Pub Date : 2019-01-01DOI: 10.26907/2541-7746.2019.2.205-229
Y. Poveshchenko, V. Podryga, I. Popov, S. B. Popov, P. Rahimly, G. I. Kazakevich
{"title":"Numerical Simulation in Problems with Dissociation of Gas Hydrates in a Porous Medium in One-Dimensional Formulation","authors":"Y. Poveshchenko, V. Podryga, I. Popov, S. B. Popov, P. Rahimly, G. I. Kazakevich","doi":"10.26907/2541-7746.2019.2.205-229","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.2.205-229","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"38 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75521778","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 : 2019-01-01DOI: 10.26907/2541-7746.2019.3.468-480
A. Akchurin, G. Smirnov
{"title":"Interrelation of Traveling Ionospheric Disturbances Above and Below the F-Layer Peak according to the Ionosonde and the SWARM Constellation Data","authors":"A. Akchurin, G. Smirnov","doi":"10.26907/2541-7746.2019.3.468-480","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.3.468-480","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"2 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80618541","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 : 2019-01-01DOI: 10.26907/2541-7746.2019.3.327-340
V. Alekseev, M. Vasilyeva, V. Vasilyev, N. Sidnyaev’
{"title":"Numerical Simulation of Natural Convection in a Freezing Soil","authors":"V. Alekseev, M. Vasilyeva, V. Vasilyev, N. Sidnyaev’","doi":"10.26907/2541-7746.2019.3.327-340","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.3.327-340","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"29 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90533443","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 : 2019-01-01DOI: 10.26907/2541-7746.2019.3.438-455
A. Malyugina, V. Shurygin
A smooth manifold over the algebra of dual numbers D (a D -smooth manifold) carries the canonical foliation whose leaves are affine manifolds. Extension of charts on a D -smooth manifold along leaf paths allows ones to associate with an immersed transversal of the canonical foliation a pseudogroup of local D -diffeomorphisms called the holonomy pseudogroup. In the present paper, holonomy pseudogroups are applied to the study of D -diffeomorphisms between quotient manifolds of the algebra D by lattices. In particular, it is shown that a D diffeomorphism between two such manifolds exists if and only if one of the lattices is obtained from the other by the multiplication by a dual number. In addition, it is shown that some D -smooth manifolds naturally associated with an affine manifold are D -diffeomorphic if and only if this manifold is radiant.
{"title":"Holonomy Pseudogroups as Obstructions to Equivalence of Manifolds over the Algebra of Dual Numbers","authors":"A. Malyugina, V. Shurygin","doi":"10.26907/2541-7746.2019.3.438-455","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.3.438-455","url":null,"abstract":"A smooth manifold over the algebra of dual numbers D (a D -smooth manifold) carries the canonical foliation whose leaves are affine manifolds. Extension of charts on a D -smooth manifold along leaf paths allows ones to associate with an immersed transversal of the canonical foliation a pseudogroup of local D -diffeomorphisms called the holonomy pseudogroup. In the present paper, holonomy pseudogroups are applied to the study of D -diffeomorphisms between quotient manifolds of the algebra D by lattices. In particular, it is shown that a D diffeomorphism between two such manifolds exists if and only if one of the lattices is obtained from the other by the multiplication by a dual number. In addition, it is shown that some D -smooth manifolds naturally associated with an affine manifold are D -diffeomorphic if and only if this manifold is radiant.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"23 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75097057","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 : 2019-01-01DOI: 10.26907/2541-7746.2019.4.536-542
D. Katz, B. Kats
The Beltrami differential equations are intrinsic generalizations of the Cauchy–Riemann system in complex analysis. Their solutions generalize holomorphic functions. As known, solutions to many problems of the complex analysis are based on application of the Cauchy formula, i.e., on the integral representation of analytical functions by curvilinear integrals over boundaries of the domains of analyticity. Particularly, this representation enables us to solve the Riemann boundary-value problem for holomorphic functions, to prove the Painleve theorem on erasing of singularities of analytical functions, and to obtain many other important results. A. Tungatarov established an analog of this representation of solutions to a certain simple case of the Beltrami equation (so-called beta-analytic functions). A. Tungatarov’s representation was used by R. Abreu-Blaya, J. Bory-Reyes, and D. Pe˜na-Pe˜na for solving the problems stated by B. Riemann, P. Painleve, and other researchers. In this paper, we constructed integral representations for the solutions of more extensive classes of the Beltrami equations, which are analogs of the integral Cauchy formula, and described their applications.
