Pub Date : 2023-12-24DOI: 10.26907/0021-3446-2023-12-71-89
A. M. Shelekhov
A new geometric necessary condition for regularity of a curved tree-web is found. A class of tree-webs from circles generalizing the regular tree-web of W. Blaschke from three elliptic bundles of circles with pairwise coinciding vertices is considered, and it is shown that only webs equivalent to the Blaschke web are regular in this class.
发现了曲线树状网规则性的新几何必要条件。考虑了一类从圆概括 W. Blaschke 的规则树状网的树状网，该树状网来自三个具有成对重合顶点的圆椭圆束，并证明在这一类中只有与 Blaschke 网等价的网才是规则的。
{"title":"Three-webs from circles","authors":"A. M. Shelekhov","doi":"10.26907/0021-3446-2023-12-71-89","DOIUrl":"https://doi.org/10.26907/0021-3446-2023-12-71-89","url":null,"abstract":"A new geometric necessary condition for regularity of a curved tree-web is found. A class of tree-webs from circles generalizing the regular tree-web of W. Blaschke from three elliptic bundles of circles with pairwise coinciding vertices is considered, and it is shown that only webs equivalent to the Blaschke web are regular in this class.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"1986 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139160566","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 : 2023-12-23DOI: 10.26907/0021-3446-2023-12-17-38
D. B. Katz
The review discusses two closely related problems: the solution of the Riemann boundary value problem for analytic functions and some of their generalizations in areas of the complex plane with non-rectifiable boundaries, and the construction of a generalization of the curvilinear integral to non-rectifiable curves that preserves properties important for complex analysis. This work reflects the current state of the issue, and many of the results presented in it were obtained quite recently. At the end of the article, readers are offered a number of unsolved problems, each of which can serve as a starting point for scientific research.
{"title":"Generalized integration over non-recifiable flat curves and boundary value problems","authors":"D. B. Katz","doi":"10.26907/0021-3446-2023-12-17-38","DOIUrl":"https://doi.org/10.26907/0021-3446-2023-12-17-38","url":null,"abstract":"The review discusses two closely related problems: the solution of the Riemann boundary value problem for analytic functions and some of their generalizations in areas of the complex plane with non-rectifiable boundaries, and the construction of a generalization of the curvilinear integral to non-rectifiable curves that preserves properties important for complex analysis. This work reflects the current state of the issue, and many of the results presented in it were obtained quite recently. At the end of the article, readers are offered a number of unsolved problems, each of which can serve as a starting point for scientific research.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"33 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139162545","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 : 2023-12-23DOI: 10.26907/0021-3446-2023-12-3-16
D. K. Durdiev, A. A. Boltaev, A. Rahmonov
This article is concerned with the study of the inverse problem of determining the difference kernel in a Volterra type integral term function in the third-order Moore–Gibson–Thompson (MGT) equation. First, the initial-boundary value problem is reduced to an equivalent problem. Using the Fourier spectral method, the equivalent problem is reduced to a system of integral equations. The existence and uniqueness of the solution to the integral equations are proved. The obtained solution to the integral equations of Volterra-type is also the unique solution to the equivalent problem. Based on the equivalence of the problems, the theorem of the existence and uniqueness of the classical solutions of the original inverse problem is proved.
{"title":"Convolution kernel determination problem in the third order Moore–Gibson–Thompson equation","authors":"D. K. Durdiev, A. A. Boltaev, A. Rahmonov","doi":"10.26907/0021-3446-2023-12-3-16","DOIUrl":"https://doi.org/10.26907/0021-3446-2023-12-3-16","url":null,"abstract":"This article is concerned with the study of the inverse problem of determining the difference kernel in a Volterra type integral term function in the third-order Moore–Gibson–Thompson (MGT) equation. First, the initial-boundary value problem is reduced to an equivalent problem. Using the Fourier spectral method, the equivalent problem is reduced to a system of integral equations. The existence and uniqueness of the solution to the integral equations are proved. The obtained solution to the integral equations of Volterra-type is also the unique solution to the equivalent problem. Based on the equivalence of the problems, the theorem of the existence and uniqueness of the classical solutions of the original inverse problem is proved.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"31 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139161586","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 : 2023-12-09DOI: 10.26907/0021-3446-2023-11-41-58
S. Khodjiev
This paper presents a calculation method and algorithm, as well as numerical results of studying chemically reacting turbulent jets based on three-dimensional parabolic systems of Navier-Stokes equations for multicomponent gas mixtures.Continuity equations are used to calculate the mass imbalance when solving with constant pressure, and with variable pressures, with the equations of motion and continuity.Diffusion combustion of a propane-butane mixture flowing from a square-shaped nozzle in a submerged flow of an air oxidizer has been numerically studied. Pressure variability significantly affects the velocity (temperature) profiles in the initial sections of the jet, and when moving away from the nozzle exit, the pressure effect can be considered imperceptible, but the flame length is longer than at constant pressure, but it does not significantly affect the shape of the flame.The saddle-shaped behavior of the longitudinal velocity in the direction of the major axis is numerically obtained for large initial values of the turbulence kinetic energy of the main jet.Given method allows the study of non-reacting and reactive turbulent jets flowing from a rectangular nozzle.
