Информатика, вычислительная техника и управление. Рубрика в журнале - Сибирский аэрокосмический журнал
Статья научная
Nowadays tree modeling algorithms are used in different fields of activity: from computer games to the plantation forest management. Tree modeling algorithm parameters can depend on different factors: it could be features of land- scape, climate or geographical location. Depending on the tasks to be solved, the detail level of the created model is chosen. Forest management tasks often do not require a high detail level, it is sufficient to construct a schematic plantation model. For computer games the creation of photorealistic models is required. The paper proposes an algorithm of 3D tree modeling which consists of the following steps: first step - building a tree framework (modeling the growth of a tree and adding new nodes), while under the framework is meant a set of three-dimensional vectors with attributive data for each vector; then building a tree and overlaying textures. The trunk and branches of the modeled tree are approximated by truncated cones, the axes of which are the vectors of the frame. The tree model constructing algorithm is iterative. Every iteration is a tree growth stage. Thus, the tree is gradually grown to the required level. The developed algorithm allows modeling trees of different state categories. The feature of the proposed algorithm is the possibility of constructing a three-dimensional tree model with any detail level. For example, for coniferous trees it is possible to built a tree up to each needle.
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6-апериодические слова над трехбуквенным алфавитом
Статья научная
Работа посвящена изучению множеств апериодических слов над конечным алфавитом. Множество таких слов можно рассматривать как некоторый конечный формальный язык. У. Бернсайд задал вопрос о локальной конечности периодических групп. Отрицательный ответ был получен лишь через шестьдесят лет Е. С. Голодом. Вскоре С. В. Алешиным, Р. И. Григорчуком, В. И. Сущанским были построены еще примеры, подтверждающие отрицательный ответ на вопрос Бернсайда. Конечность свободной бернсайдовской группы периода n установлена в разное время для периодов два и три (У. Бернсайд), для периода четыре (У. Бернсайд; И. Н. Санов), для периода шесть (М. Холл). Бесконечность такой группы, для нечетных показателей, превышающих 4381, установлена в работе П. С. Новикова - С. И. Адяна (1967), а для нечетных показателей, превышающих 664, - в монографии С. И. Адяна (1975). Геометрический метод доказательства для нечетных показателей, превышающих 1010, принадлежит А. Ю. Ольшанскому (1989). В данной статье рассматриваем множество 6-апериодических слов. l-апериодическим словом называется слово Х, не содержащее нетривиальных подслов типа Yl. В книге С. И. Адяна (1975) имеется обоснование С. Е. Аршона (1937) того, что в двухбуквенном алфавите имеется бесконечно много три-апериодических слов любой длины. В книге А. Ю. Ольшанского (1989) приведено доказательство бесконечности множества шесть-апериодических слов и получена оценка количества таких слов любой данной длины. Здесь мы хотим оценить функцию количества шесть-апериодических слов любой данной длины в алфавите из трех букв. Полученные результаты могут быть полезны при кодировании информации в сеансах космосвязи.
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Algorithmic and software of the system profiling the actions of users of the information system
Статья научная
The paper describes the software of the system for profiling the actions of users of the information system. This profiling system is aimed at solving the problem of trust in users of information systems. The system should regulate access to protected resources by analyzing user behavior. The algorithmic component of the system is represented by a user behavior model and a general system operation algorithm. The user behavior model is based on the apparatus of Markov chains Software implementation allows in practice to obtain the foundations of the proposed approach to work. At the development stages, the choice of software architecture is carried out. The client-server architecture was chosen as a reasonable decision. The software component of the user activity profiling system consists of five separate software modules. At the end of development, a brief testing of the components is carried out. The novelty of this work lies in the proposal of an approach that uses the profiling of user actions as an additional determining factor in managing access to objects, as a way to strengthen the basic measures “Controlling access of subjects to access objects” in the order system of FSTEC of Russia.
