Pub Date : 2021-01-01DOI: 10.21638/11701/spbu10.2021.401
V. Amoskov, V. Vasiliev, E. Gapionok, G. Gulbekyan, N. Edamenko, I. Ivanenko, N. Kazarinov, I. Kalagin, M. Kaparkova, V. Kukhtin, E. Lamzin, A. Makarov, A. Nezhentzev, D. Ovsyannikov, Dmitry A. (Jr.) Ovsyannikov, Nikolai F. Osipov, I. Rodin, Sergey E. Sytcheusky, Alexey A. Firsov
The design and specification choices are described for a PM quadrupole used to enable beam transport in a cyclotron. First an analytic study with a simplified 2D model is performed to give initial values for magnet configuration and performance. Characteristics of PM blocks and cylinders are analysed. Then a 3D parametrized model is used to solve the direct magnetostatic problem and accurately define quad specifications. Simulations are carried out with KOMPOT electromagnetic code utilizing the differential formulation. The regulariza- tion method is applied to solve the inverse problem. Magnetic characteristics, dimensions and shapes of the PM units and iron parts are determined in order to reach the specified field gradient. Possible correction of the resulting the ideal specification is discussed with respect to additional constraints put by practical implementation. Candidate PM materials are proposed. Simulated field maps are presented. The method described may serve as a basis for virtual prototyping and be integrated into end-to-end design and construction of magnet systems.
{"title":"Modelling and design of permanent magnet multipoles for beam transport and focusing. I. Selection of optimal design and parameters","authors":"V. Amoskov, V. Vasiliev, E. Gapionok, G. Gulbekyan, N. Edamenko, I. Ivanenko, N. Kazarinov, I. Kalagin, M. Kaparkova, V. Kukhtin, E. Lamzin, A. Makarov, A. Nezhentzev, D. Ovsyannikov, Dmitry A. (Jr.) Ovsyannikov, Nikolai F. Osipov, I. Rodin, Sergey E. Sytcheusky, Alexey A. Firsov","doi":"10.21638/11701/spbu10.2021.401","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.401","url":null,"abstract":"The design and specification choices are described for a PM quadrupole used to enable beam transport in a cyclotron. First an analytic study with a simplified 2D model is performed to give initial values for magnet configuration and performance. Characteristics of PM blocks and cylinders are analysed. Then a 3D parametrized model is used to solve the direct magnetostatic problem and accurately define quad specifications. Simulations are carried out with KOMPOT electromagnetic code utilizing the differential formulation. The regulariza- tion method is applied to solve the inverse problem. Magnetic characteristics, dimensions and shapes of the PM units and iron parts are determined in order to reach the specified field gradient. Possible correction of the resulting the ideal specification is discussed with respect to additional constraints put by practical implementation. Candidate PM materials are proposed. Simulated field maps are presented. The method described may serve as a basis for virtual prototyping and be integrated into end-to-end design and construction of magnet systems.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84057593","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 : 2021-01-01DOI: 10.21638/11701/spbu10.2021.302
N. Grigoreva
The problem of minimizing the maximum delivery times while scheduling tasks on a single processor is a classical combinatorial optimization problem. Each task ui must be processed without interruption for t(ui) time units on the machine, which can process at most one task at time. Each task uw; has a release time r(ui), when the task is ready for processing, and a delivery time g(ui). Its delivery begins immediately after processing has been completed. The objective is to minimize the time, by which all jobs are delivered. In the Graham notation this problem is denoted by 1|rj,qi|Cmax, it has many applications and it is NP-hard in a strong sense. The problem is useful in solving owshop and jobshop scheduling problems. The goal of this article is to propose a new 3/2-approximation algorithm, which runs in O(n log n) times for scheduling problem 1|rj.qi|Cmax. An example is provided which shows that the bound of 3/2 is accurate. To compare the effectiveness of proposed algorithms, random generated problems of up to 5000 tasks were tested.
