Pub Date : 2023-12-01DOI: 10.1134/s1063454123040118
Abstract
The paper is devoted to studying the sufficient conditions for the asymptotical separability of distinct terms in the linear combination of harmonics by singular spectrum analysis (SSA). Namely, the series x0, …, ({{x}_{{N - 1}}}) with xn = (sumnolimits_{i = 1}^r {{{f}_{{i,n}}}} ), where ({{f}_{{i,n}}}) = ({{b}_{i}}cos ({{omega }_{i}}n + {{gamma }_{i}})) and both amplitudes |bi| and frequencies ωi ∈ (0, 1/2) are pairwise different, are considered. Then, as is proved in this study, under some relationship between amplitudes |bi| and the choice of standard SSA parameters, the so-called reconstructed values ({{tilde {f}}_{{i,n}}}) prove to be very close to ({{f}_{{i,n}}}) for large N. Moreover, ({{max }_{n}}left( {left| {{{{tilde {f}}}_{{i,n}}} - {{f}_{{i,n}}}} right|} right)) = (O({{N}^{{ - 1}}})) for any i, if N → ∞.
{"title":"Asymptotical Separation of Harmonics by Singular Spectrum Analysis","authors":"","doi":"10.1134/s1063454123040118","DOIUrl":"https://doi.org/10.1134/s1063454123040118","url":null,"abstract":"<span> <h3>Abstract</h3> <p>The paper is devoted to studying the sufficient conditions for the asymptotical separability of distinct terms in the linear combination of harmonics by singular spectrum analysis (SSA). Namely, the series <em>x</em><sub>0</sub>, …, <span> <span>({{x}_{{N - 1}}})</span> </span> with <em>x</em><sub><em>n</em></sub> = <span> <span>(sumnolimits_{i = 1}^r {{{f}_{{i,n}}}} )</span> </span>, where <span> <span>({{f}_{{i,n}}})</span> </span> = <span> <span>({{b}_{i}}cos ({{omega }_{i}}n + {{gamma }_{i}}))</span> </span> and both amplitudes |<em>b</em><sub><em>i</em></sub>| and frequencies ω<sub><em>i</em></sub> ∈ (0, 1/2) are pairwise different, are considered. Then, as is proved in this study, under some relationship between amplitudes |<em>b</em><sub><em>i</em></sub>| and the choice of standard SSA parameters, the so-called reconstructed values <span> <span>({{tilde {f}}_{{i,n}}})</span> </span> prove to be very close to <span> <span>({{f}_{{i,n}}})</span> </span> for large <em>N</em>. Moreover, <span> <span>({{max }_{n}}left( {left| {{{{tilde {f}}}_{{i,n}}} - {{f}_{{i,n}}}} right|} right))</span> </span> = <span> <span>(O({{N}^{{ - 1}}}))</span> </span> for any <em>i</em>, if <em>N</em> → ∞.</p> </span>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"118 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139557990","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 : 2023-12-01DOI: 10.1134/s1063454123040167
Abstract
The paper discusses the development of scientific areas of mechanics in the research by the honorary professor of St. Petersburg State University, Honored Worker of Science and Technology of the Russian Federation, and Doctor of Physical and Mathematical Sciences Viktor Sergeevich Novoselov, founder of the scientific school of analytical mechanics, space dynamics, biomechanics, and applied mathematics. He extended the basic theorems of analytical dynamics to mechanical systems of variable composition. Using variational methods, he obtained a number of remarkable results on the dynamics of controllable systems. In particular, he proposed a general scheme for constructing analytical approximations, which has been used to solve a variety of equations.
{"title":"Modeling Problems of Dynamics and Development of Scientific Areas of Mechanics and Applied Mathematics","authors":"","doi":"10.1134/s1063454123040167","DOIUrl":"https://doi.org/10.1134/s1063454123040167","url":null,"abstract":"<span> <h3>Abstract</h3> <p>The paper discusses the development of scientific areas of mechanics in the research by the honorary professor of St. Petersburg State University, Honored Worker of Science and Technology of the Russian Federation, and Doctor of Physical and Mathematical Sciences Viktor Sergeevich Novoselov, founder of the scientific school of analytical mechanics, space dynamics, biomechanics, and applied mathematics. He extended the basic theorems of analytical dynamics to mechanical systems of variable composition. Using variational methods, he obtained a number of remarkable results on the dynamics of controllable systems. In particular, he proposed a general scheme for constructing analytical approximations, which has been used to solve a variety of equations.</p> </span>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"5 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139559236","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 : 2023-12-01DOI: 10.1134/s1063454123040039
Abstract
This paper presents a very brief review of models constructed in cooperation with ophthalmologists, namely, for the change in the stress-strain state of the eye membrane after vision-correction operations and the change in the intraocular pressure after the injection of drugs into the vitreous body. The mathematical models describing the process of measuring the true intraocular pressure (IOP) by applanation methods are discussed. The models of eye biomechanics provide the possibility to obtain a series of new results in solid mechanics, i.e., to solve the problem of the stability of a spherical shell under a concentrated force and inner pressure and the stability of an axisymmetric equilibrium state of inhomogeneous annular orthotropic plates under a uniformly distributed normal load. The problems of the deformation of transversally isotropic spherical and cylindrical layers under inner and outer pressure are analyzed and the solutions obtained within the framework of the three-dimensional theory are compared with those found by the non-classical theories of shells. This comparison makes it possible to estimate the precision of some theories.
