Informatics, computer technology and management. Рубрика в журнале - Siberian Aerospace Journal
6-aperiodic words over the three-letter alphabet
Статья научная
The work is devoted to the study of sets of aperiodic words over a finite alphabet. A set of such words can be considered as some kind of finite formal language. W. Burnside raised the issue of local finiteness of periodic groups. The negative answer was given only sixty years later by E. S. Golod. Soon S. V. Aleshin, R. I. Hryhorczuk, V. I. Sushchanskii constructed more examples confirming the negative answer to Burnside's question. Finiteness of the free Burnside group of period n was established for periods two and three (W. Burnside), for period four (W. Burnside, I. N. Sanov), for period six (M. Hall). The infinity of such a group, for odd indicators exceeding 4381, is established in the work of P. S. Novikov and S. I. Adyan (1967), and for odd indicators exceeding 664 in the book by S. I. Adian (1975). A more intuitive version of the proof for odd n > 1010 was proposed by A. Yu. Olshansky (1989). In this article, we consider the set of 6-aperiodic words. In the monograph by S. I. Adyan (1975) it was shown the proof of S. E. Arshon (1937) theory that there are infinitely many three-aperiodic words of any length in the two-letter alphabet. In the book of A. Y. Olshansky (1989), a proof of the infinity of the set of six-aperiodic words is given and an estimate of the number of such words of any given length is obtained. Here we try to estimate the function of the number of six-aperiodic words of any given length in a three-letter alphabet. The results obtained can be useful for encoding information in space communication sessions.
Бесплатно
A routing algorithm for the Cayley graphs generated by permutation groups
Статья научная
The purpose of this work is to create an effective routing algorithm on the Cayley graphs of permutation groups, superior in its characteristics to an algorithm using an automatic group structure. In the first section of the article we describe the auxiliary algorithm A–1 which allows numbering elements of a given permutation group. In the second section we present the algorithm A–2 for calculating the routing table on the Cayley graph and algorithm A–3 for determination the optimal route between two arbitrary vertices of the graph. Estimates of time and space complexity are also obtained for these algorithms. In the third section we describe the algorithm A–4 for calculation the minimal word of a group element. It is proved that the computational complexity of the algorithm will be proportional to the length of the input word. The fourth section presents the results of computer experiments for some groups of permutation groups, which compare the time for calculating the minimum words using algorithm A – 4 and an algorithm based on the construction of an automatic group structure. It is shown that A – 4 is much faster than its competitor.
Бесплатно
About non-parametric identification of partial-parametred discrete-continuous process
Статья научная
The paper considers a new class of models under conditions of incomplete information. We are talking about multidimensional discrete-continuous processes for the case where the components of the vector of output variables are stochastically dependent. The nature of this dependence is a priori unknown, but for some channels the a priori information corresponds to both nonparametric and parametric type of the initial data in the process under study. Such a situation leads to a system of nonlinear equations, some of which will be unknown, while others are known accurate to the vector of parameters. The main purpose of the model is to determine the forecast of output variables with known input, and for implicit nonlinear equations it is only known that one or another component of the output depends on other variables that determine the state of the object. Thus, a rather nontrivial situation arises when solving a system of implicit nonlinear equations under conditions where in one channel of a multidimensional system equations themselves are not in the usual sense, while in others they are known up to parameters. Therefore, an object model cannot be constructed using the methods of the existing identification theory as a result of a lack of a priori information. If it was possible to parameterize the system of nonlinear equations, then with a known input this system should be solved, since it is known and the parameterization stage is over. However, in this case it is still necessary to evaluate parameters. The main content of this article is the solution of the identification problem in the presence of a partially-parameterized discrete-continuous process, despite the fact that the parameterization stage cannot be overcome without additional a priori information on the process under study. In this regard, the scheme for solving the system of nonlinear equations can be represented as a certain sequential algorithmic chain. First, on the basis of the available training sample, including all components of the input and output variables observation, a residual vector is formed. After that, an estimate of the object output with known values of the input variables is constructed based on the estimates of Nadarai-Watson. Thus, for given values of the input variables of such a process, it is proposed to carry out a procedure for evaluating the forecast of output variables in accordance with the developed algorithmic chain. Numerous computational experiments, studying the proposed models of partially-parameterized discrete-continuous processes have shown their rather high efficiency. The article presents the results of computational experiments illustrating the effectiveness of the proposed technology for predicting values of output variables from known input variables.
