Pub Date : 2023-01-01DOI: 10.21638/11701/spbu10.2023.103
Aleksandr N. Prokaev
The paper considers the relationship between search theory and information theory. The traditional problem of search theory is to develop a search plan for a physical object in the sea or on land. The search plan has to develop the distribution of available search resources in such a way that the probability of detection the search object is to be maximum. The optimal solution is traditionally considered as so-called "uniformly optimal search plan", which provides a uniform distribution of the posterior probability of the location of the object as the search is conducted. At the same time, optimality simultaneously according to the criteria of maximum detection probability and equality of a posteriori probability is possible only for the exponential detection function, which is used most often in search theory. For other kinds of detection functions, the optimal solutions according to the specified criteria do not match. In this paper, the approach to this problem is considered on the basis of the maximum entropy principle. For a situation of discrete distribution, it is shown that, within the framework of information theory, the search problem has a simpler solution that does not depend on the kind of the detection function.
{"title":"The maximum entropy principle in search theory","authors":"Aleksandr N. Prokaev","doi":"10.21638/11701/spbu10.2023.103","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.103","url":null,"abstract":"The paper considers the relationship between search theory and information theory. The traditional problem of search theory is to develop a search plan for a physical object in the sea or on land. The search plan has to develop the distribution of available search resources in such a way that the probability of detection the search object is to be maximum. The optimal solution is traditionally considered as so-called \"uniformly optimal search plan\", which provides a uniform distribution of the posterior probability of the location of the object as the search is conducted. At the same time, optimality simultaneously according to the criteria of maximum detection probability and equality of a posteriori probability is possible only for the exponential detection function, which is used most often in search theory. For other kinds of detection functions, the optimal solutions according to the specified criteria do not match. In this paper, the approach to this problem is considered on the basis of the maximum entropy principle. For a situation of discrete distribution, it is shown that, within the framework of information theory, the search problem has a simpler solution that does not depend on the kind of the detection function.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"55 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81046562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21638/11701/spbu10.2023.213
Elizaveta A. Kalinina, A. M. Kamachkin, N. Stepenko, G. Tamasyan
The rank of the Kalman’s controllability matrix of linear systems depends on the bases of the invariant cyclic subspaces of the state matrix generated by the columns of the input matrix. The case of the Jordan form of the state matrix and scalar control is studied in detail. It is shown that the dimension of cyclic subspaces is determined by the index numbers of the first non-zero elements of the coordinate blocks of the columns of the input matrix. The formation of the bases of these subspaces is completely disclosed. Based on this, the basis of the space of a constructive control system is constructed.
{"title":"On the question of a constructive controllability criterion. Pt I. Cyclic invariant subspaces","authors":"Elizaveta A. Kalinina, A. M. Kamachkin, N. Stepenko, G. Tamasyan","doi":"10.21638/11701/spbu10.2023.213","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.213","url":null,"abstract":"The rank of the Kalman’s controllability matrix of linear systems depends on the bases of the invariant cyclic subspaces of the state matrix generated by the columns of the input matrix. The case of the Jordan form of the state matrix and scalar control is studied in detail. It is shown that the dimension of cyclic subspaces is determined by the index numbers of the first non-zero elements of the coordinate blocks of the columns of the input matrix. The formation of the bases of these subspaces is completely disclosed. Based on this, the basis of the space of a constructive control system is constructed.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"10 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87925982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21638/11701/spbu10.2023.209
V. Mazalov, V. Khitraya
A method for ranking the vertices of a graph based on Kirchhoff’s laws for determining the potentials of an electrical network is proposed. The graph is represented as an electrical network, where the edge weights are interpreted as electrical conductivities. Next, the current is supplied to one of the vertices, and the absolute potentials of all vertices are determined by the Kirchhoff method. Based on the obtained potential values, the vertices are ranked. Then the current is sequentially applied to all vertices and the ranking is performed each time. For the final ranking, it is proposed to apply the ranking procedure based on the tournament matrix. The operation of the ranking algorithm is illustrated by numerical examples related to graphs of specific transport networks.
