Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva最新文献

{"title":"Anisotropic Transport of Dielectric Particles by a Uniform Electric Field in an Inhomogeneously Heated Viscous Fluid","authors":"S. I. Martynov","doi":"10.15507/2079-6900.25.202302.53-61","DOIUrl":"https://doi.org/10.15507/2079-6900.25.202302.53-61","url":null,"abstract":"The anisotropic transfer of dielectric particles by a uniform electric field in a nonuniformly heated fluid is modeled. The transport anisotropy is determined by the mechanism of interaction between particles whose permittivity depends on temperature. The temperature distribution in the particles and in the fluid is determined by their thermal diffusivity and does not depend on the motion of the fluid, thus corresponding to small Peclet numbers. The fluid flow is considered in the approximation of small Reynolds numbers. The transfer of particles is due to the action of an anisotropic force exerted by applied uniform electric field and friction forces exerted by the fluid. The interaction of particles is taken into account. Numerical modeling of anisotropic transport dynamics of two dielectric particles is carried out. The process mentioned depends on the mutual orientation of electric field vector, temperature gradient, and initial orientation of the vector connecting the particle centers. For the case of a large number of particles, an anisotropic equilibrium distribution of the particle concentration in an external electric field is found taking into account the mechanisms of their diffusion and interaction.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128788910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the reduction of the topological classification of gradient-like flows problem to the classification of polar flows\u0000I. A. Saraev","authors":"Ilya A. Saraev","doi":"10.15507/2079-6900.25.202302.62-75","DOIUrl":"https://doi.org/10.15507/2079-6900.25.202302.62-75","url":null,"abstract":"In this paper we consider a class G(Mn)\u0000 of gradient-like flows on connected closed manifolds of dimension n≥4\u0000 such that for any flow ft∈G(Mn)\u0000 stable and unstable invariant manifolds of saddle equilibria do not intersect invariant manifolds of other saddle equilibria. It is known that the ambient manifold of any flow from the class G(Mn)\u0000 can be splitted into connected summ of the sphere Sn\u0000, gft≥0\u0000 copies of direct products Sn−1×S1\u0000, and a simply connected manifold which is not homeomorphic to the sphere. The number gft\u0000 is determined only by the number of nodal equilibria and the number of saddle equilibria such that one of their invariant manifolds has the dimension (n−1)\u0000 (we call such equilibria trivial saddles). A simply connected manifold which is not homeomorphic to the sphere presents in the splitting if and only if the set of saddle equilibria contains points with unstable manifolds of dimension i∈{2,…,n−2}\u0000 (we call such equilibria non-trivial saddles). Moreover, the complete topological classification was obtained for flows from the class G(Mn)\u0000 without non-trivial saddles. In this paper we prove that for any flow ft∈G(Mn)\u0000 the carrier manifold can be splitted into a connected sum along pairwise disjoint smoothly embedded spheres (separating spheres) that do not contain equilibrium states of the flow ft\u0000 and transversally intersect its trajectories. The restriction of the flow ft\u0000 to the complements to these spheres uniquely (up to topological equivalence and numbering) defines a finite set of flows ft1,…,ftl\u0000 defined on the components of a connected sum. Moreover, for any j∈1,…,l\u0000, the set of saddle equilibria of the flow ftj\u0000 consists either only of trivial saddles or only of of non-trivial ones and then the flow ftj\u0000 is polar. We introduce the notion of consistent topological equivalence for flows ft1,…ftj\u0000 and show that flows ft,f′t∈G(Mn)\u0000 are topologically equivalent if and only if for each of these flows the set of separating spheres exists that defines consistently topologically equivalent flows on the components of the connected sum.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114187741","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":"Bicolor Graph of Morse-Smale Cascades on Manifolds of Dimension Three","authors":"Elena Ya. Elena Ya., Elena K. Rodionova","doi":"10.15507/2079-6900.25.202302.37-52","DOIUrl":"https://doi.org/10.15507/2079-6900.25.202302.37-52","url":null,"abstract":"The purpose of this study is to single out a class of Morse-Smale cascades (diffeomorphisms) with a three-dimensional phase space that allow topological classification using combinatorial invariants. In the general case, an obstacle to such a classification is the possibility of wild embedding of separatrix closures in the ambient manifold, which leads to a countable set of topologically nonequivalent systems. To solve the problem, we study the orbit space of a cascade. The ambient manifold of a diffeomorphism can be represented as a union of three pairwise disjoint sets: a connected attractor and a repeller whose dimension does not exceed one, and their complement consisting of wandering points of a cascade called the characteristic set. It is known that the topology of the orbit space of the restriction of the Morse-Smale diffeomorphism to the characteristic set and the embedding of the projections of two-dimensional separatrices into it is a complete topological invariant for Morse-Smale cascades on three-dimensional manifolds. Moreover, a criterion for the inclusion of Morse-Smale cascades in the topological flow was obtained earlier.These results are used in this paper to show that the topological conjugacy classes of Morse-Smale cascades that are included in a topological flow and do not have heteroclinic curves admit a combinatorial description. More exactly, the class of Morse-Smale diffeomorphisms without heteroclinic intersections, defined on closed three-dimensional manifolds included in topological flows and not having heteroclinic curves, is considered. Each cascade from this class is associated with a two-color graph describing the mutual arrangement of two-dimensional separatrices of saddle periodic points. It is proved that the existence of an isomorphism of two-color graphs that preserves the color of edges is a necessary and sufficient condition for the topological conjugacy of cascades. It is shown that the speed of the algorithm that distinguishes two-color graphs depends polynomially on the number of its vertices. An algorithm for constructing a representative of each topological conjugacy class is described.