Due to this fact, the solution to the simulated equation satisfies the necessary boundary conditions. And this is the novelty and difference of the approach developed in this work from the methods known in the scientific literature. We develop a theory of an operator equation with a small parameter and a numerical method based on Chebyshev polynomials with weights that take into account the behavior at the boundary. The efficiency of the numerical method is shown.
Numerical Research of the Mathematical Model for Traffic Flow
The problems of distribution of transport flows are currently relevant in connection with the increase in vehicles. In the 50s of the last century, the first macroscopic (hydrodynamic) models appeared, where the transport flow resembles the flow “motivated” compressible liquid. The scientific approach based on the Navier–Stokes system. The main idea of the scholars is consideration the hydrodynamic models on the grounds of interrelation between the transport flow and incompressible fluid. For modelling traffic flows we examine Oskolkov equation on the geometric graph, where the edge has two positive values corresponding to it “length” and “width”. Certainly, in the context of mathematical model the values lk and bk are dimensionless, but for clarity it is convenient to imagine that lk is measured in linear metric units, for example, kilometers or miles, and bk is equal to the number of traffic lanes on the roadway in one direction. In terms of the Oskolkov model, we obtained a nonclassical multipoint initial-final value condition. We will study such a model using the idea and methods of the Sobolean equation theory. These notes describe a numerical experiment based on the Galerkin method for the Oskolkov equation with a multipoint initial-final condition on the graph.
Application of the Method of Assessing Own States in a Statistical Analysis of Sustainable Economic and Environmental Development of Enterprises
The article presents the results of statistical analysis of sustainable economic and ecological development of enterprice. The purpose of the analysis is to identify the main trends in the studied features of economic objects. In this paper, we present a comparative analysis of the data using the method “Analysis of the functioning environment” (ASF) and the method of assessing own states, focused on the allocation of states corresponding to the standard, that is, certain criteria.
Architecture of the Information System for Determining the Competence Portrait of Trained on the Basis of Status Functions
We present the architecture of an information system for determining and analyzing the competency portrait of trainees. Assessments are formed as status functions that are complex-valued. Moreover, each estimate contains an ordered pair, including estimates of the current state and its expected trend. The significance of the contribution of each of the estimates is calculated based on the correlations of all the estimates in the system. We propose an algorithm for interpreting and transforming information using the mathematical apparatus of status functions to support decision-making using an information system. At the input of the information system, a list of competencies, a description of the curriculum, content of disciplines, and assessments of individual competencies are set. At the output, estimates of the competency portrait of the trainees are formed on the basis of the calculated integral moments. Also, we propose and describe an algorithm to estimate the values of the indicators of competence of students. We develop the corresponding modules of the software information system in the JavaScript language. As an example, to verify the program, we use the formation of a competency portrait of a university graduate in the field of 44.03.01 “Pedagogical education”
Mathematical Models and Software Package for Extrusion Control at Flexible Multi-Assortment Productions of Polymeric Materials
We develop mathematical models of extrusion and the software package helping production staff to solve problems of resource and energy saving control of the extruders applied in flexible multi-assortment productions of packing polymeric materials. Also, we propose the combined modelling method for complex assessment of throughput, energy consumption of extrusion and quality indices of material in the extruders differing in hardware flexibility and complexity of flow structure. The method is based on use of static and dynamic models. The software package is adjusted according to production method, type of products, as well as requirements to throughput and energy consumption. The software package includes databank of extrusion characteristics, module for extrusion equipment choice, module for design of virtual models of extruder screws, subsystem for structural and parametrical synthesis of mathematical model and calculation of output parameters for extrusion, subsystem for visualization of results, in particular, in the form of trends of output parameters and 3D graphs of their dependences on controlling actions. The operability was confirmed by testing of the software package according to data from productions of polyvinylchloride and polyethylene films at the factories in Russia and Germany. The software package can be used as the effective instrument for support of decision-making when determining configurations and operation modes of the extruders that ensure the set consumer characteristics of the products.
