{"title":"关于卡西尼椭圆的几何,它的非凸度和$\\varepsilon$偏移层","authors":"O. Kuvshinov","doi":"10.35634/2226-3594-2022-60-03","DOIUrl":null,"url":null,"abstract":"The paper studies the geometry of a closed nonconvex smooth simply connected curve on a plane — of the Cassini oval, as well as the geometry of the $\\varepsilon$-layer around the set whose boundary is the Cassini oval. Various analytical representations of the $\\varepsilon$-layer boundary are formed, and special points of this boundary are described. The measure of nonconvexity $\\alpha$ of a simply connected set whose boundary is the Cassini oval is determined, and the angular characteristic of nonconvexity of its $\\varepsilon$-neighborhood is defined.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"About the geometry of the Cassini oval, its non-convexity degree and $\\\\varepsilon$-offset layer\",\"authors\":\"O. Kuvshinov\",\"doi\":\"10.35634/2226-3594-2022-60-03\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper studies the geometry of a closed nonconvex smooth simply connected curve on a plane — of the Cassini oval, as well as the geometry of the $\\\\varepsilon$-layer around the set whose boundary is the Cassini oval. Various analytical representations of the $\\\\varepsilon$-layer boundary are formed, and special points of this boundary are described. The measure of nonconvexity $\\\\alpha$ of a simply connected set whose boundary is the Cassini oval is determined, and the angular characteristic of nonconvexity of its $\\\\varepsilon$-neighborhood is defined.\",\"PeriodicalId\":42053,\"journal\":{\"name\":\"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2022-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.35634/2226-3594-2022-60-03\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.35634/2226-3594-2022-60-03","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
About the geometry of the Cassini oval, its non-convexity degree and $\varepsilon$-offset layer
The paper studies the geometry of a closed nonconvex smooth simply connected curve on a plane — of the Cassini oval, as well as the geometry of the $\varepsilon$-layer around the set whose boundary is the Cassini oval. Various analytical representations of the $\varepsilon$-layer boundary are formed, and special points of this boundary are described. The measure of nonconvexity $\alpha$ of a simply connected set whose boundary is the Cassini oval is determined, and the angular characteristic of nonconvexity of its $\varepsilon$-neighborhood is defined.