{"title":"Models of Solid Mechanics in the Problems of Ophthalmology","authors":"","doi":"10.1134/s1063454123040039","DOIUrl":"https://doi.org/10.1134/s1063454123040039","url":null,"abstract":"<span> <h3>Abstract</h3> <p>This paper presents a very brief review of models constructed in cooperation with ophthalmologists, namely, for the change in the stress-strain state of the eye membrane after vision-correction operations and the change in the intraocular pressure after the injection of drugs into the vitreous body. The mathematical models describing the process of measuring the true intraocular pressure (IOP) by applanation methods are discussed. The models of eye biomechanics provide the possibility to obtain a series of new results in solid mechanics, i.e., to solve the problem of the stability of a spherical shell under a concentrated force and inner pressure and the stability of an axisymmetric equilibrium state of inhomogeneous annular orthotropic plates under a uniformly distributed normal load. The problems of the deformation of transversally isotropic spherical and cylindrical layers under inner and outer pressure are analyzed and the solutions obtained within the framework of the three-dimensional theory are compared with those found by the non-classical theories of shells. This comparison makes it possible to estimate the precision of some theories.</p> </span>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"386 1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139558054","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 : 2023-12-01DOI: 10.1134/s106345412304009x
Abstract
This is a review of the works of the research school of V.A. Yakubovich in the field of artificial intelligence, machine learning, adaptive systems, and robotics. The method of recurrent objective inequalities is considered in detail. The significance of the presented results for the further development of cybernetics and artificial intelligence is discussed. Special emphasis is put on Yakubovich’s seminal works on machine learning and development of the concept of finitely convergent algorithms for solving recurrent objective inequalities. Typical results of their convergence are discussed in detail as a specific illustration. The study distinguishes the contribution of the school to the formation and development of modern theories of adaptive control and mathematical robotics, particularly, the theory of adaptive robots. A special section is devoted to adaptive suboptimal control.
{"title":"Review of Works by V. A. Yakubovich’s Scientific School on Artificial Intelligence and Robotics","authors":"","doi":"10.1134/s106345412304009x","DOIUrl":"https://doi.org/10.1134/s106345412304009x","url":null,"abstract":"<span> <h3>Abstract</h3> <p>This is a review of the works of the research school of V.A. Yakubovich in the field of artificial intelligence, machine learning, adaptive systems, and robotics. The method of recurrent objective inequalities is considered in detail. The significance of the presented results for the further development of cybernetics and artificial intelligence is discussed. Special emphasis is put on Yakubovich’s seminal works on machine learning and development of the concept of finitely convergent algorithms for solving recurrent objective inequalities. Typical results of their convergence are discussed in detail as a specific illustration. The study distinguishes the contribution of the school to the formation and development of modern theories of adaptive control and mathematical robotics, particularly, the theory of adaptive robots. A special section is devoted to adaptive suboptimal control.</p> </span>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"55 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139558065","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 : 2023-09-01DOI: 10.1134/s1063454123030032
E. A. Blagoveshchenskaya, A. V. Mikhalev
{"title":"Matrix Representations of Endomorphism Rings for Torsion-Free Abelian Groups","authors":"E. A. Blagoveshchenskaya, A. V. Mikhalev","doi":"10.1134/s1063454123030032","DOIUrl":"https://doi.org/10.1134/s1063454123030032","url":null,"abstract":"","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134994522","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 : 2023-09-01DOI: 10.1134/s1063454123030056
B. I. Konosevich, Yu. B. Konosevich
{"title":"Computer Analysis of a Model of a Synchronous No-Current Electric Motor","authors":"B. I. Konosevich, Yu. B. Konosevich","doi":"10.1134/s1063454123030056","DOIUrl":"https://doi.org/10.1134/s1063454123030056","url":null,"abstract":"","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134994706","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 : 2023-09-01DOI: 10.1134/s1063454123030081
A. A. Tikhonov
{"title":"Rigid-Body Dynamics from the Euler Equations to the Attitude Control of Spacecraft in the Works of Scientists from Saint Petersburg State University. Part 1","authors":"A. A. Tikhonov","doi":"10.1134/s1063454123030081","DOIUrl":"https://doi.org/10.1134/s1063454123030081","url":null,"abstract":"","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134994429","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 : 2023-09-01DOI: 10.1134/s1063454123030044
A. N. Frolov
{"title":"On the Probabilities of Large Deviations of Combinatorial Sums of Independent Random Variables That Satisfy the Linnik Condition","authors":"A. N. Frolov","doi":"10.1134/s1063454123030044","DOIUrl":"https://doi.org/10.1134/s1063454123030044","url":null,"abstract":"","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134994702","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 : 2023-09-01DOI: 10.1134/s1063454123030111
Yu. N. Voroshilova, V. A. Istomin, O. V. Kunova, E. V. Kustova, E. A. Nagnibeda, M. A. Rydalevskaya
{"title":"Scientific School of Nonequilibrium Aeromechanics at St. Petersburg State University","authors":"Yu. N. Voroshilova, V. A. Istomin, O. V. Kunova, E. V. Kustova, E. A. Nagnibeda, M. A. Rydalevskaya","doi":"10.1134/s1063454123030111","DOIUrl":"https://doi.org/10.1134/s1063454123030111","url":null,"abstract":"","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"77 11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134995302","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 : 2023-09-01DOI: 10.1134/s1063454123030020
U. M. Ahanger, W. M. Shah
{"title":"Inequalities for the Derivatives of Rational Functions with Prescribed Poles and Restricted Zeros","authors":"U. M. Ahanger, W. M. Shah","doi":"10.1134/s1063454123030020","DOIUrl":"https://doi.org/10.1134/s1063454123030020","url":null,"abstract":"","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134994698","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号