{"title":"3/2-approximation algorithm for a single machine scheduling problem","authors":"N. Grigoreva","doi":"10.21638/11701/spbu10.2021.302","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.302","url":null,"abstract":"The problem of minimizing the maximum delivery times while scheduling tasks on a single processor is a classical combinatorial optimization problem. Each task ui must be processed without interruption for t(ui) time units on the machine, which can process at most one task at time. Each task uw; has a release time r(ui), when the task is ready for processing, and a delivery time g(ui). Its delivery begins immediately after processing has been completed. The objective is to minimize the time, by which all jobs are delivered. In the Graham notation this problem is denoted by 1|rj,qi|Cmax, it has many applications and it is NP-hard in a strong sense. The problem is useful in solving owshop and jobshop scheduling problems. The goal of this article is to propose a new 3/2-approximation algorithm, which runs in O(n log n) times for scheduling problem 1|rj.qi|Cmax. An example is provided which shows that the bound of 3/2 is accurate. To compare the effectiveness of proposed algorithms, random generated problems of up to 5000 tasks were tested.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78604618","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 : 2021-01-01DOI: 10.21638/11701/spbu10.2021.303
N. Moldovyan, A. Moldovyan
The article considers the structure of the 2x2 matrix algebra set over a ground finite field GF(p). It is shown that this algebra contains three types of commutative subalgebras of order p2, which differ in the value of the order of their multiplicative group. Formulas describing the number of subalgebras of every type are derived. A new post-quantum digital signature scheme is introduced based on a novel form of the hidden discrete logarithm problem. The scheme is characterized in using scalar multiplication as an additional operation masking the hidden cyclic group in which the basic exponentiation operation is performed when generating the public key. The advantage of the developed signature scheme is the comparatively high performance of the signature generation and verification algorithms as well as the possibility to implement a blind signature protocol on its base.
{"title":"Digital signature scheme on the 2 x 2 matrix algebra","authors":"N. Moldovyan, A. Moldovyan","doi":"10.21638/11701/spbu10.2021.303","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.303","url":null,"abstract":"The article considers the structure of the 2x2 matrix algebra set over a ground finite field GF(p). It is shown that this algebra contains three types of commutative subalgebras of order p2, which differ in the value of the order of their multiplicative group. Formulas describing the number of subalgebras of every type are derived. A new post-quantum digital signature scheme is introduced based on a novel form of the hidden discrete logarithm problem. The scheme is characterized in using scalar multiplication as an additional operation masking the hidden cyclic group in which the basic exponentiation operation is performed when generating the public key. The advantage of the developed signature scheme is the comparatively high performance of the signature generation and verification algorithms as well as the possibility to implement a blind signature protocol on its base.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80140326","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 : 2021-01-01DOI: 10.21638/11701/spbu10.2021.305
V. Provotorov, S. Sergeev, Hoang Van Nguyen
The article considers the problem of point control of the differential-difference equation with distributed parameters on the graph in the class of summable functions. The differential- difference system is closely related to the evolutionary differential system and moreover the properties of the differential system are preserved. This connection is established by the universal method of semi-discretization in a time variable for a differential system, which provides an effective tool in order to find conditions for unique solvability and continuity on the initial data for the differential-difference system. For this differential-difference system, a special case of the optimal control problem is studied: the problem of point control action on the controlled differential-difference system is considered by the control, concentrated at all internal nodes of the graph. At the same time, the restrictive set of permissible controls is set by the means of conditions depending on the nature of the applied tasks. In this case, the controls are concentrated at the end points of the edges adjacent to each inner node of the graph. This is a characteristic feature of the study presented, quite often used in practice when building a mechanism for managing the processes of transportation of different kinds of masses over network media. The study essentially uses the conjugate state of the system and the conjugate system for a differential-difference system — obtained ratios that determine optimal point control. The obtained results underlie the analysis of optimal control problems for differential systems with distributed parameters on the graph, which have interesting analogies with multi-phase problems of multidimensional hydrodynamics.
