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

{"title":"Approximation of supremum and infimum processes as a stochastic approach to the providing of homeostasis","authors":"G. Beliavsky, N. Danilova, G. Ougolnitsky","doi":"10.21638/11701/spbu10.2022.101","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.101","url":null,"abstract":"We consider the calculation of bounded functional of the trajectories of a stationary diffusion process. Since an analytical solution to this problem does not exist, it is necessary to use numerical methods. One possible direction for obtaining the numerical method is applying the Monte Carlo (MC) method. This involves reproducing the trajectory of a random process with subsequent averaging over the trajectories. To simplify the reproduction of the trajectory, the Girsanov transform is used in this paper. The main goal is to approximate the supremum and infimum processes, which allows us to more accurately compute the mathematical expectation of a function depending on the values of the supremum and infimum processes at the end of the time interval compared to the classical method. The method is based on randomly dividing the interval of the time axis by stopping times passages of the Wiener process, approximating the density to replace the measure, and using the MC method to calculate the expectation. One of the applications of the method is the task of keeping a random process in a given area the problem of homeostasis.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"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":"81136604","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":"IMPACT OF COLLISIONS ON THE DYNAMICS OF WAVES OF FINITE AMPLITUDE IN A PLASMA","authors":"A. Karimov, Vladislav K. Bogdanov","doi":"10.21638/11701/spbu10.2022.204","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.204","url":null,"abstract":"The problem of determining wave dynamics, considering the evolution of nonlinear waves of finite amplitude in a weakly collisional, Maxwellian plasma, is the focus of this article. Considering this medium with a certain interaction potential associated with a certain limited core of pairwise interaction, the dynamics of the distribution function was studied using the Vlasov equation. Collisions of electrons with neutral particles are described using the collision integral in the Bhatnagar - Gross- Krook form. Having constructed its particular solution and the equilibrium distribution function in the form of a series, an equation was obtained that makes it possible to determine the potential function. Considering the case of a Maxwellian plasma, an integral potential equation was obtained. Based on it, an equation was constructed that determines the perturbation of the potential relative to the spatially homogeneous one. At the same time, this perturbation appears due to the existence of some spatial-temporal stable structure. Based on this, a dispersion relation was obtained, which makes it possible to estimate the spatial scales of the coherent structure.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"107 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78929421","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":"Procedure for regularization of bilinear optimal control problems based on a finite-dimensional model","authors":"A. Arguchintsev, V. Srochko","doi":"10.21638/11701/spbu10.2022.115","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.115","url":null,"abstract":"An optimization problem of a linear system of ordinary differential equations on a set of piecewise continuous scalar controls with two-sided restrictions is considered. The cost functional contains the bilinear part (control, state) and a control square with a parameter, which plays the role of a regularization term. An approximate solution of the optimal control problem is carried out on a subset of piecewise constant controls with a non-uniform grid of possible switching points. As a result of the proposed parametrization, reduction to the finite-dimensional problem of quadratic programming was carried out with the parameter in the objective function and the simplest restrictions. In the case of a strictly convex objective function, the finite-dimensional problem can be solved in a finite number of iterations by the method of special points. For strictly concave objective functions, the corresponding problem is solved by simple or specialized brute force methods. In an arbitrary case, parameter conditions and switching points are found at which the objective function becomes convex or concave. At the same time, the corresponding problems of mathematical programming allow a global solution in a finite number of iterations. Thus, the proposed approach allows to approximate the original non-convex variation problem with a finite-dimensional model that allows to find a global solution in a finite number of iterations.