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Applied classification problems using ridge regression
Статья научная
The rapid development of technical devices and technology allows monitoring the properties of different physical nature objects with very small discreteness of the data. As a result, one can accumulate large amounts of data that can be used with advantage to manage an object, a multiply connected system, and a technological enterprise. However, regardless of the field of activity, the tasks associated with small amounts of data remains. In this case the dynamics of data accumulation depends on the objective limitations of the external world and the environment. The conducted research concerns high-dimensional data with small sample sizes. In this connection, the task of selecting informative features arises, which will allow both to improve the quality of problem solving by eliminating “junk” features, and to increase the speed of decision making, since algorithms are usually dependent on the dimension of the feature space, and simplify the data collection procedure (do not collect uninformative data). As the number of features can be large, it is impossible to use a complete search of all features spaces. Instead of it, for the selection of informative features, we propose a two-step random search algorithm based on the genetic algorithm uses: at the first stage, the search with limiting the number of features in the subset to reduce the feature space by eliminating “junk” features, at the second stage - without limitation, but on a reduced set features. The original problem formulation is the task of supervised classification when the object class is determined by an expert. The object attributes values vary depending on its state, which makes it belong to one or another class, that is, statistics has an offset in class. Without breaking the generality, for carrying out simulation modeling, a two-alternative formulation of the supervised classification task was used. Data from the field of medical diagnostics of the disease severity were used to generate training samples.
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Applying software-mathematical models of onboard equipment to develop onboard software
Статья научная
This paper deals with the testing of the functioning logic of spacecraft subsystems at the stage of developing system onboard software. The increasing complexity of the structure and operation logic of spacecraft due to the increased requirements in terms of providing consumers with information services (navigation, satellite monitoring of transport, geodesy, communications etc.) demands maintaining the reliability of uninterrupted operation, the implementation of automated parrying of emergency situations during the operation of spacecraft onboard equipment. In order to meet these requirements, it is necessary to test the interaction of onboard equipment and onboard integrated computing complex software that implements the target-oriented operation of spacecraft onboard systems. In such a case, meeting the requirements for reliability increase of onboard software should not lead to the increase of the manufacturing period of spacecraft. In this work we propose the approach for testing information and logical interaction between onboard equipment and software of a spacecraft onboard integrated computing complex with the use of a laboratory testing sample unit and a software-mathematical model. We described the basic concepts of conducting two-stage testing of onboard soft-ware, involving autonomous and system testing on the ground testing complex. The proposed approach is applied as part of the onboard software development cycle in accordance with the standards of the JSC “Academician M.F. Reshetnev “Information Satellite Systems”. The approach proposed in this work helps reduce the number of errors during onboard software development and testing of information and logical interaction between onboard equipment and a spacecraft as a whole in every operation mode.
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Compound bending of an orthotropic plate
Статья научная
The problem of longitudinal-transverse deformation and strength of an orthotropic plate on the action of a local transverse force and stretching along the contour of the membrane forces is studied. The direction of laying the fiber of a unidirectional composite that provides the lowest level of stress and deflection is determined. In the zone of application of concentrated force in thin-walled structures, significant bending moments and shear forces occur, which are a source of stress concentration. To reduce stresses, the method of plate tension by membrane forces applied along the contour is chosen. The maximum possible order of membrane tension forces is selected, which provides conditions for the strength and rigidity of the solar panel plate structure, which has a hinge-fixed support along the contour. Pretensioning the plate web allows to reduce the stress by 50 times. The problem of compound bending of isotropic and anisotropic plates when applying transverse and selection of longitudinal loads, with restrictions on strength and stiffness, can be called a problem of rational design of the structure. The resulting equations and calculation program can be used in the design of plate structures, as well as in the educational process.
