Some properties of p-cross-section bodies and generalazation(p-截面体的性质与推广)
对p≥-1, GARDNER R J和GIANNOPOULOS A A引进了p-截面体CpK,并就p的不同取值,对CpK的凸性作了探讨.首先证明了CpK的一些性质,诸如原点对称的n维椭球E的p-截面体是它的极体的一个伸缩、CpCqE=CqCpE, V(CnK) =V(IK)等.而后通过探讨混合径向平均体Rp(K, L)与混合p-截面体Cp(K, L)的相关性,将p-截面体的一些性质推广到了Cp(K, L),并证明了当K和L是En中的凸体且K⊆L时, C1(K, L)是一个凸体....
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| Format: | Article |
| Language: | zho |
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Zhejiang University Press
2010-03-01
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| Series: | Zhejiang Daxue xuebao. Lixue ban |
| Subjects: | |
| Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2010.02.005 |
| _version_ | 1797236121353060352 |
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| author | SHENYa-jun(沈亚军) |
| author_facet | SHENYa-jun(沈亚军) |
| author_sort | SHENYa-jun(沈亚军) |
| collection | DOAJ |
| description | 对p≥-1, GARDNER R J和GIANNOPOULOS A A引进了p-截面体CpK,并就p的不同取值,对CpK的凸性作了探讨.首先证明了CpK的一些性质,诸如原点对称的n维椭球E的p-截面体是它的极体的一个伸缩、CpCqE=CqCpE, V(CnK) =V(IK)等.而后通过探讨混合径向平均体Rp(K, L)与混合p-截面体Cp(K, L)的相关性,将p-截面体的一些性质推广到了Cp(K, L),并证明了当K和L是En中的凸体且K⊆L时, C1(K, L)是一个凸体. |
| first_indexed | 2024-04-24T16:58:49Z |
| format | Article |
| id | doaj.art-3a49c2ab65a84552917d230d13065ffe |
| institution | Directory Open Access Journal |
| issn | 1008-9497 |
| language | zho |
| last_indexed | 2024-04-24T16:58:49Z |
| publishDate | 2010-03-01 |
| publisher | Zhejiang University Press |
| record_format | Article |
| series | Zhejiang Daxue xuebao. Lixue ban |
| spelling | doaj.art-3a49c2ab65a84552917d230d13065ffe2024-03-29T01:58:28ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972010-03-0137214414710.3785/j.issn.1008-9497.2010.02.005Some properties of p-cross-section bodies and generalazation(p-截面体的性质与推广)SHENYa-jun(沈亚军)0Department of Applied Mathematics, College of Sciences, Zhejiang Forestry University, Lin'an 311300, Zhejiang Province, China(浙江林学院应用数学系，浙江 临安 311300)对p≥-1, GARDNER R J和GIANNOPOULOS A A引进了p-截面体CpK,并就p的不同取值,对CpK的凸性作了探讨.首先证明了CpK的一些性质,诸如原点对称的n维椭球E的p-截面体是它的极体的一个伸缩、CpCqE=CqCpE, V(CnK) =V(IK)等.而后通过探讨混合径向平均体Rp(K, L)与混合p-截面体Cp(K, L)的相关性,将p-截面体的一些性质推广到了Cp(K, L),并证明了当K和L是En中的凸体且K⊆L时, C1(K, L)是一个凸体.https://doi.org/10.3785/j.issn.1008-9497.2010.02.005p-截面体混合p-截面体凸性推广 |
| spellingShingle | SHENYa-jun(沈亚军) Some properties of p-cross-section bodies and generalazation(p-截面体的性质与推广) Zhejiang Daxue xuebao. Lixue ban p-截面体 混合p-截面体 凸性 推广 |
| title | Some properties of p-cross-section bodies and generalazation(p-截面体的性质与推广) |
| title_full | Some properties of p-cross-section bodies and generalazation(p-截面体的性质与推广) |
| title_fullStr | Some properties of p-cross-section bodies and generalazation(p-截面体的性质与推广) |
| title_full_unstemmed | Some properties of p-cross-section bodies and generalazation(p-截面体的性质与推广) |
| title_short | Some properties of p-cross-section bodies and generalazation(p-截面体的性质与推广) |
| title_sort | some properties of p cross section bodies and generalazation p 截面体的性质与推广 |
| topic | p-截面体 混合p-截面体 凸性 推广 |
| url | https://doi.org/10.3785/j.issn.1008-9497.2010.02.005 |
| work_keys_str_mv | AT shenyajunshěnyàjūn somepropertiesofpcrosssectionbodiesandgeneralazationpjiémiàntǐdexìngzhìyǔtuīguǎng |