Pub Date : 2020-03-29DOI: 10.33581/2520-6508-2020-1-59-69
R. Sharykin, Alexander N. Kourbatski
This article proposes an approach that allows us to study a mathematical model of a virus protection system at the stage of its design using statistical analysis of an executable model specification based on the formalism of Distributed Object Based Stochastic Hybrid Systems (DOBSHS). Important aspects of the model are its distributed and probabilistic nature. These aspects make the model more difficult to carry out attacks, but at the same time significantly complicate the understanding of its properties by the developer. In this example, we show how, using the specification of the system as a DOBSHS model, coupled with its statistical analysis, we can investigate its properties at an early stage of design and how, using this approach, we can detect «defects» of the model and correct them during the process of creating the model.
{"title":"Application of formal methods in the design of a collaborative virus defense system","authors":"R. Sharykin, Alexander N. Kourbatski","doi":"10.33581/2520-6508-2020-1-59-69","DOIUrl":"https://doi.org/10.33581/2520-6508-2020-1-59-69","url":null,"abstract":"This article proposes an approach that allows us to study a mathematical model of a virus protection system at the stage of its design using statistical analysis of an executable model specification based on the formalism of Distributed Object Based Stochastic Hybrid Systems (DOBSHS). Important aspects of the model are its distributed and probabilistic nature. These aspects make the model more difficult to carry out attacks, but at the same time significantly complicate the understanding of its properties by the developer. In this example, we show how, using the specification of the system as a DOBSHS model, coupled with its statistical analysis, we can investigate its properties at an early stage of design and how, using this approach, we can detect «defects» of the model and correct them during the process of creating the model.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69454937","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 : 2019-11-29DOI: 10.33581/2520-6508-2019-3-6-17
A. Antonevich, C. Dolicanin
In the paper some new constructions of extensions of nonclosable operators is proposed and several examples of applications are given. One of particular cases of the problem under consideration is the question on multiplication of distributions, a solution to which can be given by introduction of the so-called new generalized functions. It was demonstrated that the main obstacle for multiplication of distributions is nonclosablility of classical multiplication and the construction of new generalized functions is based on the ideas similar to that used under construction of the extension of nonclosable operators.
{"title":"Extensions of nonclosable operators and multiplication of distributions","authors":"A. Antonevich, C. Dolicanin","doi":"10.33581/2520-6508-2019-3-6-17","DOIUrl":"https://doi.org/10.33581/2520-6508-2019-3-6-17","url":null,"abstract":"In the paper some new constructions of extensions of nonclosable operators is proposed and several examples of applications are given. One of particular cases of the problem under consideration is the question on multiplication of distributions, a solution to which can be given by introduction of the so-called new generalized functions. It was demonstrated that the main obstacle for multiplication of distributions is nonclosablility of classical multiplication and the construction of new generalized functions is based on the ideas similar to that used under construction of the extension of nonclosable operators.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45125522","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 : 2019-11-29DOI: 10.33581/2520-6508-2019-3-48-56
A. P. Shilin
The linear hypersingular integro-differential equation of arbitrary order on a closed curve located on the complex plane is considered. A scheme is proposed to study this equation in the case when its coefficients have some particular structure. This scheme providers for the use of generalized Sokhotsky formulas, the solution of the Riemann boundary value problem and the solution in the class of analytical functions of linear differential equations. According to this scheme, the equations are explicitly solved, the coefficients of which contain power factors, so that along with the Riemann problem the arising differential equations are constructively solved. Solvability conditions, solution formulas, examples are given.
{"title":"Hypersingular integro-differential equations with power factors in coefficients","authors":"A. P. Shilin","doi":"10.33581/2520-6508-2019-3-48-56","DOIUrl":"https://doi.org/10.33581/2520-6508-2019-3-48-56","url":null,"abstract":"The linear hypersingular integro-differential equation of arbitrary order on a closed curve located on the complex plane is considered. A scheme is proposed to study this equation in the case when its coefficients have some particular structure. This scheme providers for the use of generalized Sokhotsky formulas, the solution of the Riemann boundary value problem and the solution in the class of analytical functions of linear differential equations. According to this scheme, the equations are explicitly solved, the coefficients of which contain power factors, so that along with the Riemann problem the arising differential equations are constructively solved. Solvability conditions, solution formulas, examples are given.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69454889","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 : 2019-11-29DOI: 10.33581/2520-6508-2019-3-134-138
V. Kotov, Natallia S. Bogdanova
Bunch technique for semionline with two groups of items is proposed in this paper. Algorithm to solve this problem is to distribute items from the first group bunch approach and after that apply LS-algorithm to assign items from the se cond group. In order to prove the estimation of our algorithm is introduced different types of bunches to distribute all items from the first group such a way that only one of the entered types of bunches are obtained. During the second stage we use LS with worst case performance is at most 17/9.