{"title":"Point control of a differential-difference system with distributed parameters on the graph","authors":"V. Provotorov, S. Sergeev, Hoang Van Nguyen","doi":"10.21638/11701/spbu10.2021.305","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.305","url":null,"abstract":"The article considers the problem of point control of the differential-difference equation with distributed parameters on the graph in the class of summable functions. The differential- difference system is closely related to the evolutionary differential system and moreover the properties of the differential system are preserved. This connection is established by the universal method of semi-discretization in a time variable for a differential system, which provides an effective tool in order to find conditions for unique solvability and continuity on the initial data for the differential-difference system. For this differential-difference system, a special case of the optimal control problem is studied: the problem of point control action on the controlled differential-difference system is considered by the control, concentrated at all internal nodes of the graph. At the same time, the restrictive set of permissible controls is set by the means of conditions depending on the nature of the applied tasks. In this case, the controls are concentrated at the end points of the edges adjacent to each inner node of the graph. This is a characteristic feature of the study presented, quite often used in practice when building a mechanism for managing the processes of transportation of different kinds of masses over network media. The study essentially uses the conjugate state of the system and the conjugate system for a differential-difference system — obtained ratios that determine optimal point control. The obtained results underlie the analysis of optimal control problems for differential systems with distributed parameters on the graph, which have interesting analogies with multi-phase problems of multidimensional hydrodynamics.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74059385","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 : 2021-01-01DOI: 10.21638/11701/spbu10.2021.409
A. G. Karpov, V. Trofimov, A. G. Fedorov
The research of thin films of various materials on nano- and microlevel is undoubtedly topical. Three-dimensional images of thin films can significantly increase the level of the received results. Intellectual computer support of researches assumes the existence or creation of mathematical and the software that implements the experimental program. Such support can most effectively be realized with the help of an information and expert system, based on a holographic electron microscope. In this work we presented an information and expert system for solving this problem. When creating instrumental, hardware and software tools for non-destructive research of the 3D structure of objects, we proceeded from the assumption that the most complete information about the object of research can be obtained only with a comprehensive approach to the analysis of the structure of the object using complementary techniques that allow obtaining data as a 3D image.
{"title":"Information and program support of the analysis and processing of holographic information","authors":"A. G. Karpov, V. Trofimov, A. G. Fedorov","doi":"10.21638/11701/spbu10.2021.409","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.409","url":null,"abstract":"The research of thin films of various materials on nano- and microlevel is undoubtedly topical. Three-dimensional images of thin films can significantly increase the level of the received results. Intellectual computer support of researches assumes the existence or creation of mathematical and the software that implements the experimental program. Such support can most effectively be realized with the help of an information and expert system, based on a holographic electron microscope. In this work we presented an information and expert system for solving this problem. When creating instrumental, hardware and software tools for non-destructive research of the 3D structure of objects, we proceeded from the assumption that the most complete information about the object of research can be obtained only with a comprehensive approach to the analysis of the structure of the object using complementary techniques that allow obtaining data as a 3D image.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75389990","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 : 2021-01-01DOI: 10.21638/11701/spbu10.2021.307
A. S. Popkov
The article considers the problem of constructing reachability and controllability sets for a control problem. The motion of an object is described by a linear system of ordinary differential equations, and control is selected from the class of piecewise-constant functions. Straight boundaries are also set on the controls. The article provides definitions of reacha- bility and controllability sets. It is shown that the problems of constructing these sets are equivalent and can be reduced to the problem of linear mapping of a multidimensional cube. The properties of these sets are also given. In addition, the existing approaches to solving the problem are analyzed. Since they are all too computationally complex, the question of creating a more efficient algorithm arises. The work proposes an algorithm for constructing the required sets as a system of linear inequalities. A proof of the theorem showing the correctness of the algorithm is provided. The complexity of the presented approach is estimated.