{"title":"Graph vertices ranking using absolute potentials of electric circuit nodes","authors":"V. Mazalov, V. Khitraya","doi":"10.21638/11701/spbu10.2023.209","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.209","url":null,"abstract":"A method for ranking the vertices of a graph based on Kirchhoff’s laws for determining the potentials of an electrical network is proposed. The graph is represented as an electrical network, where the edge weights are interpreted as electrical conductivities. Next, the current is supplied to one of the vertices, and the absolute potentials of all vertices are determined by the Kirchhoff method. Based on the obtained potential values, the vertices are ranked. Then the current is sequentially applied to all vertices and the ranking is performed each time. For the final ranking, it is proposed to apply the ranking procedure based on the tournament matrix. The operation of the ranking algorithm is illustrated by numerical examples related to graphs of specific transport networks.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"23 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90630479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21638/11701/spbu10.2023.208
G. Kurbatova, V. A. Klemeshev
An efficient method for calculating the location of stationary gas leakage in wells and gas pipelines with medium and ultra-high pressures is presented. An algorithm for constructing the dependence of the compressibility factor of the gas mixture with a predominance of methane in the region of ultra-high pressures based on experimental data of pressure and temperature is proposed. The algorithm for calculating the leakage location is based on the Bellman method of quasi-linearization of nonlinear problems, with an additional hypothesis of the linear dependence of pressure and temperature on the leakage location coordinates used at each iteration. The issue of selecting the initial approximation is considered, and the advantage of calculating the initial approximation using a simplified non-isothermal flow model is justified. Examples of solving practical problems of high interest are given, and the high accuracy of calculating the gas leakage location using the proposed algorithm in gas pipelines with medium pressures (around 9 MPa) and ultra-high pressures (around 20 MPa) for small and medium gas leaks is demonstrated.
{"title":"Identification of low and medium intensity gas leakage location in medium and ultra-high pressure gas pipelines","authors":"G. Kurbatova, V. A. Klemeshev","doi":"10.21638/11701/spbu10.2023.208","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.208","url":null,"abstract":"An efficient method for calculating the location of stationary gas leakage in wells and gas pipelines with medium and ultra-high pressures is presented. An algorithm for constructing the dependence of the compressibility factor of the gas mixture with a predominance of methane in the region of ultra-high pressures based on experimental data of pressure and temperature is proposed. The algorithm for calculating the leakage location is based on the Bellman method of quasi-linearization of nonlinear problems, with an additional hypothesis of the linear dependence of pressure and temperature on the leakage location coordinates used at each iteration. The issue of selecting the initial approximation is considered, and the advantage of calculating the initial approximation using a simplified non-isothermal flow model is justified. Examples of solving practical problems of high interest are given, and the high accuracy of calculating the gas leakage location using the proposed algorithm in gas pipelines with medium pressures (around 9 MPa) and ultra-high pressures (around 20 MPa) for small and medium gas leaks is demonstrated.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"15 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90180270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21638/11701/spbu10.2023.108
I. V. Olemskoy, O. S. Firyulina
The paper proposes an algorithm for solving the configuration-optimization coloring problem for square (0,1)-matrices, which is based on the method of selection their structural features. The algorithm belongs to the method's of backtracking, however, the construction of the optimal solution is carried out among the options that provide a certain configuration, due to which the size of the search tree is significantly reduced. A detailed scheme of its operation is given, and the effectiveness of the solution is demonstrated by the example of calculating the chromatic number of a specific (0,1)-matrix.