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128362204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On global extrema of power Takagi functions","authors":"O. Galkin, S. Galkina, A. Tronov","doi":"10.15507/2079-6900.25.202302.22-36","DOIUrl":"https://doi.org/10.15507/2079-6900.25.202302.22-36","url":null,"abstract":"By construction, power Takagi functions Sp\u0000 are similar to Takagi's continuous nowhere differentiable function described in 1903. These real-valued functions Sp(x)\u0000 have one real parameter p>0\u0000. They are defined on the real axis R\u0000 by the series Sp(x)=∑∞n=0(S0(2nx)/2n)p\u0000, where S0(x)\u0000 is the distance from real number x\u0000 to the nearest integer number. We show that for every p>0\u0000, the functions Sp\u0000 are everywhere continuous, but nowhere differentiable on R\u0000. Next, we derive functional equations for Takagi power functions. With these, it is possible, in particular, to calculate the values Sp(x)\u0000 at rational points x\u0000. In addition, for all values of the parameter p\u0000 from the interval (0;1)\u0000, we find the global extrema of the functions Sp\u0000, as well as the points where they are reached. It turns out that the global maximum of Sp\u0000 equals to 2p/(3p(2p−1))\u0000 and is reached only at points q+1/3\u0000 and q+2/3\u0000, where q\u0000 is an arbitrary integer. The global minimum of the functions Sp\u0000 equals to 0\u0000 and is reached only at integer points. Using the results on global extremes, we obtain two-sided estimates for the functions Sp\u0000 and find the points at which these estimates are reached.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"15 9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130267650","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":"Energy Function for Direct Products of Discrete Dynamical Systems","authors":"M. Barinova, Evgenia K. Shustova","doi":"10.15507/2079-6900.25.202302.11-21","DOIUrl":"https://doi.org/10.15507/2079-6900.25.202302.11-21","url":null,"abstract":"This paper is devoted to the construction of an energy function, i.e. a smooth Lyapunov function, whose set of critical points coincides with the chain-recurrent set of a dynamical system — for a cascade that is a direct product of two systems. One of the multipliers is a structurally stable diffeomorphism given on a two-dimensional torus, whose non-wandering set consists of a zero-dimensional non-trivial basic set without pairs of conjugated points and without fixed source and sink, and the second one is an identical mapping on a real axis. It was previously proved that if a non-wandering set of a dynamical system contains a zero-dimensional basic set, as the diffeomorphism under consideration has, then such a system does not have an energy function, namely, any Lyapunov function will have critical points outside the chain-recurrent set. For an identical mapping, the energy function is a constant on the entire real line. In this paper, it is shown that the absence of an energy function for one of the multipliers is not a sufficient condition for the absence of such a function for the direct product of dynamical systems, that is, in some cases it is possible to select the second cascade in such a way that the direct product will have an energy function.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126534934","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":"Methods of numerical analysis for some integral dynamical systems with delay arguments","authors":"A. Tynda","doi":"10.15507/2079-6900.25.202301.565-577","DOIUrl":"https://doi.org/10.15507/2079-6900.25.202301.565-577","url":null,"abstract":"The aim of this work is to construct direct and iterative numerical methods for solving functional equations with hereditary components. Such equations are a convenient tool for modeling dynamical systems. In particular, they are used in population models structured by age with a finite life span. Models based on integro-differential and integral equations with various kinds of delay arguments are considered. For nonlinear equations, the operators are linearized according to the modified Newton-Kantorovich scheme. Direct quadrature and simple iteration methods are used to discretize linear equations. These methods are constructed in the paper: an iterative method for solving a nonlinear integro-differential equation on the semiaxis (−∞,0]\u0000, a direct method for solving the signal recovery problem, and iterative methods for solving a nonlinear Volterra integral equation with a constant delay. Special quadrature formulas based on orthogonal Lagger polynomials are used to approximate improper integrals on the semiaxis. The results of numerical experiments confirm the convergence of suggested methods. The proposed approaches can also be applied to other classes of nonlinear equations with delays.