Вестник Санкт-Петербургского университета最新文献

{"title":"Stability of Lurie-type systems with asynchronous and synchronous switching and constant delays","authors":"Natalya R. Andriyanova","doi":"10.21638/11701/spbu10.2023.302","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.302","url":null,"abstract":"The problems of analysis for systems with synchronous and asynchronous switching have been actively studied for the linear case. In this paper, a switched system of difference-differential equations, in which the right-hand side consists of a linear term and an essentially nonlinear part containing sector-type components is considered. This kind of systems belongs to the class of Lurie indirect control systems. Sufficient conditions on the system parameters and the switching law are investigated for asymptotic stability to be guaranteed both in the case of synchronous switching between subsystems and in asynchronous one. In the latter case it is supposed that the nonlinear delayed part switches with a lag equal to the corresponding delay. It is required that stability should be preserved for any constant positive delays. The problem is solved using the Lyapunov — Krasovsky approach. The functional is chosen that includes a quadratic form and integrals of nonlinearities. Restrictions that ensure asymptotic stability for an arbitrary switching law are found. With such an approach for the asynchronous case these conditions turn out to be less restrictive. By using multiple functionals the restrictions on the lengths of intervals between switchings are also obtained. This type of conditions are similar for both cases of synchronous and asynchronous switching. Theoretical results are demonstrated by a specially selected example.","PeriodicalId":477285,"journal":{"name":"Вестник Санкт-Петербургского университета","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135153037","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}

{"title":"Natural vibrations of a cylindrical shell with the end cap. I. Asymptotic analysis","authors":"Sergei B. Filippov, Andrei L. Smirnov, Grigory A. Nesterchuk","doi":"10.21638/spbu01.2023.110","DOIUrl":"https://doi.org/10.21638/spbu01.2023.110","url":null,"abstract":"Low natural frequencies and vibration modes of the structure, consisting of a closed circular cylindrical shell with the end cap, having the shape of a shallow spherical segment, are examined in the paper using numerical and asymptotic methods. There are three types natural vibrations of the structure. Natural frequencies and vibration modes of the first type are close to the frequencies and vibration modes of a shallow spherical shell, modes and frequencies of the second type - to frequencies and modes of a cylindrical shell, and those of the third type - to frequencies and modes of vibration of a cantilever beam with a load at the end. In the first part of the research approximate values for the frequencies of vibrations of the first type are found by asymptotic methods. Asymptotic and numerical results obtained with finite element method are in good agreement.","PeriodicalId":477285,"journal":{"name":"Вестник Санкт-Петербургского университета","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135535036","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}

{"title":"Stationary reversibles processes MA and ARMA","authors":"Tatiana M. Tovstik","doi":"10.21638/spbu01.2023.307","DOIUrl":"https://doi.org/10.21638/spbu01.2023.307","url":null,"abstract":"The term mathematical diagnostics was introduced by V. F. Demyanov in the early 2000s. The simplest problem of mathematical diagnostics is to determine the relative position of a certain point p and the convex hull C of a finite number of given points in n-dimensional Euclidean space. Of interest is the answer to the following questions: does the point p belong to the set C or not? If p does not belong to C, then what is the distance from p to C? In general problem of mathematical diagnostics two convex hulls are considered. The question is whether they have common points. If there are no common points, then it is required to find the distance between these hulls. From an algorithmic point of view, the problems of mathematical diagnostics are reduced to special problems of linear or quadratic programming, for the solution of which there are finite methods. However, when implementing this approach in the case of large data arrays, serious computational difficulties arise. Infinite but easily implemented methods come to the rescue, which allow obtaining an approximate solution with the required accuracy in a finite number of iterations. These methods include the MDM method. It was developed by Mitchell, Demyanov and Malozemov in 1971 for other purposes, but later found application in machine learning. From a modern point of view, the original version of the MDM method can be used to solve the simplest problems of mathematical diagnostics. This article gives a natural generalization of the MDM-method, oriented towards solving general problems of mathematical diagnostics. The equivalence of the general problem of mathematical diagnostics and the problem of linear separation of two finite sets with the largest width of the margin is established.","PeriodicalId":477285,"journal":{"name":"Вестник Санкт-Петербургского университета","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135913095","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}

