Pub Date : 2024-07-31DOI: 10.1134/s1064562424601240
N. A. Rautian
Abstract
Volterra integro-differential equations with operator coefficients in Hilbert spaces are studied. Previously obtained results are used to establish the relationship between the spectra of operator functions that are the symbols of the specified integro-differential equations and the spectra of generators of operator semigroups. Representations of solutions for the considered integro-differential equations are obtained on the basis of spectral analysis of generators of operator semigroups and corresponding operator functions.
{"title":"Representations of Solutions for Volterra Integro-Differential Equations in Hilbert Spaces","authors":"N. A. Rautian","doi":"10.1134/s1064562424601240","DOIUrl":"https://doi.org/10.1134/s1064562424601240","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Volterra integro-differential equations with operator coefficients in Hilbert spaces are studied. Previously obtained results are used to establish the relationship between the spectra of operator functions that are the symbols of the specified integro-differential equations and the spectra of generators of operator semigroups. Representations of solutions for the considered integro-differential equations are obtained on the basis of spectral analysis of generators of operator semigroups and corresponding operator functions.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-31DOI: 10.1134/s1064562424702107
E. E. Peskova
Abstract
A finite-volume algorithm with splitting over physical processes is developed to model nonstationary problems of laser thermochemistry with catalytic nanoparticles in subsonic gas flows. Two-phase flows in a heated pipe with laser radiation and radical kinetics of nonoxidative methane conversion are simulated. It is shown that the conversion of methane at the outlet of the pipe is more than 60% with predominant formation of ethylene and hydrogen.
{"title":"Mathematical Modeling of Nonstationary Problems Related to Laser Thermochemistry of Methane in the Presence of Catalytic Nanoparticles","authors":"E. E. Peskova","doi":"10.1134/s1064562424702107","DOIUrl":"https://doi.org/10.1134/s1064562424702107","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A finite-volume algorithm with splitting over physical processes is developed to model nonstationary problems of laser thermochemistry with catalytic nanoparticles in subsonic gas flows. Two-phase flows in a heated pipe with laser radiation and radical kinetics of nonoxidative methane conversion are simulated. It is shown that the conversion of methane at the outlet of the pipe is more than 60% with predominant formation of ethylene and hydrogen.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-31DOI: 10.1134/s1064562424601306
T. N. Fomenko
Abstract
The concept of a conic function with operator coefficients on a conic metric space is introduced. A zero existence theorem is proved for such functions. On this basis, a fixed point theorem for a multivalued self-mapping of a conic metric space is obtained, which generalizes the recent fixed point theorem of E.S. Zhukovskiy and E.A. Panasenko for a contracting multivalued mapping of a conic metric space with an operator contracting coefficient. Coincidence theorems for two multivalued mappings of conic metric spaces are obtained, which generalize the author’s previous results on coincidences of two multivalued mappings of metric spaces.
{"title":"Zeros of Conic Functions, Fixed Points, and Coincidences","authors":"T. N. Fomenko","doi":"10.1134/s1064562424601306","DOIUrl":"https://doi.org/10.1134/s1064562424601306","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The concept of a conic function with operator coefficients on a conic metric space is introduced. A zero existence theorem is proved for such functions. On this basis, a fixed point theorem for a multivalued self-mapping of a conic metric space is obtained, which generalizes the recent fixed point theorem of E.S. Zhukovskiy and E.A. Panasenko for a contracting multivalued mapping of a conic metric space with an operator contracting coefficient. Coincidence theorems for two multivalued mappings of conic metric spaces are obtained, which generalize the author’s previous results on coincidences of two multivalued mappings of metric spaces.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-31DOI: 10.1134/s1064562424702119
A. L. Semenov, A. E. Abylkassymova, T. A. Rudchenko
Abstract
The paper proposes a new approach to control the process of general education. Digital tools are used to form spaces of goals, tasks and learning activities, and to record the educational process of each student. Artificial intelligence tools are used when choosing a student’s personal goals and ways to achieve them, to make forecasts and recommendations to participants in the educational process. Big data from the entire education system and big linguistic models are used. The effects of the approach include ensuring the success of each student, objective assessment of the work of teachers and schools, and the adequacy of the succession process to higher education.