{"title":"Bunch technique for semionline with two groups of items","authors":"V. Kotov, Natallia S. Bogdanova","doi":"10.33581/2520-6508-2019-3-134-138","DOIUrl":"https://doi.org/10.33581/2520-6508-2019-3-134-138","url":null,"abstract":"Bunch technique for semionline with two groups of items is proposed in this paper. Algorithm to solve this problem is to distribute items from the first group bunch approach and after that apply LS-algorithm to assign items from the se cond group. In order to prove the estimation of our algorithm is introduced different types of bunches to distribute all items from the first group such a way that only one of the entered types of bunches are obtained. During the second stage we use LS with worst case performance is at most 17/9.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69454885","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 : 2019-08-08DOI: 10.33581/2520-6508-2019-2-52-61
R. Sharykin, Alexander N. Kourbatski
This article offers a mathematical model for distributed objectoriented stochastic hybrid systems (DOBSHS). DOBSHS are composite objects communicating with other objects through the exchange of messages through an asynchronous medium such as a network. An important component of the model is the probabilistic nature of the DOBSHS, in which the state of the system is described by stochastic differential equations with instantaneous probabilistic state changes when certain conditions are met. Also probabilistic is the nature of the messaging environment, in which the model of message delivery time is a random variable. Such problems are often encountered in practice in various areas and issues of formal modeling and verification of their properties are very important. The article presents a mathematical model of DOBSHS and proved that it has a Markov property.
{"title":"A model of distributed objectbased stochastic hybrid systems","authors":"R. Sharykin, Alexander N. Kourbatski","doi":"10.33581/2520-6508-2019-2-52-61","DOIUrl":"https://doi.org/10.33581/2520-6508-2019-2-52-61","url":null,"abstract":"This article offers a mathematical model for distributed objectoriented stochastic hybrid systems (DOBSHS). DOBSHS are composite objects communicating with other objects through the exchange of messages through an asynchronous medium such as a network. An important component of the model is the probabilistic nature of the DOBSHS, in which the state of the system is described by stochastic differential equations with instantaneous probabilistic state changes when certain conditions are met. Also probabilistic is the nature of the messaging environment, in which the model of message delivery time is a random variable. Such problems are often encountered in practice in various areas and issues of formal modeling and verification of their properties are very important. The article presents a mathematical model of DOBSHS and proved that it has a Markov property.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44359264","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 : 2019-08-08DOI: 10.33581/2520-6508-2019-2-40-51
U. V. Karalevich
The work gives a solution of the plane elasticity problem for rotating polar-orthotropic annular disks of a variable thickness. The disk is loaded with a system of equal focused forces on the outer contour applied evenly along the rim and symmetric concerning the diameter. The disk is seated with an interference fit on the flexible shaft so that a constant contact pressure acts on the interior contour. The stresses and deformations arising in such a rotating anisotropic annular disk will be non-axisymmetric. A conclusion of a fourth-order partial differential equation for the effort function is drawn. Its general solution is searched out in the form of a Fourier series of cosines with even numbers. As a result, an infinite system of ordinary differential equations is solved for the coefficients of the series. These differential equations correspond to the linear Volterra integral equations of the 2 nd kind, which are solved using resolvents. Constants of integration are determined from the border conditions. Expressions for the stress components are written through the effort function by the well-known formulas. We find the components of the displacement vector in the disk by the integration of the Hooke’s law equations for the polar-orthotropic plate. We calculate the deformation components in a ring anisotropic disk by Cauchy differential relations if we know the displacements. The solved formulas for stresses, deformations and displacements completely describe the stress-deformed state in a rotating polar-orthotropic disc of variable thickness with a system of focused forces on the outer contour. The results of the work can be used in the design of working disks of turbomachines and turbo compressors, as well as rotors of centrifugal stands.