{"title":"Construction of reachability and controllability sets in a special linear control problem","authors":"A. S. Popkov","doi":"10.21638/11701/spbu10.2021.307","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.307","url":null,"abstract":"The article considers the problem of constructing reachability and controllability sets for a control problem. The motion of an object is described by a linear system of ordinary differential equations, and control is selected from the class of piecewise-constant functions. Straight boundaries are also set on the controls. The article provides definitions of reacha- bility and controllability sets. It is shown that the problems of constructing these sets are equivalent and can be reduced to the problem of linear mapping of a multidimensional cube. The properties of these sets are also given. In addition, the existing approaches to solving the problem are analyzed. Since they are all too computationally complex, the question of creating a more efficient algorithm arises. The work proposes an algorithm for constructing the required sets as a system of linear inequalities. A proof of the theorem showing the correctness of the algorithm is provided. The complexity of the presented approach is estimated.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74096409","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 : 2021-01-01DOI: 10.21638/11701/spbu10.2021.304
S. Noskov, A. Lakeyev
The problem of solving the interval system of linear algebraic equations (ISLAEs) is one of the well-known problems of interval analysis, which is currently undergoing intensive development. In general, this solution represents a set, which may be given differently, de- pending on which quantifiers are related to the elements of the left and right sides of this system. Each set of solutions of ISLAE to be determined is described by the domain of compatibility of the corresponding system of linear inequalities and, normally, one nonlinear condition of the type of complementarity. It is difficult to work with them when solving specific problems. Therefore, in the case of nonemptiness in the process of solving the problem it is recommended to find a so-called PC-solution, based on the application of the technique known in the theory of multi-criterial choice, that presumes maximization of the solving capacity of the system of inequalities. If this set is empty, it is recommended to find a quasi- solution of ISLAE. The authors compare the approach proposed for finding PC- and/or quasi-solutions to the approach proposed by S. P. Shary, which is based on the application of the recognizing functional.
求解线性代数方程组的区间系统问题是区间分析中众所周知的问题之一，目前正处于蓬勃发展的阶段。一般来说，这个解表示一个集合，它可以以不同的方式给出，这取决于哪个量词与这个系统的左边和右边的元素相关。待确定的ISLAE的每一组解由相应的线性不等式系统的相容域和通常的互补型非线性条件来描述。在解决具体问题时，很难与他们合作。因此，在解决问题过程中的非空性的情况下，建议根据多标准选择理论中已知的技术的应用，找到所谓的pc解决方案，该解决方案假定不等式系统的解决能力最大化。如果该集合为空，建议查找ISLAE的准解。作者比较了S. P. Shary提出的基于识别泛函应用的求PC解和/或准解的方法。
{"title":"PC-solutions and quasi-solutions of the interval system of linear algebraic equations","authors":"S. Noskov, A. Lakeyev","doi":"10.21638/11701/spbu10.2021.304","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.304","url":null,"abstract":"The problem of solving the interval system of linear algebraic equations (ISLAEs) is one of the well-known problems of interval analysis, which is currently undergoing intensive development. In general, this solution represents a set, which may be given differently, de- pending on which quantifiers are related to the elements of the left and right sides of this system. Each set of solutions of ISLAE to be determined is described by the domain of compatibility of the corresponding system of linear inequalities and, normally, one nonlinear condition of the type of complementarity. It is difficult to work with them when solving specific problems. Therefore, in the case of nonemptiness in the process of solving the problem it is recommended to find a so-called PC-solution, based on the application of the technique known in the theory of multi-criterial choice, that presumes maximization of the solving capacity of the system of inequalities. If this set is empty, it is recommended to find a quasi- solution of ISLAE. The authors compare the approach proposed for finding PC- and/or quasi-solutions to the approach proposed by S. P. Shary, which is based on the application of the recognizing functional.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85752752","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 : 2021-01-01DOI: 10.21638/11701/spbu10.2021.406
D. A. Chubarov, V. Tregubov, N. K. Egorova
Based on the analysis of the mechanical models of the intervertebral disc given in the literature, it is concluded that the finite element computational grids used in them do not reflect the real structure of the intervertebral disc. In this regard, a mechanical model of the inter- vertebral disc was built, the structure of which is close to its real structure. The proposed model was used to determine the dynamics of the pressure distribution in the intervertebral disc when one of the vertebrae is rotated by a given angle. To determine the resulting bulges of each cell in the structure of the fibrous ring, the Rayleigh method and its modification were used. This made it possible to rationally calculate the volumes of cells. When calculating the pressure in each cell, its linear dependence on the deflection value of the cell was used. As a result of the proposed algorithm, the pressure dynamics in each cell of the intervertebral disc model was determined when the angle between the vertebrae changed.
