Pub Date : 2021-08-05DOI: 10.33581/2520-6508-2021-2-105-113
M. Zhuravkov, V. Savchuk, M. A. Nikolaitchik
The article describes an analytical model of mine skip dynamics taking into account the presence of the head and balancing ropes and the existing curvilinearity of the guides. Expressions for the forces acting on the skip from the side of the guides have been constructed. It is shown, that the frequencies of natural vibrations of skip depend on the vertical acceleration and the distance traveled during its lifting. A graph (diagram) of skips vertical speed which observance does not lead to the appearance of skips vertical vibrations due to elasticity of the ropes is developed. An algorithm for finding the forces principal vector and the forces principal moment acting on the skip based on the reading of three accelerometers recording horizontal accelerations of skip during its movement is presented.
{"title":"Analytical model of skip motion taking into account influence of head and balancing ropes","authors":"M. Zhuravkov, V. Savchuk, M. A. Nikolaitchik","doi":"10.33581/2520-6508-2021-2-105-113","DOIUrl":"https://doi.org/10.33581/2520-6508-2021-2-105-113","url":null,"abstract":"The article describes an analytical model of mine skip dynamics taking into account the presence of the head and balancing ropes and the existing curvilinearity of the guides. Expressions for the forces acting on the skip from the side of the guides have been constructed. It is shown, that the frequencies of natural vibrations of skip depend on the vertical acceleration and the distance traveled during its lifting. A graph (diagram) of skips vertical speed which observance does not lead to the appearance of skips vertical vibrations due to elasticity of the ropes is developed. An algorithm for finding the forces principal vector and the forces principal moment acting on the skip based on the reading of three accelerometers recording horizontal accelerations of skip during its movement is presented.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42336556","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 : 2021-08-05DOI: 10.33581/2520-6508-2021-2-60-66
A. Kharin
An important mathematical problem of computer data analysis – the problem of statistical sequential testing of simple hypotheses on parameters of probability distributions of observed binary data – is considered in the paper. This problem is being solved for two models of observation: for independent observations and for homogeneous Markov chains. Explicit expressions of the sequential tests statistics are derived, transparent for interpretation and convenient for computer realisation. An approach is developed to calculate the performance characteristics – error probabilities and mathematical expectations of the random number of observations required to guarantee the requested accuracy for decision rules. Asymptotic expansions for the mentioned performance characteristics are constructed under «contamination» of the probability distributions of observed data.
{"title":"Statistical sequential hypotheses testing on para meters of probability distributions of random binary data","authors":"A. Kharin","doi":"10.33581/2520-6508-2021-2-60-66","DOIUrl":"https://doi.org/10.33581/2520-6508-2021-2-60-66","url":null,"abstract":"An important mathematical problem of computer data analysis – the problem of statistical sequential testing of simple hypotheses on parameters of probability distributions of observed binary data – is considered in the paper. This problem is being solved for two models of observation: for independent observations and for homogeneous Markov chains. Explicit expressions of the sequential tests statistics are derived, transparent for interpretation and convenient for computer realisation. An approach is developed to calculate the performance characteristics – error probabilities and mathematical expectations of the random number of observations required to guarantee the requested accuracy for decision rules. Asymptotic expansions for the mentioned performance characteristics are constructed under «contamination» of the probability distributions of observed data.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49437158","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 : 2021-08-05DOI: 10.33581/2520-6508-2021-2-29-37
V. A. Pavlovsky, I. L. Vasiliev
Research in the theory of functions of an h-complex variable is of interest in connection with existing applications in non-Euclidean geometry, theoretical mechanics, etc. This article is devoted to the study of the properties of h-differentiable functions. Criteria for h-differentiability and h-holomorphy are found, formulated and proved a theorem on finite increments for an h-holomorphic function. Sufficient conditions for h-analyticity are given, formulated and proved a uniqueness theorem for h-analytic functions.