Бесплатно
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.
Бесплатно
Статья научная
The subject of research of this paper is anomalies in the final products of the International GNSS Service (IGS), namely in the orbits and clock drifts of navigation satellites (NSs). The purpose of research is to de-termine the influence of such anomalies on the accuracy of solving the precise point positioning (PPP) problem. The method of approximation by polynomials of high degrees previously proposed by the authors is used as a method for detecting and distinguishing anomalies in the orbits of navigation satellites. The methodology recommended by the IGS is used in solving the PPP problem. The proposed method for de-tecting and distinguishing anomalies in orbits is applied to the analysis of anomalies in the orbits of GPS navigation satellites. The examples of anomalies that can be detected using the proposed method are dem-onstrated. The brief statistical analysis and comparison of the frequencies of anomalies occurrence in the orbits of GPS navigation satellites published by various IGS analytical centers from 2010 to 2018 are pre-sented. It is shown that orbital anomalies occurring at the boundaries of daily intervals are, as a rule, cor-related with anomalies in clock drifts and have a partially mutually compensating effect on the solution of navigation problems. Experiments showed that when solving the PPP problem, anomalies significantly in-crease the root-mean-square deviation (RMSD) of the solution residual. Two options for solving the prob-lem with anomalous orbits are considered: the exclusion of satellites with anomalous boundaries of daily intervals from the solution and the "correction" of the anomaly in the orbit. The most natural method of correcting orbits (changing the orbit in order to remove large anomalies) at the boundaries of the daily segments of the published final orbits was tested. The exclusion of satellites with anomalies in the orbit turned out to be the most effective from the point of view of PPP problems, since attempts to "correct" the orbit more often led not to a decrease in the RMSD of the pseudorange residuals, but to its increase, which is associated with correlated anomalies in the navigation satellite clock drift. According to the research results, we can conclude: before solving the PPP problems, it is necessary to study the orbits and the navi-gation satellites clocks drifts for the presence of anomalies by the proposed methods and, if possible, to exclude such satellites from the data used to solve the PPP problem. Our proposed methods for detecting and accounting for anomalies in the orbits and clocks of navigation satellites, in addition to obvious appli-cations to solving ground navigation problems, are also applicable to monitoring the quality of the space and ground segments of the GLONASS and GPS systems.
Бесплатно
Статья научная
In this article authors are considering information security data integrity problem relevant for electronic archive management. In high-tech industry large electronic photo archives arise as a part of quality management. Photofixation applied for responsible operations control, documenting technological process, fixing the components state on input and output control, incongruities registration. An image substitution or reuse possibility makes necessary electronic archive proto document integrity control. These illegal actions can be both the result of an operator’s mistake and motivated by intentional defect concealment. As a solution authors suggest an electronic archive organizing method for storing photo documents. The method based on a digital watermark labeling of full-color images with orthogonal Zernike moments calculated for certain image points (and their neighborhoods). Suggested method can prevent watermark destruction by geometric image transformation (rotation, compressing, reflection etc.). Digital watermark contains both information about technological process on current image and information about other images – this fact allows talking about integrity of the whole photo documents set. One of the most important method characteristic is image format invariability and making additional metadata files unnecessary which allows user to apply standard software for a further work with photo document.
Бесплатно
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.
Бесплатно
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 software, 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.
Бесплатно
Attribute features application in specification of regression model of apartments cost
Статья научная
In the study of statistical data with a pronounced endogenous variable, it is necessary to identify factors (explanatory variables) that have a strong impact on the result. In this, factors can be both quantitative and attributive. To assess influence of numerical features, regression analysis methods can be used. Influence of attributive features is not taken into account. However, often these are they who make the decisive contribution to variation of the result. It is necessary to develop methods for analyzing influence of attributive features and accounting for these features in regression models. On the example of sets of apartments proposed for sale in the city of Krasnoyarsk, a new method is used to assess influence of attributive features on the quantitative using ranking them in accordance with their influence on the endogenous variable. Method of fictitious variables is used to analyze the attribute features. Each attribute with m values is assigned (m-1) dummy variables and a regression model is constructed. Influence of exogenous variables can be expressed using standardized regression coefficients. In this case, influence of attributes can be estimated by cumulative correlation coefficient calculated on the basis of a regression model with fictitious variables. For further research, set is proposed to rank, assigning each element a "rank" – value of a standardized coefficient which reflects closeness of the relationship with the endogenous variable. Thus, all features have a numerical value. A standardized regression model is constructed. Proposed approach can be used in the analysis of statistical aggregates, units of which are characterized by quantitative and attributive features.