{"title":"Algorithm for optimal coloring of square (0,1)-matrices","authors":"I. V. Olemskoy, O. S. Firyulina","doi":"10.21638/11701/spbu10.2023.108","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.108","url":null,"abstract":"The paper proposes an algorithm for solving the configuration-optimization coloring problem for square (0,1)-matrices, which is based on the method of selection their structural features. The algorithm belongs to the method's of backtracking, however, the construction of the optimal solution is carried out among the options that provide a certain configuration, due to which the size of the search tree is significantly reduced. A detailed scheme of its operation is given, and the effectiveness of the solution is demonstrated by the example of calculating the chromatic number of a specific (0,1)-matrix.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"136 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73662305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21638/11701/spbu10.2023.107
S. Kostyrko, B. Shershenkov
This paper examines the ability to employ the model of a wrinkled thin film coating under plane strain conditions for the generation and manipulation of sounds. It is assumed that the film-on-substrate structure represents a multilevel system consisting of four phases with different elastic properties such as surface layer, film material, interphase and substrate material. The undulation of surface and interface geometry leads to the complex stress state of the film coating resulting from the superposition of two perturbed stress fields evolved near the curved surface and interface. The analysis of the stress state reveals the periodic distribution of the longitudinal stresses smoothly changing from surface to interface. This facilitates the creation of a sound synthesis technique similar to the timbre morphing method which provides the transition between two waveforms while creating new intermediate waveform during this process. The perspective of using the wrinkled thin film model for sound generation is gained by its complex behavior, where the influence of one parameter on the stress distribution is affected by other parameters, which in turn reflects in the rich sound morphologies during the mapping of the stress oscillations onto sound.
{"title":"Sound synthesis approach based on the elastic stress analysis of a wrinkled thin film coating","authors":"S. Kostyrko, B. Shershenkov","doi":"10.21638/11701/spbu10.2023.107","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.107","url":null,"abstract":"This paper examines the ability to employ the model of a wrinkled thin film coating under plane strain conditions for the generation and manipulation of sounds. It is assumed that the film-on-substrate structure represents a multilevel system consisting of four phases with different elastic properties such as surface layer, film material, interphase and substrate material. The undulation of surface and interface geometry leads to the complex stress state of the film coating resulting from the superposition of two perturbed stress fields evolved near the curved surface and interface. The analysis of the stress state reveals the periodic distribution of the longitudinal stresses smoothly changing from surface to interface. This facilitates the creation of a sound synthesis technique similar to the timbre morphing method which provides the transition between two waveforms while creating new intermediate waveform during this process. The perspective of using the wrinkled thin film model for sound generation is gained by its complex behavior, where the influence of one parameter on the stress distribution is affected by other parameters, which in turn reflects in the rich sound morphologies during the mapping of the stress oscillations onto sound.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"134 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74484630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21638/11701/spbu10.2023.101
A. Ekimov, A. P. Zhabko, P. Yakovlev
The article considers an uncontrolled system of differential-difference equations with a homogeneous additive right side and linearly increasing delay. Sufficient conditions for asymptotic stability are known for a number of special cases of such systems. Razumikhin's theorem on the asymptotic stability of homogeneous systems with proportional delay is formulated. Sufficient conditions for asymptotic stability are obtained basing on the asymptotic stability of the initial system without delay and constructing the Lyapunov function.
{"title":"The stability of differential-difference systems with linearly increasing delay. II. Systems with additive right side","authors":"A. Ekimov, A. P. Zhabko, P. Yakovlev","doi":"10.21638/11701/spbu10.2023.101","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.101","url":null,"abstract":"The article considers an uncontrolled system of differential-difference equations with a homogeneous additive right side and linearly increasing delay. Sufficient conditions for asymptotic stability are known for a number of special cases of such systems. Razumikhin's theorem on the asymptotic stability of homogeneous systems with proportional delay is formulated. Sufficient conditions for asymptotic stability are obtained basing on the asymptotic stability of the initial system without delay and constructing the Lyapunov function.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"21 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87092780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21638/11701/spbu10.2023.105
N. Smirnov, T. Smirnova, M. Smirnova, M. N. Smirnov
In this work, the object of study is the economy of the region. To describe it, a regular method for constructing difference input - output dynamic models is proposed. This approach involves modeling not only the sphere of production, but also the sphere of consumption. To do this, the vector of phase variables includes the gross domestic product. The variability of the model consists in the ability to take into account various macroeconomic parameters depending on the ultimate goals of analysis and control of macroeconomic trends. It is shown that the dynamics of the economy with direct investment in various sectors of the economy is described by linear controlled difference systems. If there is a need to take into account other macroeconomic parameters that increase the sensitivity of the model to managerial influences, then this leads to nonlinear difference systems of various types. In the final part of the article, a scenario approach for the development of investment projects is described. This approach is based on the principles of constructing program controls and stabilizing the corresponding program movements of a controlled difference system.