{"title":"On properties of h-differentiable functions","authors":"V. A. Pavlovsky, I. L. Vasiliev","doi":"10.33581/2520-6508-2021-2-29-37","DOIUrl":"https://doi.org/10.33581/2520-6508-2021-2-29-37","url":null,"abstract":"Research in the theory of functions of an h-complex variable is of interest in connection with existing applications in non-Euclidean geometry, theoretical mechanics, etc. This article is devoted to the study of the properties of h-differentiable functions. Criteria for h-differentiability and h-holomorphy are found, formulated and proved a theorem on finite increments for an h-holomorphic function. Sufficient conditions for h-analyticity are given, formulated and proved a uniqueness theorem for h-analytic functions.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48361441","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 : 2021-08-05DOI: 10.33581/2520-6508-2021-2-114-123
E. E. Marushko, A. Doudkin, Xiangtao Zheng
The paper proposes an identification technique of objects on the Earth’s surface images based on combination of machine learning methods. Different variants of multi-layer convolutional neural networks and support vector machines are considered as original models. A hybrid convolutional neural network that combines features extracted by the neural network and experts is proposed. Optimal values of hyperparameters of the models are calculated by grid search methods using k-fold cross-validation. The possibility of improving the accuracy of identification based on the ensembles of these models is shown. Effectiveness of the proposed technique is demonstrated by the example of images obtained by synthetic aperture radar.
{"title":"Identification of Earth’s surface objects using ensembles of convolutional neural networks.","authors":"E. E. Marushko, A. Doudkin, Xiangtao Zheng","doi":"10.33581/2520-6508-2021-2-114-123","DOIUrl":"https://doi.org/10.33581/2520-6508-2021-2-114-123","url":null,"abstract":"The paper proposes an identification technique of objects on the Earth’s surface images based on combination of machine learning methods. Different variants of multi-layer convolutional neural networks and support vector machines are considered as original models. A hybrid convolutional neural network that combines features extracted by the neural network and experts is proposed. Optimal values of hyperparameters of the models are calculated by grid search methods using k-fold cross-validation. The possibility of improving the accuracy of identification based on the ensembles of these models is shown. Effectiveness of the proposed technique is demonstrated by the example of images obtained by synthetic aperture radar.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45550593","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 : 2021-08-05DOI: 10.33581/2520-6508-2021-2-99-104
U. V. Karalevich, D. G. Medvedev
The solution of the stationary heat conduction problem for profiled polar-orthotropic annular plates with heat-insulated bases from N extended heat sources at their external border is presented. The temperature distribution in such plates will be non-axisymmetric. The solution of the stationary heat conduction problem for anisotropic annular plates of an random profile is resolved through the solution of the corresponding Volterra integral equation of the second kind. The formula of a temperature calculations in anisotropic annular plates of an random profile is given. The exact solution of stationary heat conduction problem for polar-orthotropic annular plate of an exponential profile is recorded. The temperature distribution in such anisotropic plate from N extended heat sources at its outer border is more complex than in the case of temperature distribution from N point heat sources at their external border.
{"title":"Influence of extended heat sources on the temperature distribution in profiled polar-orthotropic annular plates with heat-insulated bases","authors":"U. V. Karalevich, D. G. Medvedev","doi":"10.33581/2520-6508-2021-2-99-104","DOIUrl":"https://doi.org/10.33581/2520-6508-2021-2-99-104","url":null,"abstract":"The solution of the stationary heat conduction problem for profiled polar-orthotropic annular plates with heat-insulated bases from N extended heat sources at their external border is presented. The temperature distribution in such plates will be non-axisymmetric. The solution of the stationary heat conduction problem for anisotropic annular plates of an random profile is resolved through the solution of the corresponding Volterra integral equation of the second kind. The formula of a temperature calculations in anisotropic annular plates of an random profile is given. The exact solution of stationary heat conduction problem for polar-orthotropic annular plate of an exponential profile is recorded. The temperature distribution in such anisotropic plate from N extended heat sources at its outer border is more complex than in the case of temperature distribution from N point heat sources at their external border.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":"60 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41310908","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 : 2021-08-05DOI: 10.33581/2520-6508-2021-2-67-81
Y. Sotskov
A problem of scheduling partially ordered unit-time tasks processed on dedicated machines is formulated as a mixed graph colouring problem, i. e., as an assignment of integers (colours) {1, 2, …, t} to the vertices (tasks) V {ν1, ν2, …, νn}, of the mixed graph G = (V, A, E) such that if vertices vp and vq are joined by an edge [νp, νq] ∈ E their colours have to be different. Further, if two vertices νp and νq are joined by an arc (νi, νj) ∈ A the colour of vertex νi has to be no greater than the colour of vertex νj. We prove that an optimal colouring of a mixed graph G = (V, A, E) is equivalent to the scheduling problem GcMPT|pi = 1|Cmax of finding an optimal schedule for partially ordered multi-processor tasks with unit (equal) processing times. Contrary to classical shop-scheduling problems, several dedicated machines are required to process an individual task in the scheduling problem GcMPT|pi = 1|Cmax. Moreover, along with precedence constraints given on the set V {ν1, ν2, …, νn}, it is required that a subset of tasks must be processed simultaneously. Due to the theorems proved in this article, most analytical results that have been proved for the scheduling problems GcMPT |pi = 1|Cmax so far, have analogous results for optimal colourings of the mixed graphs G = (V, A, E), and vice versa.