{"title":"The field of tensions of a rotating anisotropic disc of a variable thickness loaded with undistracted forces on the outer contour","authors":"U. V. Karalevich","doi":"10.33581/2520-6508-2019-2-40-51","DOIUrl":"https://doi.org/10.33581/2520-6508-2019-2-40-51","url":null,"abstract":"The work gives a solution of the plane elasticity problem for rotating polar-orthotropic annular disks of a variable thickness. The disk is loaded with a system of equal focused forces on the outer contour applied evenly along the rim and symmetric concerning the diameter. The disk is seated with an interference fit on the flexible shaft so that a constant contact pressure acts on the interior contour. The stresses and deformations arising in such a rotating anisotropic annular disk will be non-axisymmetric. A conclusion of a fourth-order partial differential equation for the effort function is drawn. Its general solution is searched out in the form of a Fourier series of cosines with even numbers. As a result, an infinite system of ordinary differential equations is solved for the coefficients of the series. These differential equations correspond to the linear Volterra integral equations of the 2 nd kind, which are solved using resolvents. Constants of integration are determined from the border conditions. Expressions for the stress components are written through the effort function by the well-known formulas. We find the components of the displacement vector in the disk by the integration of the Hooke’s law equations for the polar-orthotropic plate. We calculate the deformation components in a ring anisotropic disk by Cauchy differential relations if we know the displacements. The solved formulas for stresses, deformations and displacements completely describe the stress-deformed state in a rotating polar-orthotropic disc of variable thickness with a system of focused forces on the outer contour. The results of the work can be used in the design of working disks of turbomachines and turbo compressors, as well as rotors of centrifugal stands.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45535241","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 : 2019-08-08DOI: 10.33581/2520-6508-2019-2-34-39
Natalia V. Semenchuk
The article proposes a new method for determining the number of splitting intervals and the number of observations in them when building estimates of the spectral densities of stationary random processes with a given accuracy over intersecting observation intervals based on asymptotic results, obtained for the first moment of convergence rate under the assumption that the spectral density satisfies the Lipschitz condition. Two cases are considered: with a single and arbitrary data taper. As a result, an algorithm is proposed for constructing estimates for intersecting intervals of observations with a given accuracy. This algorithm was tested on model examples for random AR(4) processes, using data taper of Riesz, Bochner, Parzen. The proposed method will be useful to the researcher in analyzing data in the form of stationary random processes using nonparametric methods of spectral analysis in an automated mode.
{"title":"Construction of estimates of spectral densities with a given accuracy over intersecting intervals of observations","authors":"Natalia V. Semenchuk","doi":"10.33581/2520-6508-2019-2-34-39","DOIUrl":"https://doi.org/10.33581/2520-6508-2019-2-34-39","url":null,"abstract":"The article proposes a new method for determining the number of splitting intervals and the number of observations in them when building estimates of the spectral densities of stationary random processes with a given accuracy over intersecting observation intervals based on asymptotic results, obtained for the first moment of convergence rate under the assumption that the spectral density satisfies the Lipschitz condition. Two cases are considered: with a single and arbitrary data taper. As a result, an algorithm is proposed for constructing estimates for intersecting intervals of observations with a given accuracy. This algorithm was tested on model examples for random AR(4) processes, using data taper of Riesz, Bochner, Parzen. The proposed method will be useful to the researcher in analyzing data in the form of stationary random processes using nonparametric methods of spectral analysis in an automated mode.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42652968","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 : 2019-08-08DOI: 10.33581/2520-6508-2019-2-62-66
V. Savchuk, P. A. Savenkov
This article illustrates the solution of a differential equation describing oscillations of an elastic tensioned guide rail, which consist of string bundle enclosed in an elastic cylindrical shell, while concentrated load, simulated by a material point, moves along it. The oscillatory system is considered in such way that the guide rail supports freely. The existing external and internal forces of resistance to movement of the guide rail are also taken into account. Initial and boundary conditions are zero. In article «A string bend under a moving load», published in the journal «Vestnik BGU. Seriya 1, Fizika. Matematika. Informatika» (2004, No. 1), the deflection of a flexible guide rail under load was obtained by solving an equation with deviating argument. In this article, an algorithm is constructed for finding deflection of an elastic tensioned guide rail in the form of a cubic splines. All the results of calculations are presented in a dimensionless form.