Diagnostics of Instant Decomposition of Solution in the Nonlinear Equation of Theory of Waves in Semiconductors
The paper considers a method for numerical diagnostics of the solution’s blow-up in a nonlinear equation of the theory of waves in semiconductors. One feature of the problem under consideration is that there is not even a weak local solution to the problem in time on the positive half-line in spatial variable, while there exists a classical solution local in time in the spatial interval from 0 to L. We numerically show that the lifetime of the solution tends to zero as L tends to infinity. The numerical diagnostics of the solution’s blow-up is based on the method of calculating a posterior asymptotically accurate estimate of the error of the obtained numerical solution according to the Richardson extrapolation method.
Numerical Study of the Dynamics of Air Separation Process by Pressure Swing Adsorption
Using mathematical modelling and the finite element method, we carry out the calculation experiments to study the system connections and regularities of pressure swing adsorption process under the conditions of air separation and oxygen concentration (production). We study the influence of mode and construction variables on the dynamics and technological indicators of the effectiveness of this process. Namely, we study the influence of input variables (composition and temperature of atmospheric air, air pressure at the compressor outlet) on output variables (extraction degree, oxygen purity, unit capacity, etc.) of the studied object in a wide range of control variables (adsorption-desorption cycle time, pressure ratios at adsorption and desorption stages, and oxygen-enriched reverse air flow coefficient). Also, we study the influence of construction parameters (layer height, particle diameter and maximum adsorption volume of the adsorbent) on the amount of adsorption, which is equilibrium with the current concentration of the adsorptive in the gas mixture flow on the outer surface of the adsorbent granules, the value of the kinetic adsorption coefficient (the coefficient of external mass transfer of the adsorptive (mainly nitrogen) from the gas phase into the adsorbent). The results of calculation experiments allow to establish the most promising mode and construction parameters for the optimal design of oxygen enrichment systems by pressure swing adsorption with varying pressure.
Procedure for Constructing Soft Models of Complex Systems by Time Series
The problem of creating models of complex systems for assessing their state is considered. The analysis of approaches to construction of diagnostic models is given and their features are marked. For a complex system with a hierarchical structure, a procedure for constructing the models to assess its state using a scalar time series is proposed. In this case, each hierarchical level is described by a lumped-parameter differential equation. The procedure is based on the concept of soft modelling. The efficiency of the proposed procedure is demonstrated by the example of constructing a model for assessing the state of a complex heart rhythm regulation system.
Resource Allocation in Cloud Computing Via Optimal Control to Queuing Systems
We consider resource allocation problem in the cloud computing. We use queuing model to model the process of entering into the cloud and to schedule and to serve incoming jobs. In this paper, the main problem is to allocate resources in the queuing systems as a general optimization problem for controlled Markov process with finite state space. For this purpose, we study a model of cloud computing where the arrival jobs follow a stochastic process. We reduce this problem to a routing problem. In the case of minimizing, cost is given as a mixture of an average queue length and number of lost jobs. We use dynamic programming approach. Finally, we obtain the explicit form of the optimal control by the Bellman equation.
Mathematical Model of Multichannel Advertising Management with Continuously Distributed Lags
The dynamic model of optimal distribution of advertising costs on the planning period is analyzed. It is assumed that companies can use several media channels of different quality and influence on demand. We consider the delayed reaction of consumers to advertising and non-advertising factors. Unlike such classical dynamic optimization models as NerloveArrow model, Vidal-Wolf model and their extensions, the proposed model takes into account accumulated effects of advertising of several media channels and previous sales. In the framework of the proposed model, we consider the problem of optimal control of advertising costs with a nonlinear Volterra integral equation, which is generated by the natural constraints. The theorem on existence of solution to this equation is proved. Also, we formulate the theorem on existence of solution to the total profit maximization problem for the planning period under restriction. The maximum principle is applied to the problem and the necessary conditions for constructing an optimal strategy are found.