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126181726","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":"Exact Solutions of One Nonlinear Countable-Dimensional System of Integro-Differential Equations","authors":"A. Rassadin","doi":"10.15507/2079-6900.25.202301.542-553","DOIUrl":"https://doi.org/10.15507/2079-6900.25.202301.542-553","url":null,"abstract":"In the present paper, a nonlinear countable-dimensional system of integrodifferential equations is investigated, whose vector of unknowns is a countable set of functions of two variables. These variables are interpreted as spatial coordinate and time. The nonlinearity of this system is constructed from two simultaneous convolutions: first convolution is in the sense of functional analysis and the second one is in the sense of linear space of double-sided sequences. The initial condition for this system is a doublesided sequence of functions of one variable defined on the entire real axis. The system itself can be written as a single abstract equation in the linear space of double-sided sequences. As the system may be resolved with respect to the time derivative, it may be presented as a dynamical system. The solution of this abstract equation can be interpreted as an approximation of the solution of a nonlinear integro-differential equation, whose unknown function depends not only on time, but also on two spatial variables. General representation for exact solution of system under study is obtained in the paper. Also two kinds of particular examples of exact solutions are presented. The first demonstrates oscillatory spatio-temporal behavior, and the second one shows monotone in time behavior. In the paper typical graphs of the first components of these solutions are plotted. Moreover, it is demonstrated that using some procedure one can generate countable set of new exact system’s solutions from previously found solutions. From radio engineering point of view this procedure just coincides with procedure of upsampling in digital signal processing.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124308343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the 80th anniversary of the birth of Vladislav Sergeevich Medvedev","authors":"","doi":"10.15507/2079-6900.25.202301.578-582","DOIUrl":"https://doi.org/10.15507/2079-6900.25.202301.578-582","url":null,"abstract":"","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131273341","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":"Link as a complete invariant of Morse-Smale 3-diffeomorphisms","authors":"Alexey A. Nozdrinov, Arseniy I. Pochinka","doi":"10.15507/2079-6900.25.202301.531-541","DOIUrl":"https://doi.org/10.15507/2079-6900.25.202301.531-541","url":null,"abstract":"In this paper we consider gradient-like Morse-Smale diffeomorphisms defined on the three-dimensional sphere S3\u0000. For such diffeomorphisms, a complete invariant of topological conjugacy was obtained in the works of C. Bonatti, V. Grines, V. Medvedev, E. Pecu. It is an equivalence class of a set of homotopically non-trivially embedded tori and Klein bottles embedded in some closed 3-manifold whose fundamental group admits an epimorphism to the group Z\u0000. Such an invariant is called the scheme of the gradient-like diffeomorphism f:S3→S3\u0000. We single out a class G\u0000 of diffeomorphisms whose complete invariant is a topologically simpler object, namely, the link of essential knots in the manifold S2×S1\u0000. The diffeomorphisms under consideration are determined by the fact that their non-wandering set contains a unique source, and the closures of stable saddle point manifolds bound three-dimensional balls with pairwise disjoint interiors. We prove that, in addition to the closure of these balls, a diffeomorphism of the class G\u0000 contains exactly one nonwandering point, which is a fixed sink. It is established that the total invariant of topological conjugacy of class G\u0000 diffeomorphisms is the space of orbits of unstable saddle separatrices in the basin of this sink. It is shown that the space of orbits is a link of non-contractible knots in the manifold S2×S1\u0000 and that the equivalence of links is tantamount to the equivalence of schemes. We also provide a realization of diffeomorphisms of the considered class along an arbitrary link consisting of essential nodes in the manifold S2×S1\u0000.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"412 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133088393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solution of integral equations of linear antenna theory by finite element method","authors":"D. Tarasov","doi":"10.15507/2079-6900.25.202301.554-564","DOIUrl":"https://doi.org/10.15507/2079-6900.25.202301.554-564","url":null,"abstract":"The aim of the work is to construct a computational scheme of the finite element method in relation to integral equations describing current distributions in thin wire antennas. In particular, for linear antennas of small thickness, the problem can be reduced to the integral Gallen equation. As a research method, preference is given to the finite element method, since it has quite a lot of flexibility in terms of choosing basis functions and selecting a grid of nodes. In addition, this method is a powerful and effective means of solving mathematical physics’ problems, which makes it possible to accurately describe complex curved boundaries of the solution domain and boundary conditions. The paper builds a numerical method for solving the integral Gallen equation using the finite element approach. According to the proposed computational scheme, a software implementation was built and a comparative analysis of the results was carried out. This approach as a whole showed low accuracy, which is probably due to the fact that this problem belongs to the class of incorrect ones and, in general, is due to the issue of determining the limits of applicability of the Gallen equation.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126031456","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}