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Differential evolution in the decision tree learning algorithm
Статья научная
Decision trees (DT) belong to the most effective classification methods. The main advantage of decision trees is a simple and user-friendly interpretation of the results obtained. But despite its well-known advantages the method has some disadvantages as well. One of them is that DT training on high-dimensional data is very time-consuming. The paper considers the way to reduce the DT learning process duration without losses of classification accuracy. There are different algorithms of DT training; the main of them being ID3 and CART algorithms. The paper proposes a modification of DT learning algorithms by means of the information criterion optimization for some selected attribute. The use of this modification allows avoiding optimization by means of enumeration search over the entire data set. The Separation Measure method is used to select the attribute. The method selects the attribute whose class-based averages are most distant from each other. Optimization of the selected attribute is carried out using the method of differential evolution, which is one of the evolutionary modeling methods designed to solve problems of multidimensional optimization. Self-configuring at the population level based on the probabilities of using mutation operator's variants was applied for differential evolution. The classification problems were solved to compare standard DT learning algorithms with the modified ones. Algorithm efficiency refers to the percentage of correctly classified test sample objects. Statistical analysis based on Student's t-test was carried out to compare the efficiency of the algorithms. The analysis showed that the use of the proposed modification of the DT learning algorithm makes it possible to significantly speed up the training process without losses in the classification effectiveness.
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Efficient method of calculating layered conical shells with Lagrange multigrid elements use
Статья научная
The increased requirements for strength calculations of space-rocket and aviation technology designs cause the need for the development and improvement of approximate solutions for elasticity theory tasks with small error algo- rithms. The article considers the numerical method of calculating elastic layered conical shells (LCS) of various thickness under static loading which are widely used in space-rocket technology. The suggested method uses three-dimensional curvilinear Lagrange multigrid finite elements (MGFE). A system of nested grids is used for MGFE constructing. The fine grid is generated by the basic partition that takes into account MGFE heterogeneous structure. The basic partition dimensionality is reduced with the help of large grids which leads to the system of linear algebraic equations of the small dimension finite elements method. Three-dimensional elasticity theory equations use allows to apply MGFE for calculating LCS of any thickness. Displacements in MGFE are approximated by Lagrange polynomials which, in con- trast to power polynomials, gives the opportunity to design big size three-dimensional thin shell elements. Lagrange polynomials nodes coincide in shell thickness with the nodes of MGFE large grids which lie on the shared borders of multi-module layers. The efficiency of the presented method is that the suggested MGFE generate small dimension discrete models that require 103-107 times less electronic computing machine (ECM) memory than basic models. The suggested law of dis- crete models grinding generates uniform and fast convergence of numerical solutions which allows to make solutions with the specified (small) error. Examples of LCS calculating (whole ones as well as with holes) under axisymmetric and local loading are given. Comparative analysis of solutions obtained with the help of MGFE, single-grid finite elements and the program com- plex ANSYS has been conducted.
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Статья научная
A lot of sets of subjects and objects in biology, industry, management can be divided into a number of classes, each of which corresponds to a certain distribution component. When analyzing a mixture of distributions, it is necessary to estimate its parameters (task 1) and to assess the correspondence of empirical and theoretical distribution functions (task 2). To solve the first problem, numerical algorithms that implement the method of moments and the maximum likelihood method are used. In this paper, the problem of estimating the distribution parameters is solved by minimizing the good- ness measure by the Quasi-Newton method. The second problem is solved by comparing the empirical and theoretical distribution functions by one or several statistical goodness measures. Statistics of the distribution of these measures depends on the sample size, the method of forming data and estimating distribution parameters. The paper examines the goodness measure between Frocini and omega-square (Kramer - Mises - Smirnov). The evaluation of the statistics of the goodness measure was carried out by the simulation method based on the results of 50000 statistical tests. In each of the tests, the distribution parameters were estimated by minimizing the calculated value of the corresponding goodness measure. The results of simulation modeling allow estimating the statistics of the parameters of a mixture of distributions. The results of solving the considered problems for a mixture of two normal distributions of size 240 are pre- sented.