{"title":"Mathematical modeling of pressure distribution during deformations of the intervertebral disc","authors":"D. A. Chubarov, V. Tregubov, N. K. Egorova","doi":"10.21638/11701/spbu10.2021.406","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.406","url":null,"abstract":"Based on the analysis of the mechanical models of the intervertebral disc given in the literature, it is concluded that the finite element computational grids used in them do not reflect the real structure of the intervertebral disc. In this regard, a mechanical model of the inter- vertebral disc was built, the structure of which is close to its real structure. The proposed model was used to determine the dynamics of the pressure distribution in the intervertebral disc when one of the vertebrae is rotated by a given angle. To determine the resulting bulges of each cell in the structure of the fibrous ring, the Rayleigh method and its modification were used. This made it possible to rationally calculate the volumes of cells. When calculating the pressure in each cell, its linear dependence on the deflection value of the cell was used. As a result of the proposed algorithm, the pressure dynamics in each cell of the intervertebral disc model was determined when the angle between the vertebrae changed.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88497916","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 : 2021-01-01DOI: 10.21638/11701/spbu10.2021.301
M. I. Varayun', E. Vinogradova, A. Y. Antonov
Within the framework of a computer statistical experiment, the test problem of identifying the parameters of a field electron emission signal using a regression model based on the Fowler— Nordheim law is considered. Two approaches to determining the parameter estimates are used in the work: ordinary least squares and random search with training. It is shown that the random search error can be neglected if, for the considered ratios of the noise level to the signal power, the number of statistical tests is approximately 103. The result allows us to expand the class of functionals used to identify the response without changing the method. The article notes the advantages of the random search method for the problem under consideration and the prospects of its applicability to tasks in a more general setting.
{"title":"Random search method for estimating the parameters of the emission system signal","authors":"M. I. Varayun', E. Vinogradova, A. Y. Antonov","doi":"10.21638/11701/spbu10.2021.301","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.301","url":null,"abstract":"Within the framework of a computer statistical experiment, the test problem of identifying the parameters of a field electron emission signal using a regression model based on the Fowler— Nordheim law is considered. Two approaches to determining the parameter estimates are used in the work: ordinary least squares and random search with training. It is shown that the random search error can be neglected if, for the considered ratios of the noise level to the signal power, the number of statistical tests is approximately 103. The result allows us to expand the class of functionals used to identify the response without changing the method. The article notes the advantages of the random search method for the problem under consideration and the prospects of its applicability to tasks in a more general setting.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81745066","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 : 2021-01-01DOI: 10.21638/11701/spbu10.2021.411
A. Zhabko, V. Provotorov, A. I. Shindyapin
In the paper be considered the problem of optimal control of the differential-difference equation with distributed parameters on the graph in the class of summable functions. Particular attention is given to the connection of the differential-differential system with the evolutionary differential system and the search conditions in which the properties of the differential system are preserved. This connection establishes a universal method of semi- digitization by temporal variable for differential system, providing an effective tool in finding conditions of uniqueness solvability and continuity on the initial data for the differential- differential system. A priori estimates of the norms of a weak solution of differential- differential system give an opportunity to establish not only the solvability of this system but also the existence of a weak solution of the evolutionary differential system. For the differential-difference system analysis of the optimal control problem is presented, containing natural in that cases a additional study of the problem with a time lag. This essentially uses the conjugate state of the system and the conjugate system for a differential-difference system — defining ratios that determine optimal control or the set optimal controls. The work shows courses to transfer the results in case of analysis of optimal control problems in the class of functions with bearer in network-like domains. The transition from an evolutionary differential system to a differential-difference system was a natural step in the study of applied problems of the theory of the transfer of solid mediums. The obtained results underlie the analysis of optimal control problems for differential systems with distributed parameters on a graph, which have interesting analogies with multiphase problems of multidimensional hydrodynamics.
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