Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya最新文献

{"title":"The method of successive approximations for constructing a model of dynamic polynomial regression","authors":"Anna Golovkina, V. Kozynchenko, Ilia S. Klimenko","doi":"10.21638/11701/spbu10.2022.404","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.404","url":null,"abstract":"Predicting the behavior of a certain process in time is an important task that arises in many applied areas, and information about the system that generated this process can either be completely absent or be partially limited. The only available knowledge is the accumulated data on past states and process parameters. Such a task can be successfully solved using machine learning methods, but when it comes to modeling physical experiments or areas where the ability of a model to generalize and interpretability of predictions are important, then the most machine learning methods do not fully satisfy these requirements. The forecasting problem is solved by building a dynamic polynomial regression model, and a method for finding its coefficients is proposed, based on the connection with dynamic systems. Thus, the constructed model corresponds to a deterministic process, potentially described by differential equations, and the relationship between its parameters can be expressed in an analytical form. As an illustration of the applicability of the proposed approach to solving forecasting problems, we consider a synthetic data set generated as a numerical solution of a system of differential equations that describes the Van der Pol oscillator.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"126 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88030603","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":"Equilibrium in the problem of choosing the meeting time for N persons","authors":"V. Mazalov, Vladimir V. Yashin","doi":"10.21638/11701/spbu10.2022.405","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.405","url":null,"abstract":"A game-theoretic model of competitive decision on a meet time is considered. There are n players who are negotiating the meeting time. The objective is to find a meet time that satisfies all participants. The players' utilities are represented by linear unimodal functions ui(x), x∈ [0, 1], i=1,2,...,n. The maximum values of the utility functions are located at the points i/(n-1), i=0,...,n-1. Players take turns 1 → 2→ 3 → ...→ (n-1) → n → 1→... . Players can indefinitely insist on a profitable solution for themselves. To prevent this from happening, a discounting factor δ is greater than 1 is introduced to limit the duration of negotiations. We will assume that after each negotiation session, the utility functions of all players will decrease proportionally to δ. Thus, if the players have not come to a decision before time t, then at time t their utilities are represented by the functions δt-1ui(x), i = 1, 2,..., n. We will look for a solution in the class of stationary strategies, when it is assumed that the decisions of the players will not change during the negotiation time, i. e. the player i will make the same offer at step i and at subsequent steps n+i, 2n+i, ... . This will allow us to limit ourselves to considering the chain of sentences 1 → 2 → 3 → ... →(n-1) → n→ 1. We will use the method of backward induction. To do this, assume that player n is looking for his best responce, knowing player 1's proposal, then player (n-1) is looking for his best responce, knowing player n's solution, etc. In the end, we find the best responce of the player 1, and it should coincide with his offer at the beginning of the procedure. Thus, the reasoning in the method of backward induction has the form 1 ← 2← 3← ... ←(n-1)← n← 1. The subgame perfect equilibrium in the class of stationary strategies is found in analytical form. It is shown that when δ changes from 1 to 0, the optimal offer of player 1 changes from 1/2 to 1. That is, when the value of δ is close to 1, the players have a lot of time to negotiate, so the offer of player 1 should be fair to everyone. If the discounting factor is close to 0, the utilities of the players decreases rapidly and they must quickly make a decision that is beneficial to player 1.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"7 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88902938","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 superposition method in the problem of bending of a thin isotropic plate clamped along the contour","authors":"G. O. Alcybeev, Dmitriy P. Goloskokov, A. Matrosov","doi":"10.21638/11701/spbu10.2022.305","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.305","url":null,"abstract":"In this work, the general solution of the differential equation for the bending of a thin isotropic plate under the action of a normal load applied to its plane is constructed by the superposition method. The solutions obtained by the method of initial functions in the form of trigonometric series are taken as two solutions, each of which allows satisfying the boundary conditions on two opposite sides of the plate. Two ways of satisfying the boundary conditions of a clamped plate are studied: the method of expansion into trigonometric Fourier series and the collocation method. It is shown that both methods give the same results and sufficiently fast convergence of the solution at all points of the plate except for small neighborhoods of the corner points. The constructed solution made it possible to study the behavior of the shear force in the corner points. Computational experiments have shown that when keeping 390 terms in the trigonometric series of the solution, the shear force is close to zero, but not identically equal.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"9 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91273981","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":"FAMILIES OF EMBEDDED METHODS OF ORDER SIX","authors":"I. V. Olemskoy, O. S. Firyulina, O. A. Tumka","doi":"10.21638/11701/spbu10.2022.209","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.209","url":null,"abstract":"In the paper embedded methods of order six, with seven stages for solving systems of ordinary differential equations, are derived. A family of Runge- Kutta methods, of order six with seven stages and having three free parameters, is presented. This family is extended in two different ways with embedded methods to form families of embedded method pairs. Numerical comparison is given for certain examples of the embedded pairs from the constructed families.