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Статья научная
In this paper the approach for external boundary of pole localization region formulation for transfer function with interval-given parameters is proposed. The boundary is formulated as analytic piecewise function of characteristic polynomial parameters of the given transfer function. Analytic formulation of external boundary of poles localization region allows to reduce computations since existing methods require iterative numeric calculations of characteristic equation roots with fixed step size for edges mapping or full interval root locus mapping as well. Formulated boundary allows to clearly describe system behavior and calcu- late variation ranges of performance indexes. In addition, piecewise function that constrains gives new opportunities for parametric controller synthesis for systems introduced by transfer functions with interval-given parameters. The results can find its practical application in aerospace engineering problems of mathematical analysis and syn- thesis for highly-precise systems of self-direction missiles. In the research the boundary formulation is performed for third order transfer function. Transfer function order was chosen due to the fact that many physical systems and objects can be described mathematically with the third order transfer function, e.g. model of missile target-seeking head with gyro stabilized drive is described with this model. The research was performed on the basis of the following step sequence: firstly, analytical solving of cubic equation applying Cardano’s formula; secondly, interval root locus edges functions obtaining, next external vertexes set obtaining and, finally, external border formulation and plotting.
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Improvement of the construction technique of substitution blocks for symmetric encryption algorithms
Статья научная
As it is known, block symmetric encryption algorithms are widely used to ensure information confidentiality. The re- sistance of encryption algorithms to the most common types of cryptanalysis is determined the quality of the blocks of substitutions. In the present work, the development of a methodology for constructing substitution blocks is being continued. In the first approach, Boolean functions with given cryptographic properties are used as component functions of substitution blocks. Previously, one of the authors proposed a reasonable methodology for the phased selection of Boolean functions for construction block. In this paper, in addition to such cryptographic properties of Boolean functions, such as: balance, possessing a strict avalanche effect, possessing correlation immunity, for the first time the nonlinearity distances of the first and second orders of Boolean functions are considered simultaneously. A study of the full set of Boolean functions of four variables was conducted. The result of it is the optimal set of Boolean functions for building substitution blocks when encrypted with the GOST 28147-89 algorithm. In the second approach, the substitution block are determined by an irreducible polynomial over the Galois field, such a scheme, used in the Rijndael encryption algorithm, is considered to be strong. The growth of calculating power of the computer necessitates an increase of the cryptographic strength of encryp- tion algorithms. The authors have proposed substitution blocks for each round of the Rijndael scheme, based on different irreducible polynomials. A study of compositions representing a different combination of specially selected irreducible polynomials for ten rounds was carried out and the optimal set of polynomials with the best values of the encryption quality indica- tors by the Rijndael scheme was obtained.
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Library of mathematical functions with parallelism at the operational level in the Pythagor language
Статья научная
At present, developed tools and libraries have been designed for imperative and functional programming languages that provide parallelism through processes or threads. There are other alternative approaches to the organization of parallel computing, one of which is implemented in Pythagor - the language of functional-streaming parallel programming, and involves parallelism at the level of operations. The tools of the Pythagor programming language are actively developing, and the repository of predefined functions is expanding. Many mathematical functions have been designed to provide a developer with no less functionality than the math library math.h of the C programming language. A large part of the mathematical functions have been implemented using the Maclaurin’s series. It is both used as an approach of faster and less accurate calculations, in which a predetermined number of elements of the series is calculated without cycles and recursions with the substitution of pre-calculated coefficients in the function code, and as an approach of less rapid and more accurate calculations, in which the elements of the series are calculated dynamically until the desired accuracy is achieved. The development of a library of mathematical functions of a programming language is an applied algorithmic task already implemented in one way or another for a number of existing programming languages. But in many languages, the implementation of algorithms for mathematical functions is hidden from the user, while modern tools of the Pythagor language support an open repository of functions. Additional interest is the possibility of parallelism at the level of operations in the calculation of mathematical formulas in the Pythagor language.