{"title":"Method and algorithm for calculating isobaric and non-isobaric three-dimensional turbulent jets of reacting gases","authors":"S. Khodjiev","doi":"10.26907/0021-3446-2023-11-41-58","DOIUrl":"https://doi.org/10.26907/0021-3446-2023-11-41-58","url":null,"abstract":"This paper presents a calculation method and algorithm, as well as numerical results of studying chemically reacting turbulent jets based on three-dimensional parabolic systems of Navier-Stokes equations for multicomponent gas mixtures.Continuity equations are used to calculate the mass imbalance when solving with constant pressure, and with variable pressures, with the equations of motion and continuity.Diffusion combustion of a propane-butane mixture flowing from a square-shaped nozzle in a submerged flow of an air oxidizer has been numerically studied. Pressure variability significantly affects the velocity (temperature) profiles in the initial sections of the jet, and when moving away from the nozzle exit, the pressure effect can be considered imperceptible, but the flame length is longer than at constant pressure, but it does not significantly affect the shape of the flame.The saddle-shaped behavior of the longitudinal velocity in the direction of the major axis is numerically obtained for large initial values of the turbulence kinetic energy of the main jet.Given method allows the study of non-reacting and reactive turbulent jets flowing from a rectangular nozzle.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"25 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139184813","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 : 2023-12-09DOI: 10.26907/0021-3446-2023-11-92-97
D. M. Korosteleva, S. I. Solov’ev
For the problem on eigenvibrations of the plate with an attached oscillator, the new symmetric linear variational statement is proposed. It is established the existence of the sequence of positive eigenvalues of finite multiplicity with limit point at infinity and the corresponding complete orthonormal system of eigenvectors. The new symmetric scheme of the finite element method with Hermite finite elements is formulated. Error estimates consistent with the solution smoothness for the approximate eigenvalues and approximate eigenvectors are proved. The results of numerical experiments illustrating the influence of the solution smoothness on the computation accuracy are presented.
{"title":"Finite element modeling of the eigenvibrations of the square plate with attached oscillator","authors":"D. M. Korosteleva, S. I. Solov’ev","doi":"10.26907/0021-3446-2023-11-92-97","DOIUrl":"https://doi.org/10.26907/0021-3446-2023-11-92-97","url":null,"abstract":"For the problem on eigenvibrations of the plate with an attached oscillator, the new symmetric linear variational statement is proposed. It is established the existence of the sequence of positive eigenvalues of finite multiplicity with limit point at infinity and the corresponding complete orthonormal system of eigenvectors. The new symmetric scheme of the finite element method with Hermite finite elements is formulated. Error estimates consistent with the solution smoothness for the approximate eigenvalues and approximate eigenvectors are proved. The results of numerical experiments illustrating the influence of the solution smoothness on the computation accuracy are presented.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"8 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139184877","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 : 2023-12-09DOI: 10.26907/0021-3446-2023-11-75-85
I. A. Shakirov
The Lebesgue constant of the classical Fourier operator is uniformly approximated by a logarithmic-fractional-rational function depending on three parameters; they are defined using the specific properties of logarithmic and rational approximations. A rigorous study of the corresponding residual term having an indefinite (non-monotonic) behavior has been carried out. The obtained approximation results strengthen the known results by more than two orders of magnitude.
{"title":"Approximation of the Lebesgue constant of the Fourier operator by a logarithmic-fractional-rational function","authors":"I. A. Shakirov","doi":"10.26907/0021-3446-2023-11-75-85","DOIUrl":"https://doi.org/10.26907/0021-3446-2023-11-75-85","url":null,"abstract":"The Lebesgue constant of the classical Fourier operator is uniformly approximated by a logarithmic-fractional-rational function depending on three parameters; they are defined using the specific properties of logarithmic and rational approximations. A rigorous study of the corresponding residual term having an indefinite (non-monotonic) behavior has been carried out. The obtained approximation results strengthen the known results by more than two orders of magnitude.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"8 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139184764","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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