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Gradient-Like Diffeomorphisms and Periodic Vector Fields
Moscow Mathematical Journal. 2023. Vol. 23. No. 4. P. 533–544.
A class of gradient-like nonautonomous vector fields (NVFs) on a smooth closed manifold M is studied and the following problems are solved: 1) can a gradient-like NVF be constructed by means of the nonautonomous suspension over a diffeomorphism of this manifold, and if so, 1) under what conditions on the diffeomorphism? 2) let a diffeomorphism f be gradient-like (see the definition in the text) and diffeotopic to the identity map idM, when the NVF obtained by means of the nonautonomous suspension over f be gradient-like? Necessary and sufficient conditions to this have been found in the paper. All these questions arise, when studying NVFs on M admitting the uniform classification and a description via combinatorial type invariants.
Keywords: suspension flowgradient-like cascadeexponential dichotomynonautonomous vector fielduniform equivalence
Publication based on the results of:
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In schemes S for placing r particles in n distinguishable cells, their placement in selected m cells – schemes S∗ is studied, for which the analysis is carried out by a new enumerative method (EM) in extended areas of enumerative combinatorics: finding the number of outcomes and, based on the construction of a model of ...
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Benzenoid hydrocarbons are structurally regular aromatic compounds, which makes them well suited for quantitative structure–property relationship (QSPR) studies. This study presents a QSPR analysis of nineteen benzenoid hydrocarbon species using degree-based topological co-indices. We developed a Python program to compute eleven degree-based topological co-indices from molecular graphs and evaluated their ability to explain variations in ...
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A planar dual billiard is a planar curve γ equipped with a family (σP)|P∈γ of projective involutions of the projective lines LP tangent to γ at P that fix P. A dual billiard is called rationally integrable, if there exists a rational function R(x,y) of two variables (called first integral) whose restriction to each tangent ...
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Ismailov A., Constructive Approximation 2026
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In the present paper we construct an example of 4-dimensional flows on $S^3\times S^1$ whose saddle periodic orbit has a wildly embedded 2-dimensional unstable manifold. We prove that such a property has every suspension under a non-trivial Pixton's diffeomorphism. Moreover we give a complete topological classification of these suspensions. ...
Added: October 14, 2019
Kuzmina L., Osipov Y., , in: MATEC Web of Conferences 117Vol. 117: RSP 2017 – XXVI R-S-P Seminar 2017 Theoretical Foundation of Civil Engineerin.: EDP Sciences, 2017. Ch. 00097 P. 1–6.
The study of filtration of the suspension in a porous medium is a vital problem in the design and construction of tunnels and hydraulic structures. An exact solution is constructed for an unsteady flow of a monodisperse suspension in a homogeneous porous medium with size-exclusion mechanism for particle retention. The concentrations of suspended and precipitated ...
Added: July 4, 2018
Kuzmina L., Osipov Y., MATEC Web of Conferences 2017 Vol. 117 No. 00097 P. 1–6
The study of filtration of the suspension in a porous medium is a vital problem in the design and construction of tunnels and hydraulic structures. An exact solution is constructed for an unsteady flow of a monodisperse suspension in a homogeneous porous medium with sizeexclusion mechanism for particle retention. The concentrations of suspended and precipitated ...
Added: September 7, 2017
Gurevich E., Сяинова Д. Т., Журнал Средневолжского математического общества 2014 Т. 16 № 2 С. 46–56
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