{"title":"Difference dynamic input-output models","authors":"N. Smirnov, T. Smirnova, M. Smirnova, M. N. Smirnov","doi":"10.21638/11701/spbu10.2023.105","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.105","url":null,"abstract":"In this work, the object of study is the economy of the region. To describe it, a regular method for constructing difference input - output dynamic models is proposed. This approach involves modeling not only the sphere of production, but also the sphere of consumption. To do this, the vector of phase variables includes the gross domestic product. The variability of the model consists in the ability to take into account various macroeconomic parameters depending on the ultimate goals of analysis and control of macroeconomic trends. It is shown that the dynamics of the economy with direct investment in various sectors of the economy is described by linear controlled difference systems. If there is a need to take into account other macroeconomic parameters that increase the sensitivity of the model to managerial influences, then this leads to nonlinear difference systems of various types. In the final part of the article, a scenario approach for the development of investment projects is described. This approach is based on the principles of constructing program controls and stabilizing the corresponding program movements of a controlled difference system.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"73 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84793690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21638/11701/spbu10.2023.207
N. Egorov, A. G. Karpov, Sergey P. Sobolev
One of the most informative methods for studying dielectric materials is the analysis of their polarization and depolarization processes. The most suitable representation is the dielectric diagram in the complex plane (Argand diagram). Often, the dielectric diagram is represented as a collection of intersecting parts of circles, at least for preprocessing. The paper proposes means of modeling the dielectric diagram by means of a set of parts of circles.
{"title":"Mathematical methods for analyzing the results of investigation of dielectric","authors":"N. Egorov, A. G. Karpov, Sergey P. Sobolev","doi":"10.21638/11701/spbu10.2023.207","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.207","url":null,"abstract":"One of the most informative methods for studying dielectric materials is the analysis of their polarization and depolarization processes. The most suitable representation is the dielectric diagram in the complex plane (Argand diagram). Often, the dielectric diagram is represented as a collection of intersecting parts of circles, at least for preprocessing. The paper proposes means of modeling the dielectric diagram by means of a set of parts of circles.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"13 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81905984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21638/11701/spbu10.2023.102
Vitaly A. Kochevadov, A. Sedakov
The paper studies a dynamic network game that models the competitive behavior of firms in a market. It is assumed that firms, under the condition of simultaneous and independent choice of their actions, implement the behavior that determines their production and investment behavior in each period. The production behavior of the firm reflects the ongoing quantities that it should produce and supply to the market. The investment behavior specifies the ongoing amounts of investment that the firm allocates to the modernization of its production technology in order to prevent it from becoming obsolete. Next, the unit cost is assumed to depend on the firm's investment and the investment of its competitors, which are determined by an exogenous network. Two types of Nash equilibria are characterized: open-loop and feedback. Finally, we analyze the impact of the network and related model parameters on firms' behavior, profits, and competitive advantage.
{"title":"Dynamic network model of production and investment","authors":"Vitaly A. Kochevadov, A. Sedakov","doi":"10.21638/11701/spbu10.2023.102","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.102","url":null,"abstract":"The paper studies a dynamic network game that models the competitive behavior of firms in a market. It is assumed that firms, under the condition of simultaneous and independent choice of their actions, implement the behavior that determines their production and investment behavior in each period. The production behavior of the firm reflects the ongoing quantities that it should produce and supply to the market. The investment behavior specifies the ongoing amounts of investment that the firm allocates to the modernization of its production technology in order to prevent it from becoming obsolete. Next, the unit cost is assumed to depend on the firm's investment and the investment of its competitors, which are determined by an exogenous network. Two types of Nash equilibria are characterized: open-loop and feedback. Finally, we analyze the impact of the network and related model parameters on firms' behavior, profits, and competitive advantage.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"27 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72516789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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