{"title":"Mixed graph colouring as scheduling multi-processor tasks with equal processing times","authors":"Y. Sotskov","doi":"10.33581/2520-6508-2021-2-67-81","DOIUrl":"https://doi.org/10.33581/2520-6508-2021-2-67-81","url":null,"abstract":"A problem of scheduling partially ordered unit-time tasks processed on dedicated machines is formulated as a mixed graph colouring problem, i. e., as an assignment of integers (colours) {1, 2, …, t} to the vertices (tasks) V {ν1, ν2, …, νn}, of the mixed graph G = (V, A, E) such that if vertices vp and vq are joined by an edge [νp, νq] ∈ E their colours have to be different. Further, if two vertices νp and νq are joined by an arc (νi, νj) ∈ A the colour of vertex νi has to be no greater than the colour of vertex νj. We prove that an optimal colouring of a mixed graph G = (V, A, E) is equivalent to the scheduling problem GcMPT|pi = 1|Cmax of finding an optimal schedule for partially ordered multi-processor tasks with unit (equal) processing times. Contrary to classical shop-scheduling problems, several dedicated machines are required to process an individual task in the scheduling problem GcMPT|pi = 1|Cmax. Moreover, along with precedence constraints given on the set V {ν1, ν2, …, νn}, it is required that a subset of tasks must be processed simultaneously. Due to the theorems proved in this article, most analytical results that have been proved for the scheduling problems GcMPT |pi = 1|Cmax so far, have analogous results for optimal colourings of the mixed graphs G = (V, A, E), and vice versa.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43406834","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: 10.33581/2520-6508-2021-2-38-50
Dz. A. Kastsiukevich, N. Dmitruk
This paper deals with an optimal control problem for a linear discrete system subject to unknown bounded disturbances, where the control goal is to steer the system with guarantees into a given terminal set while minimising the terminal cost function. We define an optimal control strategy which takes into account the state of the system at one future time instant and propose an efficient numerical method for its construction. The results of numerical experiments show an improvement in performance under the optimal control strategy in comparison to the optimal open-loop worst-case control while maintaining comparable computation times.
{"title":"A method for constructing an optimal control strategy in a linear terminal problem","authors":"Dz. A. Kastsiukevich, N. Dmitruk","doi":"10.33581/2520-6508-2021-2-38-50","DOIUrl":"https://doi.org/10.33581/2520-6508-2021-2-38-50","url":null,"abstract":"This paper deals with an optimal control problem for a linear discrete system subject to unknown bounded disturbances, where the control goal is to steer the system with guarantees into a given terminal set while minimising the terminal cost function. We define an optimal control strategy which takes into account the state of the system at one future time instant and propose an efficient numerical method for its construction. The results of numerical experiments show an improvement in performance under the optimal control strategy in comparison to the optimal open-loop worst-case control while maintaining comparable computation times.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69454942","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: 10.33581/2520-6508-2021-2-51-59
Kiryl G. Atrokhau, E. V. Gromak
The Chazy system determines the necessary and sufficient conditions for the absence of movable critical points of solutions of the particular third order differential equation that was considered by Chazy in one of the first papers on the classification of higher-order ordinary differential equations with respect to the Painlevé property. The solution of the complete Chazy system in the case of constant poles has been already obtained. However, the question of integrating the Chazy equation remained open until now. In this paper, we prove that in the case of constant poles, under some additional conditions, this equation is integrated in elliptic functions.