{"title":"Elastic guide rail oscillation due to moving concentrated load","authors":"V. Savchuk, P. A. Savenkov","doi":"10.33581/2520-6508-2019-2-62-66","DOIUrl":"https://doi.org/10.33581/2520-6508-2019-2-62-66","url":null,"abstract":"This article illustrates the solution of a differential equation describing oscillations of an elastic tensioned guide rail, which consist of string bundle enclosed in an elastic cylindrical shell, while concentrated load, simulated by a material point, moves along it. The oscillatory system is considered in such way that the guide rail supports freely. The existing external and internal forces of resistance to movement of the guide rail are also taken into account. Initial and boundary conditions are zero. In article «A string bend under a moving load», published in the journal «Vestnik BGU. Seriya 1, Fizika. Matematika. Informatika» (2004, No. 1), the deflection of a flexible guide rail under load was obtained by solving an equation with deviating argument. In this article, an algorithm is constructed for finding deflection of an elastic tensioned guide rail in the form of a cubic splines. All the results of calculations are presented in a dimensionless form.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45504638","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 : 2019-07-12DOI: 10.33581/2520-6508-2019-2-27-33
V. P. Kirlitsa
In article the problem of construction exact D-optimal designs of experiments for linear multiple regression in a case when variance of errors of observations depend on a point in which is made is investigated. Class of functions which describe change variance of heteroscedastic observations is defined for which it is possible construct D-optimal continues designs of experiments. For linear multiple regression with three factors it is constructed five different types of D-optimal continues designs of experiments with heteroscedastic observations. For each of these types the own class of functions describing change variance of observations is defined.
{"title":"Construction D-optimal designs of experiments for linear multiple regression with heteroscedastic observations","authors":"V. P. Kirlitsa","doi":"10.33581/2520-6508-2019-2-27-33","DOIUrl":"https://doi.org/10.33581/2520-6508-2019-2-27-33","url":null,"abstract":"In article the problem of construction exact D-optimal designs of experiments for linear multiple regression in a case when variance of errors of observations depend on a point in which is made is investigated. Class of functions which describe change variance of heteroscedastic observations is defined for which it is possible construct D-optimal continues designs of experiments. For linear multiple regression with three factors it is constructed five different types of D-optimal continues designs of experiments with heteroscedastic observations. For each of these types the own class of functions describing change variance of observations is defined.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":"136 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41278052","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 : 2019-04-26DOI: 10.33581/2520-6508-2019-1-4-11
V. Bernik, F. Götze, N. Kalosha
In 2012 it was proved that real algebraic numbers follow a nonuniform but regular distribution, where the respective definitions go back to H. Weyl (1916) and A. Baker and W. Schmidt (1970). The largest deviations from the uniform distribution occur in neighborhoods of rational numbers with small denominators. In this article the authors are first to specify a gene ral condition that guarantees the presence of a large quantity of real algebraic numbers in a small interval. Under this condition, the distribution of real algebraic numbers attains even stronger regularity properties, indicating that there is a chance of proving Wirsing’s conjecture on approximation of real numbers by algebraic numbers and algebraic integers.
{"title":"Counting algebraic numbers in short intervals with rational points","authors":"V. Bernik, F. Götze, N. Kalosha","doi":"10.33581/2520-6508-2019-1-4-11","DOIUrl":"https://doi.org/10.33581/2520-6508-2019-1-4-11","url":null,"abstract":"In 2012 it was proved that real algebraic numbers follow a nonuniform but regular distribution, where the respective definitions go back to H. Weyl (1916) and A. Baker and W. Schmidt (1970). The largest deviations from the uniform distribution occur in neighborhoods of rational numbers with small denominators. In this article the authors are first to specify a gene ral condition that guarantees the presence of a large quantity of real algebraic numbers in a small interval. Under this condition, the distribution of real algebraic numbers attains even stronger regularity properties, indicating that there is a chance of proving Wirsing’s conjecture on approximation of real numbers by algebraic numbers and algebraic integers.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41629762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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