Бесплатно
Статья научная
For successful technological process in automated control systems it is necessary to maintain technological parameters constantly at the required level, which is ensured by the use of automated process control systems (APCS). The classical solution of this problem is the application of control devices of various types, the choice of which directly depends on the system under consideration and the requirements to it. The leading position among the automatic control system regulators for the last decades belongs to the proportional-integral-differentiating (PID) regulator, which efficiency of application in the technological process is defined by the speed and accuracy of its work. These qualities directly depend on the correct setting of the regulator parameters. The synthesis of regulators requires using of modern computer-aided design systems. The article presents the method of automatic setting of PID-regulator of the dynamic system of high order with negative feedback on the example of automatic room temperature control system. The modern Russian environment of dynamic simulation of technical systems SimInTech applied at a number of nuclear, oil refining and aerospace enterprises is used as the environment for system model development, as well as the process of its analysis and optimization. The main components of the system and transfer functions of its elements are presented. The stepby- step description of the process of project construction from standard software blocks and submodels, interacting through a single database with the use of built-in programming language, is described. The use of the built-in block of SimInTech visual simulation environment optimization for automated search of PID-regulator parameters is described in details and illustrated. The advantages and disadvantages of this adjustment method revealed during the project implementation are listed.
Бесплатно
Статья научная
Modern and promising dynamic systems of aviation weapon systems of the Aerospace Forces (hereinaf-ter for brevity in the text – the system) are characterized by a more complex structure and increased re-quirements for reliability and efficiency of functioning. Moreover, systems of generation 4 ++ and 5 are quite unique and (or) small-scale, and their constituent elements are basically miniature and expensive, therefore, a prerequisite for fulfilling the requirements for traceability to systems and constituent elements is the maximum possible preservation of the quality of the initial basis with the inevitable new interpreta-tion of additional information. Further introduction of artificial intelligence technologies into the practice of solving problems of technical diagnostics makes it possible to obtain adequate results with almost any accuracy. The reliability of the results will be determined solely by the punctuality of the data assignment and the completeness of the mathematical description of systems, processes and events in the subject area under consideration. Therefore, it should be expected that the further development of the theory and prac-tice of technical diagnostics will follow the path of a deeper study of the physical processes occurring in systems, and a more accurate mathematical specification of procedures for finding the place of failure of systems. The aim of the work is to establish the development of an interconnected set of mathematical and logical block diagrams for obtaining and applying diagnostic knowledge in the software and mathematical support of modern and advanced onboard means of monitoring the technical state of systems. The priority direction in such studies is the differentiated selection of approved methods of technical diagnostics with the choice of the appropriate mathematical and algorithmic apparatus for direct probabilistic modeling of systems. A block diagram is presented and a variant of the practical application of the developed algorithm for sequential recognition of system failures (hereinafter referred to as an algorithm, if it is clear from the context of the presentation of the material that it is the developed algorithm) is considered. By using the algorithm, there is no need for decomposition of systems, and the potential for multiple repetitions of the results of a random process of changing the technical states of systems predetermines the possibility of ob-taining large samples with high accuracy of software compilation.