{"title":"An Analog of the Cauchy Formula for Certain Beltrami Equation","authors":"D. Katz, B. Kats","doi":"10.26907/2541-7746.2019.4.536-542","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.4.536-542","url":null,"abstract":"The Beltrami differential equations are intrinsic generalizations of the Cauchy–Riemann system in complex analysis. Their solutions generalize holomorphic functions. As known, solutions to many problems of the complex analysis are based on application of the Cauchy formula, i.e., on the integral representation of analytical functions by curvilinear integrals over boundaries of the domains of analyticity. Particularly, this representation enables us to solve the Riemann boundary-value problem for holomorphic functions, to prove the Painleve theorem on erasing of singularities of analytical functions, and to obtain many other important results. A. Tungatarov established an analog of this representation of solutions to a certain simple case of the Beltrami equation (so-called beta-analytic functions). A. Tungatarov’s representation was used by R. Abreu-Blaya, J. Bory-Reyes, and D. Pe˜na-Pe˜na for solving the problems stated by B. Riemann, P. Painleve, and other researchers. In this paper, we constructed integral representations for the solutions of more extensive classes of the Beltrami equations, which are analogs of the integral Cauchy formula, and described their applications.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"9 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82207767","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 : 2019-01-01DOI: 10.26907/2541-7746.2019.4.509-525
I. Volkov, L. Igumnov, S. Litvinchuk
The main laws of deformation and degradation processes of the initial strength properties of structural materials (metals and their alloys) according to the long-term strength mech-anism were considered. From the viewpoint of the mechanics of damaged media (MDM), a mathematical model was created to describe inelastic deformation and damage accumulation during the creep process. An experimental and theoretical methodology for determining material parameters of the derived defining relations of MDM was developed. The material parameters and scalar functions of the MDM model, its reliability and the scope of its ap-plicability were determined based on the analysis of the processes of deformation and failure of laboratory specimens in the conditions of soft loading (controlled stresses). The results of the experimental study of short-term creep of the VZh-159 heat-resistant alloy were presented. The process of deformation and damage accumulation was numerically analyzed; the obtained numerical results were compared with the data of the full-scale experiments. Comparison of the numerical and experimental data shows that the introduced defining relations of MDM adequately describe the response of materials in the conditions of degradation of the initial strength properties of structural materials according to the long-term strength mechanism.
{"title":"A Continual Model of Damaged Media for Describing the Creep Failure Process","authors":"I. Volkov, L. Igumnov, S. Litvinchuk","doi":"10.26907/2541-7746.2019.4.509-525","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.4.509-525","url":null,"abstract":"The main laws of deformation and degradation processes of the initial strength properties of structural materials (metals and their alloys) according to the long-term strength mech-anism were considered. From the viewpoint of the mechanics of damaged media (MDM), a mathematical model was created to describe inelastic deformation and damage accumulation during the creep process. An experimental and theoretical methodology for determining material parameters of the derived defining relations of MDM was developed. The material parameters and scalar functions of the MDM model, its reliability and the scope of its ap-plicability were determined based on the analysis of the processes of deformation and failure of laboratory specimens in the conditions of soft loading (controlled stresses). The results of the experimental study of short-term creep of the VZh-159 heat-resistant alloy were presented. The process of deformation and damage accumulation was numerically analyzed; the obtained numerical results were compared with the data of the full-scale experiments. Comparison of the numerical and experimental data shows that the introduced defining relations of MDM adequately describe the response of materials in the conditions of degradation of the initial strength properties of structural materials according to the long-term strength mechanism.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"29 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88633154","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 : 2019-01-01DOI: 10.26907/2541-7746.2019.2.315-321
R. Gubarev, E. Dzyuba
In the context of the national economic turbulence, it becomes important to forecast the social development of constituent entities of the Russian Federation. In order to provide highly accurate forecasting, neural network technologies are used in the research (a Bayesian assembly of the dynamic neural network of various configurations is formed). As a result of the forecasting, it is found, that the leading Russian regions should have a lower social development index in 2016–2017 as compared to 2014–2015. A slowdown of social development is also predicted for the leading regions of the Volga Federal District in 2016–2017, but only as compared to 2015. The obtained data show that the social development index in the Republic of Bashkortostan changes a little. Nevertheless, a significant lagging of Bashkortostan behind the leading regions of the Russian Federation and the Volga Federal District in the social sphere is predicted: Bashkortostan is a competitive region in terms of the living standards, but not in the sphere of scientific research and innovations. For this reason, measures encouraging innovative development of Russian regions as exemplified by the Republic of Bashkortostan are introduced and discussed in the paper.