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Статья научная
Plates, beams and shells with a non-uniform and micro-uniform regular structure are widely used in aviation and rocket and space technology. In calculating the strength of elastic composite structures using the finite element method (FEM) it is important to know the error of the approximate solution for finding where you need to build a sequence of approximate solutions that is connected with the procedure of crushing discrete models. Implementation of the procedure for grinding (within the micro-pass) discrete models of composite structures (bodies) requires large computer resources, especially for discrete models with a microinhomogeneous structure. In this paper, we propose a method of equivalent strength conditions (MESC) for calculating elastic bodies static strength with inhomogeneous and microinhomogeneous regular structures, which is implemented via FEM using multigrid finite elements. The calculation of composite bodies’ strength according to MESC is limited to the calculation of elastic isotropic homogeneous bodies strength using equivalent strength conditions, which are determined based on the strength conditions set for composite bodies. The MESC is based on the following statement. For all composite bodies V 0 , which are such a homogeneous isotropic body V b and the number of p , if the safety factor nb of the body V b satisfies the equivalent conditions of strength pn 1 (1+ da ) £ nb (1-d2 ) £ pn 2 (1-da ) , the safety factor n 0 of the body V 0 meets the defined criteria for a strength n 1 £ n 0 £ n 2 , where n 1 , n 2 specified, the safety factor n 0 ( nb ) complies with the accurate (approximate) solution of elasticity theory problem is built for body V 0 (body V b ); da b , corresponding to approximate solution. When constructing equivalent strength conditions, i. e when finding the equivalence p coefficient, a system of discrete models is used, dimensions of which are smaller than the dimensions of the basic composite bodies models. The implementation of MESC requires small computer resources and does not use procedures for grinding composite discrete models. Strength calculations for bodies with a microinhomogeneous structure using MESC show its high efficiency. The main procedures for implementing the MESC are briefly described.
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Статья научная
The purpose of developing a method for detecting quality anomalies of interactive electronic technical manuals (IETM) in application to aircraft maintenance and repair is an objective, purposeful interpretation of assessment of the specified quality. This method is a combination of the corresponding logical-mathematical model of such anomalies designed for subject content logic circuits (SCLC), and the algorithm of its performance in the technological process of compiling interactive electronic manuals. The IETM model of quality anomalies provides the analysis of the SCLC structure as some basic graph and regards the anomaly as a more specific graph. The specific graph is a graphical description of various partial distortions of the logic presented in the form of SCLC. Such a representation of quality anomaly of IETM for aircraft maintenance and repair - by a graph isomorphically nested in the structure of its SCLC - allows to reduce the detection of such anomalies to the mathematico-algorithmic problem of detection or search for the corresponding isomorphic subgraph in the configuration of the corresponding logic circuit. This allows to detect persistable structural embeddings charac- terizing logical errors in the feeding of electronic content to IETM for aircraft maintenance and repair from the list / database of predetermined anomalous logic substructures. The proposed method for detecting IETM quality anomalies in application to aircraft maintenance and repair is both a methodological toolkit and an extensive basis for design of suitable software models for automatic procedures of valid structure and content correction in concrete interactive electronic technical manuals.
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Modeling of spectroerergetic characteristics of space objects in the optical range
Статья научная
In connection with the emergence of abnormal situations at the stage of launching space vehicles (SV) for various purposes (AngoSat-1, Telkom-3, Phobos-Grunt, etc.), the problems of timely detection of such situations and remote monitoring of the technical condition of SV are of vital importance. To assess the feasibility of solving this class of problems with the use of optronic equipment (OE), it is necessary to have a priori information on the spectroenergetic characteristics (SEC) of a SV and associated backgrounds for the projected angles and conditions of observation in the operational spectral ranges of the OE taking into account the illumination by the Sun and the Earth. Due to the adapta- bility of mathematical modeling to the high degree of variability of the above factors, this method can be considered as a rational one for obtaining dynamic SEC (signatures) of SV for observation conditions that change during an or- bital flight. The technology of SEC modeling of space objects (SO) with the use of FemRad dedicated software (DS) is pre- sented, which provides the production of SO SEC taking into account the indicatrices of the scattering of optical radia- tion from materials and coatings of the external surface of the object, the dynamics of its thermal regime and the condi- tions of illumination by the Sun and Earth during the orbital flight. The advantage of the presented technology is the compatibility of the developer’s own software solutions with the widespread application programs of finite element analysis. In particular, the known CAD and CAE tools - SolidWorks, ANSYS, Gmsh - are used to develop grid geometric 3D models of SO. The method for parametric approximation of the measured indicatrices of scattering of optical radiation from mate- rials and coatings of SO on the basis of a given model of roughness is considered. The main provisions of the DS meth- odology for calculating the heat flux of the “Earth-atmosphere” system, as well as the fluxes of reflected and scattered solar radiation falling on the SO in the range 0.2-20 µm, are presented. The results of modeling the dynamic SEC of a typical SO in the infrared (IR) range are given as an illustration of the application of the DS.