Бесплатно
Comparison of methods for initializing starting points on the optimization genetic algorithm
Статья научная
The way to initialize the starting points for optimization algorithms is one of the main parameters. Currently used methods of initializing starting points are based on stochastic algorithms of spreading points. In a genetic algorithm, points are Boolean sets. These lines are formed in different ways. They are formed directly, using random sequences (with uniform distribution law) or formed using random sequences (with uniform distribution law) in the space of real numbers, and then converted to boolean numbers. Six algorithms for constructing multidimensional points for global optimization algorithms of boolean sets based on both stochastic and non-random point spreading algorithms are designed. The first four methods of initialization of Boolean lines used a random distribution law, and the fifth and sixth methods of initialization used a non-random method of forming starting points-LP sequence. A large number of optimization algorithms were restarted. Calculations of high accuracy were used. The research was carried out on the genetic algorithm of global optimization. The work is based on Acly function, Rastrigin function, Shekel function, Griewank function and Rosenbrock function. The research was based on three algorithms of srarting points spreading: LP sequence, UDC sequence, regular random spreading. The best parameters of the genetic algorithm of global optimization were used in the work. As a result, we obtained arrays of mathematical expectations and standard deviations of the solution quality for different functions and optimization algorithms. The purpose of the analysis of ways to initialize the starting points for the genetic optimization algorithm was to find the extremum quickly, accurately, cheaply and reliably simultaneously. Methods of initialization were compared with each other by expectation and standard deviation. The quality of the solution is understood as the average error of finding the extremum. The best way of initialization of starting points for genetic optimization algorithm on these test functions is revealed.
Бесплатно
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. Pre-tensioning 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.
Бесплатно
Constraint handling genetic algorithm for feature engineering in solving classification problems
Статья научная
Feature engineering in machine learning is a promising but still insufficiently studied direction. Creating new feature space from an original set allows to increase accuracy of the machine learning algorithm chosen to solve complex data mining problems. Some existing selection methods are capable of simultaneously increasing accuracy and reducing feature space. The reduction is an urgent task for big data problems. The paper considers a new machine learning approach for solving classification problems based on feature engineering methods. The design of informative features is carried out using extraction and selection methods. Based on the initial data, new sets of characteristics have been created, which include the original characteristics and characteristics obtained by the method of principal components. The choice of an effective subset of informative features is implemented using a genetic algorithm. In order to avoid overfitting and the creation of trivial classifiers, restrictions are imposed on the fitness function of the genetic algorithm, requiring a certain number of features of the original sample, as well as a certain number of features obtained by the principal component method. A comparative analysis of efficiency of the following classification algorithms is carried out: k-nearest neighbors, support vector machine, and a random forest. Efficiency research experiments are carried out by solving applied binary classification problems from the UCI Machine Learning repository of machine learning problems. The macro F1-score was chosen as an efficiency criterion. The results of numerical experiments show that the proposed approach outperforms the solutions obtained using the original data set and the performance of random feature selection (the low bound for the results). Moreover, the accuracy enhancement is obtained for all types of problems (data sets that have more features than values). All results are proved to be statistically significant.
Бесплатно
Статья научная
The article examines the role of information technology at industrial enterprises of the rocket and space industry, provides the results of the analysis of scientific sources to organize information support systems for making management decisions, an analysis of existing methods for constructing management account-ing at enterprises and methods of its automation. Conclusions are made about the insufficient elaboration of the studied solutions, both from the point of view of the logic of the organization of accounting, and from a technical point of view. The main tasks of the information support system, methods of forming effective management accounting and the goals of its implementation are determined. An approach to create an in-formation support system in the form of a built-in control database in the form of an OLAP solution is pro-posed, through which functional information systems are integrated, and detailed management accounting related to accounting and tax accounting is built into a single system in a single information space. The article describes the advantages of implementing the proposed system, which allows for a comprehensive retrospective and operational analysis of the current state of the processes oc-curring at the enterprise with a monetary value using SQL tools with a high degree of confidence in the data. The principles of creating elements of the information system for the subsequent effective plan-fact analysis and development of management decisions are discussed. A diagram of the organization of a sin-gle information space and a system that provides information support for enterprise management processes is given, the main information flows are considered. The logic of maintaining the process of forming a structured data warehouse is described, while automating the financial and economic part of the auto-mated control system based on the presented method of organizing data, which allows to link management, accounting and tax accounting with one source of relevant data, while creating an effective OLAP solution. An illustrative example of the organization of data in the form of linking the reflections of primary documents by means of a database using the proposed method, which provides the possibility of operational analysis of receivables and payables and the implementation of preliminary financial control-ling, is given. The research provides examples of user interfaces from the developed information support system based on the described methods of data organization. Conclusions are made about the effectiveness of the proposed solution.
