{"title":"由单位圆上三元组的幂生成的三角形","authors":"Charles R. Johnson, M. Newman","doi":"10.6028/jres.077b.016","DOIUrl":null,"url":null,"abstract":"Le t a, 13, y be th ree d is tin c t complex numbers of mod ulus 1. It is shown that th ere is essent ially one e xception to the followin g s tat e ment: For some posi t ive int eger Ill , 0 is in th e c losed convex hull of a\"', 13\"' , y\"'. The exception occurs for the normalized tripl e 1, e'l 1T i/7, e2krri/7, whe re k = 3 or 5. Thi s qu es tion was motivated by the proble'm of determining when a pos itive intege r III and a nonze ro n X l vee'tor X e xist such tha i X * A IIIX = 0, whe re A is a given matrix of M,,(C). Key word s: Convex hull; lInit ci rcle; \\V ey l's Theorem.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"86 2","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1973-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Triangles generated by powers of triplets on unit circle\",\"authors\":\"Charles R. Johnson, M. Newman\",\"doi\":\"10.6028/jres.077b.016\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Le t a, 13, y be th ree d is tin c t complex numbers of mod ulus 1. It is shown that th ere is essent ially one e xception to the followin g s tat e ment: For some posi t ive int eger Ill , 0 is in th e c losed convex hull of a\\\"', 13\\\"' , y\\\"'. The exception occurs for the normalized tripl e 1, e'l 1T i/7, e2krri/7, whe re k = 3 or 5. Thi s qu es tion was motivated by the proble'm of determining when a pos itive intege r III and a nonze ro n X l vee'tor X e xist such tha i X * A IIIX = 0, whe re A is a given matrix of M,,(C). Key word s: Convex hull; lInit ci rcle; \\\\V ey l's Theorem.\",\"PeriodicalId\":166823,\"journal\":{\"name\":\"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences\",\"volume\":\"86 2\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1973-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.6028/jres.077b.016\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.6028/jres.077b.016","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
摘要
让t (a, 13, y) = 3 (d) = 1的复数。结果表明:对于某些正整数i, 0位于a ' '， 13 ' '， y ' '的闭合凸包内。当rek = 3或5时，异常发生在正则化三重函数e1, e1t1 /7, e2krri/7。这个问题是由一个问题引起的，这个问题是确定当一个正整数r III和一个非整数X X X X X X X X X X X X X X X X X X X X = 0时，当re a是一个给定的矩阵M，，(C)。关键词:凸包;极限ci圆;i 's定理。
Triangles generated by powers of triplets on unit circle
Le t a, 13, y be th ree d is tin c t complex numbers of mod ulus 1. It is shown that th ere is essent ially one e xception to the followin g s tat e ment: For some posi t ive int eger Ill , 0 is in th e c losed convex hull of a"', 13"' , y"'. The exception occurs for the normalized tripl e 1, e'l 1T i/7, e2krri/7, whe re k = 3 or 5. Thi s qu es tion was motivated by the proble'm of determining when a pos itive intege r III and a nonze ro n X l vee'tor X e xist such tha i X * A IIIX = 0, whe re A is a given matrix of M,,(C). Key word s: Convex hull; lInit ci rcle; \V ey l's Theorem.
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