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"87 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86674947","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":"Mathematical model \"consumer-resource\" on a liner range and its application for modeling the spread of late blight of potato","authors":"N. A. Gasratova","doi":"10.21638/11701/spbu10.2022.409","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.409","url":null,"abstract":"A model of consumer distribution on a fixed resource, which is uniformly distributed through a linear area, is presented. The model is based on the Cauchy problem for a system of partial differential equations. The stability of the system is studied. The physical basis of the model is the spread of late blight over the territory of a trophic resource. A qualitative picture of the process under consideration coincides with field data obtained as a result of modeling. The model describes \"consumer\" development not even at the moment, but through linear range. Thus assesment of damaged field square is possible.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"217 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73143132","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":"Modelling and design of permanent magnet multipoles for beam transport and focusing. II. Configuring the quad","authors":"V. Amoskov, V. Vasiliev, E. Gapionok, Georgy G. Gulbekian, N. Edamenko, I. Ivanenko, N. Kazarinov, I. Kalagin, M. Kaparkova, V. Kukhtin, E. Lamzin, A. Makarov, A. Nezhentzev, D. Ovsyannikov, Dmitry A. Ovsyannikov (Jr), Nikolai F. Osipov, I. Rodin, S. Sytchevsky, Alexey A. Firsov, N. Shatil","doi":"10.21638/11701/spbu10.2022.402","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.402","url":null,"abstract":"An optimized magnetic specification has been searched for a PM quadrupole constructed for the DC-140 cyclotron in JINR, Dubna. The field inhomogeneity should be reduced to come closer to an ideal distribution. The quad parameters should be determined with very high mechanical and magnetic precision in order to reach the specified gradient. Results of the analytic study based on a 2D model gave initial values for the PM blocks dimensions and orientations. To ensure stringent performance criteria, parametrized 2D and 3D models of the quad were built. These models were used to optimize the magnet configuration, analyze its sensitivity to various errors and derive parameter tolerances. Additional adjustment to suitable field quality is foreseen using results of a trajectory analysis and acceptance inspection. The design parameters for the best suited magnet configuration are presented and the performance criteria are defined. However, an electromagnetic analysis of the selected configuration has revealed that the relative field error adopted previously as the optimization criterion gives low accuracy estimate. Alternative estimations are proposed utilizing the field gradient error as the basic criterion to satisfy the constraint on the field inhomogeneity.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"72 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77228079","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":"Convergence conditions for continuous and discrete models of population dynamics","authors":"A. Aleksandrov","doi":"10.21638/11701/spbu10.2022.401","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.401","url":null,"abstract":"Some classes of continuous and discrete generalized Volterra models of population dynamics are considered. It is supposed that there are relationships of the type \"symbiosis\", \"compensationism\" or \"neutralism\" between any two species in a biological community. The objective of the work is to obtain conditions under which the investigated models possess the convergence property. This means that the studying system admits a bounded solution that is globally asimptotically stable. To determine the required conditions, the V. I. Zubov's approach and its discrete-time counterpart are used. Constructions of Lyapunov functions are proposed, and with the aid of these functions, the convergence problem for the considered models is reduced to the problem of the existence of positive solutions for some systems of linear algebraic inequalities. In the case where parameters of models are almost periodic functions, the fulfilment of the derived conditions implies that limiting bounded solutions are almost periodic, as well. An example is presented illustrating the obtained theoretical conclusions.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"39 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77398698","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":"AN EPIDEMIC MODEL OF MALARIA WITHOUT AND WITH VACCINATION. PT 1. A MODEL OF MALARIA WITHOUT VACCINATION","authors":"Serine Ndiaye, E. Parilina","doi":"10.21638/11701/spbu10.2022.207","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.207","url":null,"abstract":"We propose a mathematical model of the malaria epidemic in the human population (host), where the transmission of the disease is produced by a vector population (mosquito) known as the malaria mosquito. The malaria epidemic model is defined by a system of ordinary differential equations. The host population at any time is divided into four sub-populations: susceptible, exposed, infectious, recovered. Sufficient conditions for stability of equilibrium without disease and endemic equilibrium are obtained using the Lyapunov’s function theory. We define the reproductive number characterizing the level of disease spreading in the human population. Numerical modeling is made to study the influence of parameters on the spread of vector-borne disease and to illustrate theoretical results, as well as to analyze possible behavioral scenarios.","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":"90537875","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":"To