Computational Algorithm for Optimal Control of an Object with Distributed Parameters in a Nonsmooth Area of Final States
We propose the effective computational algorithm for solving boundary-value problems of time-optimal and maximum accuracy control with a minimax estimation of the deviation of the final trajectory from a given state. The problem is reduced to a nonconvex nonlinear programming problem. The proposed algorithm takes into account the non-convex nature of the problem of nonlinear programming, provides a search in the "ravines"zone, performs a search quite efficiently under conditions of increased dimension of the definition domain of the optimized functional, and provides the required accuracy of the solution. Due to the transformation of the multidimensional non-convex nonlinear programming problem to the problem of minimizing a smooth monotonically decreasing function of one variable, the algorithm significantly reduces the computational complexity of solving boundary-value problems of optimal speed and maximum accuracy with a minimax estimate of the deviation of the final trajectory from a given state. We give an example of the solution of the test optimal control problem for induction heating of a cylindrical billet.
Cooperation in a Conflict of N Persons Under Uncertainty
The paper considers a model of a conflict system with N active participants with their own interests when exposed to an uncertain factor. At the same time, decision-makers do not have any statistical information about the possible implementation of an uncertain factor i.e. they only know the many possible realizations of this factor – uncertainties. Under the assumption that the participants of to the conflict can coordinate their actions in the decision-making process the model is formalized as a cooperative N-person game without side payments and under uncertainty. In this paper, we introduce a new principle of coalitional equilibration (CE). The integration of individual and collective rationality (from theory of cooperative games without side payments) and this principle allows us to formalize the corresponding concept of CE for a conflict of N persons under uncertainty. At the same time, uncertainty is taken into account along with using the concept of the “analogue of maximin” proposed earlier in the our works and the “strong guarantees” constracted on its basis. Next, we establish sufficient conditions for existence of coalitional equilibrium, which are reduced to saddle point design for the Germeier convolution of guaranteed payoffs. Following the above-mentioned approach of E. Borel, J. von Neumann and J. Nash, we also prove existence of coalitional equilibrium in the class of mixed strategies under standard assumptions of mathematical game theory (compact uncertainties, compact strategy sets, and continuous payoff functions). At the end of the paper, some directions or further research are given
Modelling of Electric Fields in Axisymmetric Systems for Cathode Protection of Underground Structures
The aim of this work is to carry out numerical calculation of electric fields in axisymmetric systems for cathode protection of underground structures against corrosion. As is known, cathode protection is a complex multi-parameter system, which has a number of features depending on the type and form of the protected structure, properties of the surrounding environment, etc. As a result, the modelling of protection parameters is quite complex and requires new more advanced computer technologies. In this work, we construct a mathematical model of the problem on the electric field distribution in an axisymmetric system for cathode electrochemical protection of underground structures. In addition, we propose an algorithm to solve the problem. The algorithm is based on the use of integral Green transformations and, in particular, the second Green integral formula. Also, we give an example of a computer implementation of the proposed algorithm in the case of a homogeneous half-space. The Scilab application package is used to implement the example
Anisotropic Diffusion in Anisotropic Stepanov Spaces
We consider a problem on the image processing and computer vision. A wide range of methods allows to solve problems of this type. The methods of partial differential equations are the most useful and interesting ones. A non-linear diffusion takes special place in these studies. In this context, fundamental theoretical foundation is a central part of this approach. Therefore, we introduce a new functional class of spaces, formulate and prove the lemma on the equivalent norms in anisotropic Stepanov spaces. Another important result of this study is the lemma that the anisotropic Stepanov spaces are Banach. In addition, we obtain the theorem on the solvability of the equation of anisotropic diffusion in anisotropic Stepanov spaces. The results can be applied to the image processing and computer vision. Also, the obtained results open the new view to this problem.