{"title":"Neuromathematics as an Effective Tool for Forecasting Social Development of Russian Regions","authors":"R. Gubarev, E. Dzyuba","doi":"10.26907/2541-7746.2019.2.315-321","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.2.315-321","url":null,"abstract":"In the context of the national economic turbulence, it becomes important to forecast the social development of constituent entities of the Russian Federation. In order to provide highly accurate forecasting, neural network technologies are used in the research (a Bayesian assembly of the dynamic neural network of various configurations is formed). As a result of the forecasting, it is found, that the leading Russian regions should have a lower social development index in 2016–2017 as compared to 2014–2015. A slowdown of social development is also predicted for the leading regions of the Volga Federal District in 2016–2017, but only as compared to 2015. The obtained data show that the social development index in the Republic of Bashkortostan changes a little. Nevertheless, a significant lagging of Bashkortostan behind the leading regions of the Russian Federation and the Volga Federal District in the social sphere is predicted: Bashkortostan is a competitive region in terms of the living standards, but not in the sphere of scientific research and innovations. For this reason, measures encouraging innovative development of Russian regions as exemplified by the Republic of Bashkortostan are introduced and discussed in the paper.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"32 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85397151","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 : 2019-01-01DOI: 10.26907/2541-7746.2019.3.423-437
I. Konnov, O. Kashina, E. I. Gilmanova
The rapid growth in the volume of processed information that takes place nowadays deter-mines the urgency of the development of methods for reducing the dimension of computational problems. One of the approaches to reducing the dimensionality of data is their clustering, i.e., uniting into maximally homogeneous groups. At the same time, it is desirable that rep-resentatives of different clusters should be as much as possible unlike each other. Along with the dimension reduction, clustering procedures have an independent value. For example, we know the market segmentation problem in economics, the feature typologization problem in sociology, faces diagnostics in geology, etc. Despite the large number of known clusterization methods, the development and study of new ones remain relevant. The reason is that there is no algorithm that would surpass all the rest by all criteria (speed, insensitivity to clusters’ size and shape, number of input parameters, etc.). In this paper, we propose a clustering algorithm based on the notions of the graph theory (namely, the maximum flow (the minimum cut) theorem) and compare the results obtained by it and by four other algorithms that belong to various classes of clusterization techniques.
{"title":"Solution of Clusterization Problem by Graph Optimization Methods","authors":"I. Konnov, O. Kashina, E. I. Gilmanova","doi":"10.26907/2541-7746.2019.3.423-437","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.3.423-437","url":null,"abstract":"The rapid growth in the volume of processed information that takes place nowadays deter-mines the urgency of the development of methods for reducing the dimension of computational problems. One of the approaches to reducing the dimensionality of data is their clustering, i.e., uniting into maximally homogeneous groups. At the same time, it is desirable that rep-resentatives of different clusters should be as much as possible unlike each other. Along with the dimension reduction, clustering procedures have an independent value. For example, we know the market segmentation problem in economics, the feature typologization problem in sociology, faces diagnostics in geology, etc. Despite the large number of known clusterization methods, the development and study of new ones remain relevant. The reason is that there is no algorithm that would surpass all the rest by all criteria (speed, insensitivity to clusters’ size and shape, number of input parameters, etc.). In this paper, we propose a clustering algorithm based on the notions of the graph theory (namely, the maximum flow (the minimum cut) theorem) and compare the results obtained by it and by four other algorithms that belong to various classes of clusterization techniques.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"3 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78412965","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 : 2019-01-01DOI: 10.26907/2541-7746.2019.1.53-65
A. Aganin, T. F. Khalitova
{"title":"Effect of the Liquid Temperature on Strong Compression of a Cavitation Bubble","authors":"A. Aganin, T. F. Khalitova","doi":"10.26907/2541-7746.2019.1.53-65","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.1.53-65","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"15 12 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86914466","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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