the problem of the pursuit in quasilinear differential lag games","authors":"E. M. Mukhsinov","doi":"10.21638/11701/spbu10.2022.303","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.303","url":null,"abstract":"In the field of the theory of differential games defined in a finite-dimensional space, fundamental works were carried out by L. S. Pontryagin, N. N. Krasovskiy, B. N. Pshenichny, L. S. Petrosyan, M. S. Nikol’skiy, N. Yu. Satimov and others. L. S. Pontryagin and his students consider differential games separately, from the point of view of the pursuer and from the point of view of the evader, which inevitably connects the differential game with two different problems. In this paper, in a Hilbert space, we consider the pursuit problem in the sense of L. S. Pontryagin for a quasilinear differential game, when the dynamics of the game is described by a differential equation of retarded type with a closed linear operator generating a strongly continuous semigroup. Two main theorems on the solvability of the pursuit problem are proved. In the first theorem, a set of initial positions is found from which it is possible to complete the pursuit with a guaranteed pursuit time. The second theorem defines sufficient conditions on the optimality of the pursuit time. The results obtained generalize the results of works by P. B. Gusyatnikov, M. S. Nikol’skiy, E. M. Mukhsinov, and M. N. Murodova, in which it is described by a differential equation of retarded type in a Hilbert space. Our results make it possible to study delayed-type conflict-controlled systems not only with lumped, but also with distributed parameters.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90255641","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":"Linear electron accelerator for energy 8-50 MeV with injection from an electron source based on cluster plasma systems","authors":"I. Ashanin, Yulia D. Kluchevskaia, S. Polozov, V. Rashchikov","doi":"10.21638/11401/spbu10.2022.403","DOIUrl":"https://doi.org/10.21638/11401/spbu10.2022.403","url":null,"abstract":"For many years, one of the key problems of modern accelerator physics has been an increase of the rate of the energy gain in RF linear electron accelerators. The physical limits of the accelerating field intensity for metallic accelerating structures have been practically reached; therefore, new acceleration schemes are being considered, primarily acceleration in plasma and wakefield acceleration. The second aim is the generation of ultrashort (100 fs and less) electron bunches, for which RF photoguns are traditionally used. In this case, for RF photoguns, a serious problem that limits the intensity of electrons in a bunch is the influence of the own space charge during emission and acceleration in the near-cathode region, where the beam is weakly relativistic and the influence of the space charge on its dynamics plays the determinative role. The possibility of using a plasma cathode source as an injector for RF accelerator will considered. In the future, this may make it possible to bypass the limitations inherent in RF photoguns (sufficient influence of the space charge on the beam dynamics in the near-cathode region) and acceleration in the laser-plasma channel (low electron capture coefficient in the acceleration mode, wide energy spectrum - 10% or more at energies of tens and hundreds of megaelectrons). It is proposed to develop a combined accelerator in which a bunch generated in a laser-plasma channel is injected into a traditional metal structure. It is supposed that could be possible to generate a short (from 0.1 to 1.0 ps) electron bunches with an energy of several hundred kiloelectrons, which will make it possible to consider such source as an alternative to the photocathode. Next, the beam must be captured in the acceleration mode in a normally conducting section and accelerated to an energy of 50 MeV with the possibility of energy tuning. The features of such accelerator, the features of the electron bunch capturing in the acceleration mode, and the possible values of the energy spectrum in such a system will considered.","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":"88353317","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":"Numerical methods and algorithms for reconstruction of holographic images with an flexibility choice of physical size of the object and observation area","authors":"A. G. Fedorov, V. Trofimov, A. G. Karpov","doi":"10.21638/11701/spbu10.2022.108","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.108","url":null,"abstract":"Within the framework of this work, the numerical results of simulation and reconstruction of holographic images with different physical sizes of the object and observation areas are presented. Simple and practical approaches to relatively flexibility choice of physical areas (e. g., units of m2) in both planes are proposed. Algorithms are presented in the case when the dimensions of the plane of the object and observation coincide. Two-step scattering algorithms are presented for the simulation and reconstruction of holographic images with a relatively flexibility choice of the physical areas of the object plane and observation.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"79 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74275870","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}