{"title":"On solutions of the Chazy equation","authors":"Kiryl G. Atrokhau, E. V. Gromak","doi":"10.33581/2520-6508-2021-2-51-59","DOIUrl":"https://doi.org/10.33581/2520-6508-2021-2-51-59","url":null,"abstract":"The Chazy system determines the necessary and sufficient conditions for the absence of movable critical points of solutions of the particular third order differential equation that was considered by Chazy in one of the first papers on the classification of higher-order ordinary differential equations with respect to the Painlevé property. The solution of the complete Chazy system in the case of constant poles has been already obtained. However, the question of integrating the Chazy equation remained open until now. In this paper, we prove that in the case of constant poles, under some additional conditions, this equation is integrated in elliptic functions.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69454947","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 : 2020-07-30DOI: 10.33581/2520-6508-2020-2-79-85
A. Nikitsin
The goal of this work is to study the effect of bone ingrowth into open pores of the implant and estimate of the mechanical characteristics for obtained biocomposite. Reconstruction of the isotropic model based on data acquired from computed tomography allows us to study the metallic and bone components integration under compressive load. Results are compared to performed mechanical tests of the porous specimen. The finite element modeling allows obtaining a stress-stain curve for the bone – titanium biocomposite. Young’s modulus of the metallic specimen is increased by 29 % after pores is filled with bone tissues. The conditional yield strength of the bone – titanium biocomposite is 2 times higher than that of porous open-pore titanium.
{"title":"Estimation of the mechanical properties for bone – titanium biocomposite based on computed tomography data and finite element modeling","authors":"A. Nikitsin","doi":"10.33581/2520-6508-2020-2-79-85","DOIUrl":"https://doi.org/10.33581/2520-6508-2020-2-79-85","url":null,"abstract":"The goal of this work is to study the effect of bone ingrowth into open pores of the implant and estimate of the mechanical characteristics for obtained biocomposite. Reconstruction of the isotropic model based on data acquired from computed tomography allows us to study the metallic and bone components integration under compressive load. Results are compared to performed mechanical tests of the porous specimen. The finite element modeling allows obtaining a stress-stain curve for the bone – titanium biocomposite. Young’s modulus of the metallic specimen is increased by 29 % after pores is filled with bone tissues. The conditional yield strength of the bone – titanium biocomposite is 2 times higher than that of porous open-pore titanium.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47609478","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 : 2020-03-29DOI: 10.33581/2520-6508-2020-1-38-46
S. Bauer, E. Voronkova
Unsymmetrical buckling of nonuniform circular plates with elastically restrained edge and subjected to normal pressure is studied in this paper. The unsymmetric part of the solution is sought in terms of multiples of the harmonics of the angular coordinate. A numerical method is employed to obtain the lowest load value, which leads to the appearance of waves in the circumferential direction. The effect of material heterogeneity and boundary on the buckling load is examined. It is shown that if the outer edge of a plate is elastically restrained against radial deflection, the buckling load for unsymmetrical buckling is larger than for a plate with a movable edge. The elasticity modulus decrease away from the center of a plate leads to sufficient lowering of the buckling pressure if the outer edge can move freely in the radial direction.
{"title":"Influence of boundary constraints on the appearance of asymmetrical equilibrium states in circular plates under normal pressure","authors":"S. Bauer, E. Voronkova","doi":"10.33581/2520-6508-2020-1-38-46","DOIUrl":"https://doi.org/10.33581/2520-6508-2020-1-38-46","url":null,"abstract":"Unsymmetrical buckling of nonuniform circular plates with elastically restrained edge and subjected to normal pressure is studied in this paper. The unsymmetric part of the solution is sought in terms of multiples of the harmonics of the angular coordinate. A numerical method is employed to obtain the lowest load value, which leads to the appearance of waves in the circumferential direction. The effect of material heterogeneity and boundary on the buckling load is examined. It is shown that if the outer edge of a plate is elastically restrained against radial deflection, the buckling load for unsymmetrical buckling is larger than for a plate with a movable edge. The elasticity modulus decrease away from the center of a plate leads to sufficient lowering of the buckling pressure if the outer edge can move freely in the radial direction.","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":"69454894","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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