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Статья научная
The article discusses formalization of the problem of heterogeneous distributed information processing systems (HDIPS) software and hardware configuration management. A formal description of possible optimality criteria for the HDIPS software and hardware configuration is given. The HDIPS model in terms of queuing theory is proposed. The problem of allocating the HDIPS computational resources is formulated as a transport problem according to time criterion with atomic needs. The algorithm for solving this problem is proposed and the boundaries of its applicability to the HDIPS are determined. To meet the selected optimality criterion, the analysis of the HDIPS software and hardware configuration applying its formal model, using the queuing theory methods is presented. HDIPS is presented as a queuing network, where each computing node and route control unit is a mass service system. The problem of computing resource allocation in HDIPS is presented as a transport problem according to the time criterion with atomic needs. The least time algorithm for indivisible needs takes into account the indivisibility condition.
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Multi-grid finite elements in calculations of multilayer oval cylindrical shells
Статья научная
The method of finite elements (FEM) is actively used in calculations of composite shell constructions (rotation shells, circle and oval cylindrical shells), which are widely used in space-rocket and aviation equipment. To calculate multi-layer oval cylindrical shells three-dimensional curvilinear Lagrange multi-grid finite elements (MGFE) are suggested. When building a k-grid finite element (FE), k nested grids are used. The fine grid is generated by the basic split of MGFE that takes into account its complex heterogeneous structure and shape. On k-1 large grids the move functions used for decreasing MGFE dimension are determined. The stress-strain state in MGFE is described by the elasticity theory three-dimensional task equations (without introduction of additional hypotheses) in local Cartesian coordinates systems. The procedure of building shell-type Lagrange MGFE with the use of Lagrange polynomials presented in curvilinear coordinate systems is demonstrated. With the size reduction of discrete models MGFE have constant thickness equal to the thickness of the shell. The Lagrange polynomials nodes coincide in thickness with the MGFE large grid nodes and are located on the shared borders of different module layers. The use of such MGFE generates approximate solutions sequences that uniformly and quickly converge to precise solutions. The main advantages of MGFE are as follows: they form discrete models with the dimension 102-106 times smaller than the basic models dimension and they generate small error solutions. Examples of calculations are given for four- and three-layer oval shells of various thickness and shape under both uniform and local loading with the use of 3-grid FE. Comparative analysis of the obtained solutions with the solutions built with the help of the software package ANSYS shows high efficiency of the suggested MGFE in calculations of multi-grid oval shells.
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Multilevel evaluation of quality interactive electronic technical manuals for aviation technology
Статья научная
The method of multi-level quality assessment of interactive electronic technical manuals (IETM) for aircraft con- tains the main approaches, methodological and logical-mathematical tools for the implementation of multiparameter evaluation of the quality of electronic content of these manuals. The paper postulated that the goal of assessing the quality of IETM for aviation equipment is to obtain a consolidated conclusion on the degree of satisfaction of the need to create interactive electronic technical manuals in the conditions of vagueness of the initial expert data used for evaluation. It is shown that the quality assessment of interactive electronic technical manuals for the operation and repair of aviation equipment is obviously linked to non-numeric or “soft” measurements, due to the fuzzy nature of the initial qualimetric data obtained from an expert. In this version, “measurement” should be understood as a manipulation in which some strictly ordered quality gradations correlate in accordance with the IETM for the operation and repair of aviation equipment properties. In the role of quantitative measurement results, not only real numbers are considered, but also other algebraic groups that necessarily have an order relation between their elements, that is, a similarity of the inequality relation between numbers. The multi-level quality assessment of interactive electronic technical manuals for aeronautical engineering consists of the following steps: 1. Imagery of numerical vectors of values of elementary quality indicators; 2. Calculation of ranks that determine the significance of quality indicators in their compositions based on fuzzy and (or) insufficient initial data on the compositional significance of more particular indicators in the composition of more aggregated indi- cators: 3. Calculation of elementary indicators values and ratings of importance based on numerical vectors, for the analyzed performance of IETM on the operation and repair of aircraft, the values of the integral quality indicator, as the weighted arithmetic average of mathematical similar to a particular indicators.
