{"title":"用于识别数字约旦曲面的邻接关系","authors":"Josef Šlapal","doi":"10.1007/s00010-024-01123-8","DOIUrl":null,"url":null,"abstract":"<div><p>For every positive integer, we introduce an adjacency in the digital space <span>\\({\\mathbb {Z}}^3\\)</span>. Connectedness in the graph obtained is then used to define and study digital Jordan surfaces. The surfaces are acquired as polyhedral surfaces bounding the digital polyhedra that can be face-to-face tiled with digital cubes, triangular prisms, square pyramids, and tetrahedra.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"989 - 1001"},"PeriodicalIF":0.7000,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01123-8.pdf","citationCount":"0","resultStr":"{\"title\":\"Adjacencies for recognition of digital Jordan surfaces\",\"authors\":\"Josef Šlapal\",\"doi\":\"10.1007/s00010-024-01123-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>For every positive integer, we introduce an adjacency in the digital space <span>\\\\({\\\\mathbb {Z}}^3\\\\)</span>. Connectedness in the graph obtained is then used to define and study digital Jordan surfaces. The surfaces are acquired as polyhedral surfaces bounding the digital polyhedra that can be face-to-face tiled with digital cubes, triangular prisms, square pyramids, and tetrahedra.</p></div>\",\"PeriodicalId\":55611,\"journal\":{\"name\":\"Aequationes Mathematicae\",\"volume\":\"99 3\",\"pages\":\"989 - 1001\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-09-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00010-024-01123-8.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Aequationes Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00010-024-01123-8\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Aequationes Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00010-024-01123-8","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Adjacencies for recognition of digital Jordan surfaces
For every positive integer, we introduce an adjacency in the digital space \({\mathbb {Z}}^3\). Connectedness in the graph obtained is then used to define and study digital Jordan surfaces. The surfaces are acquired as polyhedral surfaces bounding the digital polyhedra that can be face-to-face tiled with digital cubes, triangular prisms, square pyramids, and tetrahedra.
期刊介绍:
aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.