{"title":"Computer analysis of the differential equation of the model of the synchronous electric motor that does not include electric currents","authors":"Boris I. Konosevich, Yuliya B. Konosevich","doi":"10.21638/spbu01.2023.305","DOIUrl":"https://doi.org/10.21638/spbu01.2023.305","url":null,"abstract":"Phase portraits of the well-known equation of the no-current model of the synchronous electric motor are obtained with use of computer, and some properties of its solutions are noted, which are imperceptible at the phase portraits, obtained analytically. With use of computer, a graph is built for the curve, representing the critical value versus the principal stationary value of the angular variable. Linear and sinusoidal approximations are proposed for this curve, maximum absolute and relative errors of these approximations are calculated.","PeriodicalId":477285,"journal":{"name":"Вестник Санкт-Петербургского университета","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135913399","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}

{"title":"Theoretical foundation for solving search problems by the method of maximum entropy","authors":"Aleksandr N. Prokaev","doi":"10.21638/11701/spbu10.2023.304","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.304","url":null,"abstract":"The traditional problem of search theory is to develop a search plan for a physical object in the sea or on land. Known algorithms for the optimal distribution of search resources mainly use the exponential detection function. If we consider the search problem more broadly — as a problem of searching for various information, then the detection function can differ significantly from the exponential one. In this case, the solutions obtained using traditional algorithms may be correct from the point of view of mathematics, but unacceptable from the point of view of logic. In this paper, this problem is solved on the basis of the maximum entropy principle. The theorems are proved, as well as their consequences for four types of detection functions, which make it possible to create algorithms for solving various search problems based on the principle of maximum entropy.","PeriodicalId":477285,"journal":{"name":"Вестник Санкт-Петербургского университета","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135151397","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}

{"title":"Deformation of a plane modelled by John's material with a rigid elliptical inclusion loaded by force and moment","authors":"Yulia V. Malkova","doi":"10.21638/11701/spbu10.2023.303","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.303","url":null,"abstract":"An exact analytical solution is obtained for a non-linear problem of elasticity theory for a plane with a rigid elliptical inclusion. A concentrated force and a moment are applied at the center of inclusion. The elastic properties of the plane are modeled by John’s harmonic material. For this material methods of the theory of functions of a complex variable are using for solving nonlinear plane problems. Nominal stresses and displacements are expressed in terms of two analytical functions of a complex variable, which are determined from the boundary conditions on the contour of inclusion. The problems of the action of a concentrated force and moment on an elliptical core in a plane are considered separately. A comparison with a similar linear problem is made. The influence of the applied force and moment on the magnitude of stresses is studied depending on various parameters of the problem. Calculations of nominal stresses on the contour joining the plane with inclusion are performed.","PeriodicalId":477285,"journal":{"name":"Вестник Санкт-Петербургского университета","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135151406","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}

{"title":"The influence of the components of structural shifts on the level of employment in the economy of the Republic of Sakha (Yakutia)","authors":"Vladimir Myakshin, Andrei Tutygin, Tatyana Pesyakova","doi":"10.21638/spbu05.2023.305","DOIUrl":"https://doi.org/10.21638/spbu05.2023.305","url":null,"abstract":"The article is devoted to the problem of formation of an effective system of employment in the economy of the region. The structure of employment by types of economic activity is an indicator of the state of the socio-economic development of the region; when forming employment policy at the regional level, it is necessary to take into account structural shifts in employment, reflecting intersectoral overflows of labor resources. A classification of types of economic activity is proposed according to the ratio of the degree of impact of the components of structural changes (national, sectoral, regional) on the level of employment of the population, reflecting the conditions for the development of the industry in the region and allowing to identify industries that are promising for increasing employment. The main task of the classification is to identify the types of economic activity for the development of which there are favorable conditions in the region. Research hypothesis: the key points of growth in the number of people employed in the region can become economic activities for which the regional component takes a positive maximum value, which confirms the presence in the region of growth factors for these industries that can provide them with competitive advantages. To test the hypothesis, the proposed classification was tested on the example of the Republic of Sakha (Yakutia), partly included in the Arctic zone of the Russian Federation. The contribution of national, sectoral, regional factors to the change in employment by type of economic activity is analyzed, industries that have a priority impact on increasing the level of employment in the region are identified. Based on a comparison with other regions that are wholly or partially included in the Arctic zone of the Russian Federation, the significance for increasing the number of types of economic activities employed in the economy of the regions for which the regional component of structural changes is positive and exceeds the national and sectoral ones (first, second, third groups of classification) is shown. ), which confirms the hypothesis. On the basis of the carried-out classification, an assessment of the effectiveness of the regional employment policy of the Republic of Sakha (Yakutia) in the context of types of economic activity is given, directions for increasing employment are proposed.","PeriodicalId":477285,"journal":{"name":"Вестник Санкт-Петербургского университета","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135556959","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}