Solving Elliptic Equations in Polygonal Domains by the Least Squares Collocation Method
The paper considers a new version of the least squares collocation (LSC) method for the numerical solution of boundary value problems for elliptic equations in polygonal domains, in particular, in multiply connected domains. The implementation of this approach and numerical experiments are performed on the examples of the inhomogeneous biharmonic and Poisson equations. As an application, we use the nonhomogeneous biharmonic equation to simulate the stress-strain state of isotropic elastic thin plate of polygonal form under the action of transverse load. The new version of the LSC method is based on the triangulation of the original domain. Therefore, this approach is fundamentally different from the previous more complicated versions of the LSC method proposed to solve the boundary value problems for partial derivative equations in irregular domains. We make the numerical experiments on the convergence of the approximate solution to various problems on a sequence of grids. The experiments show that the solution to the problems converges with high order and, in the case of the known analytical solution, matches with high accuracy with the analytical solution to the test problems
A Numerical Method for Solving Quadratic Integer Programming Problem
We propose a new numerical method for solving quadratic integer programming problem. The algorithm is based on a special representation of a minimizer of the corresponding objective functional. The problem can be reduced to a special box-constrained integer least squares problem. The advantage of the proposed algorithm is a good computational performance (approximately O(n · ln(n)) operations) shown in numerical experiments, where the number of unknowns n can be up to 108 . The computational complexity of the algorithm is confirmed experimentally by a large number of numerical experiments. The algorithm consists of 3 steps. At the average, a solution is found at the second step in 83,6 % cases, while the third step gives solution in the remaining cases. The algorithm is realized with the use of the Python programming language. The results of numerical experiments can be found at the service GitHubGist. The elaborated software system was used to solve the problem on formation of the optimal order for education institutions in regions of the Russian Federation.
Supercomputer Simulation of Oil Spills in the Azov Sea
We present the research on microbiological destruction of oil pollution in shallow water. In order to conduct the research, we use a multiprocessor computer system with distributed memory. The research takes into account the oil fractional composition as well as hydrodynamic and chemical-biological features of water. In order to simulate the dynamics of hydrocarbon microbiological degradation in the Azov Sea, we propose the complex of interrelated precision models. For model discretization, we use the space splitting schemes taking into account the partial filling cells of computational domain. Therefore, the computational accuracy significantly increases, while the computational time decreases. On supercomputer, we implement an experimental software for predictive modelling the ecological situation under oil and other pollution conditioned by natural and industrial challenges in shallow water.
Mathematical Modelling of Reconstruction of Volumetric Images in X-Ray Computed Tomography Using Holographic Methods
We consider a computational algorithm for solving the inverse problem of x-ray tomography to reconstruct the internal structure of micro objects in the near Fresnel zone using holographic methods of visualization of three-dimensional images. Holographic methods do not give a direct solution to the problem on reconstruction of the internal structure of the object. These methods can only solve the problem on volumetric mapping of some object surface. However, using the data on the absorption of both x-ray radiation of the object and phase contrast holographic signals in the near Fresnel zone, we show the possibility to obtain a volumetric holographic image of the inner layers of the object. In order to solve this complex problem, it is necessary to use a three-dimensional (3D) radon transformation of the internal function of the object and a two-dimensional (2D) radon transformation of the phase contrast holographic projection. We obtain an algorithm to reconstruct phase-contrast tomographic images of the internal structure of an object. Based on the algorithm, we construct a computational algorithm for the practical reconstruction of volumetric tomographic images of the internal structure of microobjects. The results of the research were confirmed by the mathematical modelling of the algorithm to reconstruct three-dimensional images. To this end, we develop a mathematical model of the test phantom, and simulate the phase contrast projections for the test phantom. Then, we develop a software in order to reconstruct the phase contrast tomographic images by tomographic methods on the basis of the obtained phase contrast projections.