Бесплатно
Статья научная
The original method for encoding binary data streams based on QPSK quadrature phase shift keying in a wireless optical communication channel in the visible range is suggested. The algorithm for analyzing signals in the receiving tract is presented. It allows to analyze the presence of two or three pulses of different colors at the input, which will signal the presence of interference or the occurrence of "illumination". In addition, the algorithm provides a possibility of dynamic compensation of external "illumination" by changing the gain of the photodetectors and adjusting the brightness of emitting LEDs. The functional scheme of the device for realization of the offered coding method in the wireless channel on the basis of optical radiation has been developed. Given that most photodiodes are sufficiently wide-band in the visible range of light waves, to increase sensitivity of each color channel and selectivity of the receiving tract it is necessary to apply optical filters for each color channel. The most effective are interference filters made of optically transparent materials with different physical characteristics. The approach for calculating optical filters has been presented.
Бесплатно
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.
Бесплатно
Efficiency improving of emergency monitoring and forecasting based on the information system
Статья научная
The article is devoted to the automated information system modification to solve monitoring and forecasting problems of natural and man-made emergencies in order to increase the efficiency of its functioning, namely, to increase the execution speed of the main operations, to reduce the error probability. Monitoring and forecasting of emergencies are among the priorities in the field of population from emergencies protection, as the prevention and elimination of their consequences are carried out on the basis of these tasks. At the same time, the data collection speed, processing and analysis largely determine the efficiency of the obtained results. The existing system of monitoring and forecasting of natural and man-made emergencies, its functional model in IDEF0 notation, characteristic features, advantages and disadvantages are considered. The existing system can be improved by automating a number of tasks related to the processing, transmission and storage of large data amounts, including real time data, as well as the generation of consolidated reports on the results of monitoring and forecasting of various objects. The information architecture of the solution reviewed and the corresponding database model form the basis of the proposed solution. The IDEF0 model of emergency monitoring and forecasting has been introduced taking into account the proposed modification of the automated information system. The main operation execution time comparative analysis based on the initial and modified automated information system (AIS) using the existing hardware confirms the effectiveness of the proposed solution. Data exchange and generation automation of consolidated reports on multiple monitoring objects will simplify analysis of the obtained results and solutions development based on them aimed at prevention of natural and man-made emergencies, as well as elimination of their consequences.
Бесплатно
Elastic-plastic problem in the case of inhomogeneous plasticity under complex shear conditions
Статья научная
In this research, the authors solved a two-dimensional elastic-plastic problem of the stress state under com-plex shear conditions in the body weakened by a hole that is bounded by a piecewise smooth contour. The stress state of a complex shear occurs in a cylindrical body of infinite length under the action of loads directed along the cylinder generators and constant along the generators. At the same time, with a sufficiently large load, both elastic and plastic zones appear in the body. As in any problem of this kind, it is necessary to find a previously unknown boundary separating the elastic and plastic zones. Finding such a boundary is not an easy task, but the specificity of elastic-plastic problems of complex shear is that solving such problems is easier than solving simi-lar elastic problems. Apparently, for the first time this fact was noted by G. P. Cherepanov. A lot of research is devoted to elastic-plastic problems of complex shear in the case of homogeneous and iso-tropic plasticity. All articles that solve complex shear problems essentially use the representation of stresses and displacements in the elastic zone in a complex form. In this research, the problems of complex shear are solved using conservation laws. It is assumed that the yield strength is a function of the coordinates of the point where the stress state is being studied. It is known that the elastic properties of structural materials can be homogene-ous and isotropic, while their yield point and strength are inhomogeneous. This situation is observed, for exam-ple, in the case of neutron bombardment of structural materials. This research will examine exactly this situa-tion. The article presents conservation laws for equations describing a complex shear. It was assumed that the components of the conserved current depend on the components of the stress tensor and coordinates. The com-ponents of the stress tensor are included in them linearly. The problem of finding the components of the con-served current was reduced to the Cauchy-Riemann system. The solution of this system allowed us to reduce the calculations of the stress tensor components to a curvilinear integral along the contour of the hole and thus find the boundary between the elastic and plastic areas.
Бесплатно
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 goodness 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 presented.
Бесплатно
