Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/103169
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dc.contributor.authorUshakov, V. N.en
dc.contributor.authorPershakov, M. V.en
dc.date.accessioned2021-08-31T15:08:00Z-
dc.date.available2021-08-31T15:08:00Z-
dc.date.issued2020-
dc.identifier.citationUshakov V. N. On estimation of Hausdorff deviation of convex polygons in R2 from their differences with disks / V. N. Ushakov, M. V. Pershakov. — DOI 10.35634/VM200404 // Vestnik Udmurtskogo Universiteta: Matematika, Mekhanika, Komp'yuternye Nauki. — 2020. — Vol. 30. — Iss. 4. — P. 585-603.en
dc.identifier.issn19949197-
dc.identifier.otherFinal2
dc.identifier.otherAll Open Access, Bronze3
dc.identifier.otherhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85099285931&doi=10.35634%2fVM200404&partnerID=40&md5=68212278ad26633c203848073a2c7802
dc.identifier.otherhttp://www.mathnet.ru/php/getFT.phtml?jrnid=vuu&paperid=743&what=fullt&option_lang=engm
dc.identifier.urihttp://hdl.handle.net/10995/103169-
dc.description.abstractWe study a problem concerning the estimation of the Hausdorff deviation of convex polygons in R2 from their geometric difference with circles of sufficiently small radius. Problems with such a subject, in which not only convex polygons but also convex compacts in the Euclidean space Rn are considered, arise in various fields of mathematics and, in particular, in the theory of differential games, control theory, convex analysis. Estimates of Hausdorff deviations of convex compact sets in Rn in their geometric difference with closed balls in Rn are presented in the works of L.S. Pontryagin, his staff and colleagues. These estimates are very important in deriving an estimate for the mismatch of the alternating Pontryagin's integral in linear differential games of pursuit and alternating sums. Similar estimates turn out to be useful in deriving an estimate for the mismatch of the attainability sets of nonlinear control systems in Rn and the sets approximating them. The paper considers a specific convex heptagon in R2. To study the geometry of this heptagon, we introduce the concept of a wedge in R2. On the basis of this notion, we obtain an upper bound for the Hausdorff deviation of a heptagon from its geometric difference with the disc in R2 of sufficiently small radius. © 2020 Udmurt State University. All rights reserved.en
dc.format.mimetypeapplication/pdfen
dc.language.isoruen
dc.publisherUdmurt State Universityen
dc.rightsinfo:eu-repo/semantics/openAccessen
dc.sourceVestn. Udmurt. Univ., Matematika, Mekhanika, Kompyuternye Nauki2
dc.sourceVestnik Udmurtskogo Universiteta: Matematika, Mekhanika, Komp'yuternye Naukien
dc.subjectCIRCLEen
dc.subjectCONEen
dc.subjectCONVEX POLYGON IN R2en
dc.subjectGEOMETRIC DIFFERENCE OF SETSen
dc.subjectHAUSDORFF DEVIATIONen
dc.subjectWEDGEen
dc.titleOn estimation of Hausdorff deviation of convex polygons in R2 from their differences with disksen
dc.titleК оценке хаусдорфова отклонения выпуклых многоугольников в R2 от их геометрической разности с кругамиru
dc.typeArticleen
dc.typeinfo:eu-repo/semantics/articleen
dc.typeinfo:eu-repo/semantics/publishedVersionen
dc.identifier.doi10.35634/VM200404-
dc.identifier.scopus85099285931-
local.contributor.employeeUshakov, V.N., Department of Dynamical Systems, Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620219, Russian Federation
local.contributor.employeePershakov, M.V., Department of Dynamical Systems, Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620219, Russian Federation, Institute of Natural Sciences and Mathematics, Ural Federal University, ul. Mira 19, Yekaterinburg, 620002, Russian Federation
local.description.firstpage585-
local.description.lastpage603-
local.issue4-
local.volume30-
local.contributor.departmentDepartment of Dynamical Systems, Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620219, Russian Federation
local.contributor.departmentInstitute of Natural Sciences and Mathematics, Ural Federal University, ul. Mira 19, Yekaterinburg, 620002, Russian Federation
local.identifier.pure20385357-
local.identifier.eid2-s2.0-85099285931-
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