{"title":"欧几里得$ d $ -空间中两个规定边长仿射等价框架的存在性","authors":"V. A. Alexandrov","doi":"10.1134/s0037446623060022","DOIUrl":null,"url":null,"abstract":"<p>We study the existence of the two affine-equivalent bar-and-joint\nframeworks in Euclidean <span>\\( d \\)</span>-space which have some prescribed combinatorial\nstructure and edge lengths.\nWe show that the existence problem is always solvable theoretically and\nexplain why to propose a practical algorithm for solving the problem is impossible.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Existence of Two Affine-Equivalent Frameworks with Prescribed Edge Lengths in Euclidean $ d $ -Space\",\"authors\":\"V. A. Alexandrov\",\"doi\":\"10.1134/s0037446623060022\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study the existence of the two affine-equivalent bar-and-joint\\nframeworks in Euclidean <span>\\\\( d \\\\)</span>-space which have some prescribed combinatorial\\nstructure and edge lengths.\\nWe show that the existence problem is always solvable theoretically and\\nexplain why to propose a practical algorithm for solving the problem is impossible.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-11-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0037446623060022\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0037446623060022","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
研究了欧几里得\( d \) -空间中具有一定组合结构和边长度的两个仿射等效杆节框架的存在性。我们从理论上证明了存在性问题总是可解的，并解释了为什么不可能提出一个实用的算法来解决这个问题。
On the Existence of Two Affine-Equivalent Frameworks with Prescribed Edge Lengths in Euclidean $ d $ -Space
We study the existence of the two affine-equivalent bar-and-joint
frameworks in Euclidean \( d \)-space which have some prescribed combinatorial
structure and edge lengths.
We show that the existence problem is always solvable theoretically and
explain why to propose a practical algorithm for solving the problem is impossible.
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