{"title":"International trade disputes related to fish products and Agreement on Fisheries Subsidies: Key regulatory issues and litigation outlook","authors":"Ruoxuan Wang, Liudmila Popova","doi":"10.21638/spbu05.2023.302","DOIUrl":"https://doi.org/10.21638/spbu05.2023.302","url":null,"abstract":"Fish-related trade disputes dealt with by the World Trade Organization (WTO) arise from the complexity of the fisheries industry, and the transboundary nature of fish, combined with differing national policies and interests. The Agreement on Fisheries Subsidies (AFS) aims to strengthen the role of the WTO in regulating the fish trade and curbing unsustainable fishing practices such as illegal fishing, overcapacity, and overfishing by limiting excessive fisheries subsidies. This article reveals the legal framework of the WTO to regulate the fish trade and resolve trade disputes and outlines the prospects for fish trade in light of the Agreement on Fisheries Subsidies (AFS). It has been established that general principles, quantitative restrictions, and anti-dumping measures, rather than subsidies, are the most common legal issues in trade disputes on fish products. Technical trade barriers, sanitary and phytosanitary measures, and general national exemptions are also frequent sources of disputes in the fish trade. These measures, designed for safety, health, and environmental reasons, are increasingly used for protectionist purposes by creating trade barriers. The AFS expands the legal framework for resolving trade disputes in the field of fish trade after its ratification. However, this recent international regulation combined with climate change and tightening food standards, is expected to lead to more disputes with developing countries over the fish trade.","PeriodicalId":477285,"journal":{"name":"Вестник Санкт-Петербургского университета","volume":"273 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135556970","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}

{"title":"Peace as a natural effect of trade: A potentia ad actum","authors":"Miroslav Jovanović, Alexandra Koval, Nikita Lomagin, Fyodor Lukyanov, Sergey Sutyrin, Olga Trofimenko, Guanghua Wang","doi":"10.21638/spbu05.2023.301","DOIUrl":"https://doi.org/10.21638/spbu05.2023.301","url":null,"abstract":"Initial idea to focus a plenary panel of 19th International Conference “Evolution of International Trading System: Prospects and Challenges” held in St. Petersburg State University on March 17th–19th 2022 on the issue of interaction between political and trade dimensions of international cooperation came to the organizers as early as mid-2021. Substantial escalation of the geopolitical tension by Spring 2022, on the one hand, made the selected topic much more relevant, on the other hand additionally limited the list of potential discussants. Nevertheless, despite of this obstacle programme committee managed to arrange the international team of experts giving their answers to the questions asked by moderators. The questions included necessity and possibility for the radical reassessment of the perception traditionally prevailing among social scientists. According to this perception expansion of trade has the positive impact on political relations between trading partners. Another topical issue deals with possible repercussions of economic sanctions actively imposed by some members of international community. The experts also discussed the motives behind decisions made by many foreign companies to exit from the Russian market. At the final stage of the panel its participants expressed their views on the prospects of the global governance system reforming.","PeriodicalId":477285,"journal":{"name":"Вестник Санкт-Петербургского университета","volume":"2013 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135556972","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}

{"title":"MDM method for solving the general quadratic problem of mathematical diagnostics","authors":"Vassili N. Malozemov, Natalya A. Solovyeva","doi":"10.21638/spbu01.2023.306","DOIUrl":"https://doi.org/10.21638/spbu01.2023.306","url":null,"abstract":"The term mathematical diagnostics was introduced by V. F. Demyanov in the early 2000s. The simplest problem of mathematical diagnostics is to determine the relative position of a certain point p and the convex hull C of a finite number of given points in n-dimensional Euclidean space. Of interest is the answer to the following questions: does the point p belong to the set C or not? If p does not belong to C, then what is the distance from p to C? In general problem of mathematical diagnostics two convex hulls are considered. The question is whether they have common points. If there are no common points, then it is required to find the distance between these hulls. From an algorithmic point of view, the problems of mathematical diagnostics are reduced to special problems of linear or quadratic programming, for the solution of which there are finite methods. However, when implementing this approach in the case of large data arrays, serious computational difficulties arise. Infinite but easily implemented methods come to the rescue, which allow obtaining an approximate solution with the required accuracy in a finite number of iterations. These methods include the MDM method. It was developed by Mitchell, Demyanov and Malozemov in 1971 for other purposes, but later found application in machine learning. From a modern point of view, the original version of the MDM method can be used to solve the simplest problems of mathematical diagnostics. This article gives a natural generalization of the MDM-method, oriented towards solving general problems of mathematical diagnostics. The equivalence of the general problem of mathematical diagnostics and the problem of linear separation of two finite sets with the largest width of the margin is established.","PeriodicalId":477285,"journal":{"name":"Вестник Санкт-Петербургского университета","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135913400","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}