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Nonparametric identification of dynamic systems under normal operation
Статья научная
The research gives nonparametric identification algorithms under the conditions of incomplete a priory information. The identification case differs from the previously known ones due to the fact that, besides the control action, an uncontrollable variable, but a measurable one, impacts on the object input. In contrast to parametric identification, the research considers the situation when the equations describing dynamic objects are not given with accuracy to the parameters. In this case, there are some features to study while getting the recovery characteristics of various object channels. The main characteristic is that the transition response of a channel is taken when the other channel is in a stable position. Moreover, the identification problem is analyzed under normal object operation, opposite to the previously known nonparametric approach based on Heaviside function input to the object and further Duhamel integral application. An arbitrary signal is input to the object during normal operation as a result we have a corresponding response of the object output. It should be noted that the measurements of the input and output variables are carried out with random noise. As a result, we have a sample of input-output variables. As linear dynamical system can be described by the Duhamel integral, with known input and output object variables, corresponding values of the weight function can be found. This is achieved by discrete representation of the latter. Having such realization, nonparametric estimate of the weight function in the form of the nonparametric Nadaraya-Watson estimate is used later. Substituting this with the Duhamel integral, we obtain a nonparametric model of a linear dynamical system of unknown order. The article also describes the case of constructing nonparametric model when a delta-shaped function is input to the object. It is interesting to find out how delta-shaped function might differ from the delta function. The weight function is determined in the class of nonparametric Nadaraya-Watson estimates. Previously proposed nonparametric algorithms consider the case when Heaviside function is applied to the object; this narrows the scope of nonparametric identification practical use. It is important to construct nonparametric model of the dynamic object under conditions of normal operation.
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On necessary and sufficient conditions of simply reducibility of wreath product of finite groups
Статья научная
A finite group is considered to be real if all the values of its complex irreducible characters lie in the field of real numbers. We note that the above reality condition is equivalent to the fact that each element of the group is conjugate to its inverse. A finite group is called simply reducible or a SR-group if it is real and all the coefficients of the decomposition of the tensor product of any two of its irreducible characters are zero or one. The notion of a SR-group arose in the paper of R. Wiener in connection with the solution of eigenvalue problems in quantum theory. At present, there is a sufficient amount of literature on the theory of SR-groups and their applications in physics. The simplest examples of SR-groups are elementary Abelian 2-groups, dihedral groups, and generalized quaternion groups. From the point of view of a group theory questions of interest are connected first of all with the structure of simply reducible groups. For example A. I. Kostrikin formulated the following question: how to express the belonging of a finite group to the class of SR-groups in terms of the structural properties of the group itself. Also, for a long time it was not known whether a simply reducible group is solvable (S. P. Stunkov's question). A positive answer to the last question was obtained in the works of L. S. Kazarin, V. V. Yanishevskiy, and E. I. Chankov. Questions concerning the portability of the properties of a group to subgroups, factor groups, and also their preservation in the transition to direct (Cartesian) and semidirect products or wreath products are always of interest. The paper proves that the reality of H is the necessary condition of simply reducibility of the wreath product of the finite group H with the finite group K and the group K must be an elementary Abelian 2-group. We also indicate sufficient conditions for simply reducibility of a wreath product of a simply reducible group with a cyclic group of order
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