KMS Of Academy of mathematics and systems sciences, CAS
Hilbert Problem 15 and Nonstandard Analysis (I) | |
Li, Banghe | |
2020 | |
发表期刊 | ACTA MATHEMATICA SCIENTIA |
ISSN | 0252-9602 |
卷号 | 40期号:1页码:1-15 |
摘要 | Hilbert problem 15 required understanding Schubert's book. In this book, reducing to degenerate cases was one of the main methods for enumeration. We found that nonstandard analysis is a suitable tool for making rigorous of Schubert's proofs of some results, which used degeneration method, but are obviously not rigorous. In this paper, we give a rigorous proof for Example 4 in Schubert's book, Chapter 1. 4 according to his idea. This shows that Schubert's intuitive idea is correct, but to make it rigorous a lot of work should be done. |
关键词 | Hilbert problem 15 nonstandard analysis enumeration geometry |
DOI | 10.1007/s10473-020-0101-4 |
收录类别 | SCI |
语种 | 英语 |
WOS研究方向 | Mathematics |
WOS类目 | Mathematics |
WOS记录号 | WOS:000511674600001 |
出版者 | SPRINGER |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/50739 |
专题 | 中国科学院数学与系统科学研究院 |
通讯作者 | Li, Banghe |
作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China |
推荐引用方式 GB/T 7714 | Li, Banghe. Hilbert Problem 15 and Nonstandard Analysis (I)[J]. ACTA MATHEMATICA SCIENTIA,2020,40(1):1-15. |
APA | Li, Banghe.(2020).Hilbert Problem 15 and Nonstandard Analysis (I).ACTA MATHEMATICA SCIENTIA,40(1),1-15. |
MLA | Li, Banghe."Hilbert Problem 15 and Nonstandard Analysis (I)".ACTA MATHEMATICA SCIENTIA 40.1(2020):1-15. |
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