The Use of the Direct Sum Decomposition Algorithm for Analyzing the Strength of Some Mceliece Type Cryptosystems
We construct a polynomial algorithm for decomposing an arbitrary linear code C into a direct sum of indecomposable subcodes with pairwise disjoint supports. The main idea of the constructed algorithm is to find the basis of a linear code consisting of minimal code vectors, that is, such vectors whose supports are not contained in the supports of other code vectors of this linear code. Such a basis is found in the polynomial number of operations, which depends on the code length. We use the obtained basis and the cohesion of supports of minimal code vectors in order to find the basic vectors of indecomposable subcodes such that the original linear code is the direct sum of these subcodes. Based on the obtained algorithm, we construct an algorithm of structural attack for asymmetric McEliece type cryptosystem based on code C, which polynomially depends on the complexity of structural attacks for McEliece type cryptosystems based on subcodes. Therefore, we show that the use of a direct sum of codes does not significantly enhance the strength of a McEliece-type cryptosystem against structural attacks.
A Method to Reduce Errors of String Recognition Based on Combination of Several Recognition Results with Per-Character Alternatives
We consider the problem on recognition of a string object presented in several video stream frames. In order to maximize the output accuracy, we combine several results of the recognition. To this end, we consider a model of result of a string object recognition. The model takes into account the estimations of alternative results of per-character classification. Also, we propose an algorithm to combine results of a string recognition according to this model. The algorithm was evaluated on a MIDV-500 dataset of document images. The experimental results show that the proposed algorithm allows to achieve the high accuracy of recognition result due to an analysis of several images, and the use of the estimations of alternative results of per-character classification gives the higher results then a combination of strings that contain only the final alternatives of each character.
Mathematical Terrain Modelling with the Help of Modified Gaussian Functions
Based on a fundamentally new approach, we present a complete mathematical model for estimating the mass of water in the flooded coastal relief, taking into account the water in the basin of the reservoir in a given region. Taking into account stochastic studies, we construct an approximate model of the relief of the reservoir basin bottom, as well as the relief of a possible section of the flooding of this basin coastline. The modelling is based on the empirical data of measurements of the reservoir depths, as well as on the study on the architecture of the lines of the coastal maps of the possible flooding zone. Based on the measurements of the depths and bumps of the bottom surface, we verify the hypothesis that the use of the two-dimensional Gauss distribution is adequate. Numerous confirmation of this hypothesis on the basis of empirical measurements allows to use localized elliptic Gauss surfaces as a model function in order to construct an approximate model of hillocks and valleys. At the same time, the coordinates of local extremes of the depths, as well as the values of these extremes are constant. In order to simulate the surfaces of the underwater slopes, we construct planes according to depth measurements. This simulation is not a real copy, but is stochastic in nature and allows to take into account the main goal of the model, i.e. a full adequate estimation of the water mass of the flooded coastal relief included the water in the basin of the reservoir in the region. The equation of the model of the entire flooded region includes all local functions constructed for the mounds and troughs of the reservoir, as well as the functions of the planes of the slope models. For an approximate construction of the surface equations of the coastal zone, we use maps with detailed level lines as empirical data.
Mathematical Model of the Downward Two-Phase Flow of a Heat-Transfer Agent in an Injection Well
At the present time, the main method of developing highly viscous and bituminous oil reservoirs is the injection of hot water or steam into such reservoirs. When injecting heat-transfer agent into a porous reservoir, its characteristics at the wellhead are known. It is important to know the parameters of a heat-transfer agent (pressure, temperature, mass content of steam in a two-phase mixture “water-steam”, etc.) directly at the reservoir entrance. In order to calculate various parameters of a heat-transfer agent along the injection well depth (including the bottomhole), we propose a mathematical model of the downward flow of a hot “water-steam” mixture in a vertical channel. The model takes into account phase transitions occurring in a two-phase “water-steam” mixture, and external heat exchange of the well product with surrounding rocks (including permafrost). Based on the proposed mathematical model, we develop an algorithm to solve a quasistationary problem. In this case, we use the Runge–Kutta method in order to solve the system of differential equations describing the stationary flow of a heat-transfer agent in a well. Also, in order to solve the non-stationary problem of temperature distribution in the rocks that surround the well (including permafrost), we use the author enthalpy method with implicit scheme. For each time moment, the developed software allows to find the distributions along the well depth of various parameters of the downward two-phase flow, taking into account external heat exchange, as well as the temperature distribution in the rocks that surround the well and the permafrost thawing radius.