{"title":"AI Methods in Control of Personalized General Education","authors":"A. L. Semenov, A. E. Abylkassymova, T. A. Rudchenko","doi":"10.1134/s1064562424702119","DOIUrl":"https://doi.org/10.1134/s1064562424702119","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper proposes a new approach to control the process of general education. Digital tools are used to form spaces of goals, tasks and learning activities, and to record the educational process of each student. Artificial intelligence tools are used when choosing a student’s personal goals and ways to achieve them, to make forecasts and recommendations to participants in the educational process. Big data from the entire education system and big linguistic models are used. The effects of the approach include ensuring the success of each student, objective assessment of the work of teachers and schools, and the adequacy of the succession process to higher education.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-17DOI: 10.1134/s1064562424702077
D. I. Borisov, D. M. Polyakov
Abstract
We consider a non-self-adjoint Schrödinger operator on the unit interval with Dirichlet conditions perturbed by an operator of small translation. The main result is a three-term asymptotic expansion for the eigenvalues with respect to their index, and this asymptotics is uniform in the small translation. We also show that the system of eigenfunctions and generalized eigenfunctions of the considered operators forms a Bari basis in the space of square integrable functions on the considered unit interval.
{"title":"Asymptotics for Eigenvalues of Schrödinger Operator with Small Translation and Dirichlet Condition","authors":"D. I. Borisov, D. M. Polyakov","doi":"10.1134/s1064562424702077","DOIUrl":"https://doi.org/10.1134/s1064562424702077","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider a non-self-adjoint Schrödinger operator on the unit interval with Dirichlet conditions perturbed by an operator of small translation. The main result is a three-term asymptotic expansion for the eigenvalues with respect to their index, and this asymptotics is uniform in the small translation. We also show that the system of eigenfunctions and generalized eigenfunctions of the considered operators forms a Bari basis in the space of square integrable functions on the considered unit interval.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-17DOI: 10.1134/s1064562424601070
G. G. Lazareva, V. A. Popov, V. A. Okishev, A. V. Burdakov
Abstract
We consider a model of current distribution in a tungsten sample and a vapor layer produced when the surface is heated by an electron beam. The model is based on solving electrodynamic equations and a two-phase Stefan problem in cylindrical coordinates. Based on the temperature distribution in the computational domain, the electrical resistance and thermopower are calculated via an integral over the electron energy at each grid node. The electromagnetic field configuration is a possible source of rotation of the substance, which is observed in experiments. The simulation results demonstrate the role of thermionic emission and the way of model development. The model parameters are taken from experiments at the Beam of Electrons for materials Test Applications (BETA) facility created at the Budker Institute of Nuclear Physics of the Siberian Branch of the Russian Academy of Sciences.
摘要 我们考虑了钨样品中的电流分布模型和表面被电子束加热时产生的蒸汽层。该模型基于在圆柱坐标下求解电动力学方程和两相斯特凡问题。根据计算域中的温度分布，通过对每个网格节点上的电子能量进行积分，计算出电阻和热功率。电磁场配置是物质旋转的一个可能来源，这在实验中可以观察到。模拟结果证明了热释电的作用和模型开发的方法。模型参数取自俄罗斯科学院西伯利亚分院布德克核物理研究所（Budker Institute of Nuclear Physics of the Siberian Branch of the Russian Academy of Sciences）建立的材料测试应用电子束（BETA）设施的实验。
{"title":"Mathematical Model of Thermocurrents Based on Calculation of Electrical Resistance and Thermopower As an Integral over Electron Energy","authors":"G. G. Lazareva, V. A. Popov, V. A. Okishev, A. V. Burdakov","doi":"10.1134/s1064562424601070","DOIUrl":"https://doi.org/10.1134/s1064562424601070","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider a model of current distribution in a tungsten sample and a vapor layer produced when the surface is heated by an electron beam. The model is based on solving electrodynamic equations and a two-phase Stefan problem in cylindrical coordinates. Based on the temperature distribution in the computational domain, the electrical resistance and thermopower are calculated via an integral over the electron energy at each grid node. The electromagnetic field configuration is a possible source of rotation of the substance, which is observed in experiments. The simulation results demonstrate the role of thermionic emission and the way of model development. The model parameters are taken from experiments at the Beam of Electrons for materials Test Applications (BETA) facility created at the Budker Institute of Nuclear Physics of the Siberian Branch of the Russian Academy of Sciences.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141722352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-17DOI: 10.1134/s1064562424702089
M. D. Bragin
Abstract
Upwind bicompact schemes of third-order approximation in space are presented for the first time. A formula is obtained for the transition factor of an arbitrary fully discrete bicompact scheme with Runge–Kutta time stepping. Stability and monotonicity of a scheme of first order in time are investigated, and the dissipative and dispersion properties of a scheme of third order in time are analyzed. Advantages of the new schemes over their centered counterparts are demonstrated.