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"75 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86287628","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":"On the determination of spacetime geometry","authors":"O. Drivotin","doi":"10.21638/11701/spbu10.2022.302","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.302","url":null,"abstract":"A new approach allowing to determine the metric tensor in various points of the spacetime is proposed. Such approach gives an opportunity to investigate the simultaneity of events not only locally, but also globally, without using of the synchronization procedure, traditionally applied in the theory of the spacetime. On the base of the method of simultaineity determination described in the article, it is possible to construct broad classes of reference frames. As an example, a reference frame is considered, all ovservers of which move with the same arbitrarily changing velocity along some direction.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"SE-8 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84634971","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":"Solution of a local boundary problem for a non-linear non-stationary system in the class of discrete controls","authors":"A. N. Kvitko, N. N. Litvinov","doi":"10.21638/11701/spbu10.2022.102","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.102","url":null,"abstract":"This article proposes an algorithm of construction for the discrete controlling function which is restricted by a norm and provides transition for the wide class of the systems of nonstationary nonlinear ordinary differential equations from the initial state to the setting final state. A constructive sufficient condition that provides this transition is obtained. Efficiency of the method is demonstrated by the solution of the robot-manipulator control problem and its numerical modeling.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"183 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76261307","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":"Modeling the process of filling carbon nanocontainers with hydrogen","authors":"N. Egorov, A. Vasilyev, T. Andreeva, M. Bedrina","doi":"10.21638/11701/spbu10.2022.307","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.307","url":null,"abstract":"The problem of storing and transporting hydrogen in containers based on fullerenes and carbon nanotubes is relevant to hydrogen energy. This problem theoretically can be solved using quantum chemistry methods and powerful computer technology to calculate molecules with a large number of atoms, polymers, nanostructures and nanotubes. It is necessary to create a theoretical model of the electromagnetic field in the cavity of fullerene molecules and nanotubes in order to understand how atoms and molecules of hydrogen or any other substances behave in it. Computer simulation of the filling process by hydrogen molecules fullerenes and nanotubes was performed by quantum mechanics methods DFT with GAUSSIAN 09 program.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"10 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85445709","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":"Two-stage network games modeling the Belt and Road Initiative","authors":"Ping Suna, E. Parilina, Hongwei Gaob","doi":"10.21638/11701/spbu10.2022.107","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.107","url":null,"abstract":"Inspired by the Belt and Road Initiative, we introduce a model of two-stage network games, when players first form a directed network (the first stage) and then they may reconsider the actions made at the first stage and choose controls to influence other players in a positive or negative way (the second stage). At both stages players get their payoffs. Considering a cooperative version of the game, we examine the problem of subgame network consistency and design an imputation distribution procedure as a new system of stage payments to guarantee the long-term cooperation. The Shapley value with exogenous directed graph constraint is used as a cooperative solution concept. Finally, we prove that a cooperative subgame is convex which ensures the non-emptiness of the core.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"40 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85959498","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":"ON OPTIMAL DESIGN OF REINFORCED CONCRETE COLUMNS SUBJECTED TO COMBINED BIAXIAL BENDING AND AXIAL LOAD","authors":"A. Ibraheem, Y. Pronina","doi":"10.21638/11701/spbu10.2022.203","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.203","url":null,"abstract":"This paper presents a new procedure for designing rectangular columns subjected to combined biaxial bending and axial load. The new procedure is realized within a new comprehensive structural analysis software for building analysis and design. Compared to existing engineering packages, the new program does not require pre-setting the distribution of bars before designing and gives more detailed results: not only the required reinforcement amount, but also a distribution of bars of a certain diameter along the sides of the column section. The program starts by inserting four reinforcement bars into the corners of the column, and checks if this reinforcement bars provide required resistance to the applied loads. If the reinforced concrete column fails to withstand the applied loads, then the program increases the reinforcement by adding new bars and checks required resistance again. This process continues until the reinforced concrete column is able to withstand the applied loads. The proposed procedure is realized within following methods: (I) calculation of the so-called column capacity interaction volume using a large number of interaction curves (usually 24 curves); (II) the elliptical approximation of the column capacity interaction volume (the load contour equation). Within the second method, the program calculates two interaction curves only: the first curve is for an eccentric case in X direction and the second curve is for an eccentric case in Y direction. In both methods, the interaction curves are calculated according to American concrete institute standards. The use of the new procedure within the second method gives results very close to the first method (the most accurate), but it requires much less time for calculation. This is very important when designing large structures with multiple columns.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"46 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73704011","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":"Multi-purpose robotic arm control system","authors":"M. Smirnova, M. N. Smirnov, N. Smirnov","doi":"10.21638/11701/spbu10.2022.415","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.415","url":null,"abstract":"The purpose of this work is to create methods and algorithms for the formation of multi-purpose automatic control systems for the robotic arm, as well as to develop specialized software for computer modeling of the developed algorithms on the example of a real robotic arm. The methods of forming multi-purpose automatic motion control systems for various objects are developed, and the features of using a multi-purpose structure for control dynamic objects are studied.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"30 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76289965","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}