{"title":"Upwind Bicompact Schemes for Hyperbolic Conservation Laws","authors":"M. D. Bragin","doi":"10.1134/s1064562424702089","DOIUrl":"https://doi.org/10.1134/s1064562424702089","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Upwind bicompact schemes of third-order approximation in space are presented for the first time. A formula is obtained for the transition factor of an arbitrary fully discrete bicompact scheme with Runge–Kutta time stepping. Stability and monotonicity of a scheme of first order in time are investigated, and the dissipative and dispersion properties of a scheme of third order in time are analyzed. Advantages of the new schemes over their centered counterparts are demonstrated.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-17DOI: 10.1134/s1064562424702065
Yu. A. Basalov, N. N. Dobrovolsky, V. N. Chubarikov
Abstract
It is proved that the coefficients of the interpolation polynomial over a parallelepipedal grid for a multidimensional function are equal to the coefficients of the interpolation polynomial over a uniform grid for a one-dimensional function. These coefficients can be obtained by applying the fast Fourier transform based on various schemes.
{"title":"Multidimensional Fourier Interpolation and Fast Fourier Transforms","authors":"Yu. A. Basalov, N. N. Dobrovolsky, V. N. Chubarikov","doi":"10.1134/s1064562424702065","DOIUrl":"https://doi.org/10.1134/s1064562424702065","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>It is proved that the coefficients of the interpolation polynomial over a parallelepipedal grid for a multidimensional function are equal to the coefficients of the interpolation polynomial over a uniform grid for a one-dimensional function. These coefficients can be obtained by applying the fast Fourier transform based on various schemes.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-20DOI: 10.1134/s1064562424702041
A. I. Perov, I. D. Kostrub
Abstract
In a complex Banach algebra, under the assumptions of separateness and spectral separateness, invertibility conditions for the Vandermonde matrix are formulated and proved. Necessary and sufficient conditions for the invertibility of the Vandermonde matrix are given. Analogues of Sylvester’s theorem are formulated.
{"title":"The Vandermonde Matrix in the Commutative Case","authors":"A. I. Perov, I. D. Kostrub","doi":"10.1134/s1064562424702041","DOIUrl":"https://doi.org/10.1134/s1064562424702041","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In a complex Banach algebra, under the assumptions of separateness and spectral separateness, invertibility conditions for the Vandermonde matrix are formulated and proved. Necessary and sufficient conditions for the invertibility of the Vandermonde matrix are given. Analogues of Sylvester’s theorem are formulated.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-20DOI: 10.1134/s1064562424601185
Hafez Al-Assad
Abstract
We present a new result on the generalisation of A.G. Postnikov’s formula to the case of powers of 2. This, together with the original work of A.G. Postnikov and some structural theorems on reduced residue systems modulo prime-power ideals, is used to obtain estimates for certain character sums in algebraic number fields.
{"title":"Applying A.G. Postnikov’s Formula in Algebraic Number Fields","authors":"Hafez Al-Assad","doi":"10.1134/s1064562424601185","DOIUrl":"https://doi.org/10.1134/s1064562424601185","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We present a new result on the generalisation of A.G. Postnikov’s formula to the case of powers of 2. This, together with the original work of A.G. Postnikov and some structural theorems on reduced residue systems modulo prime-power ideals, is used to obtain estimates for certain character sums in algebraic number fields.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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