Hilbert Problem 15 and Nonstandard Analysis (I)
文献类型：期刊论文
| 作者 | Li, Banghe |
| 刊名 | ACTA MATHEMATICA SCIENTIA
 |
| 出版日期 | 2020 |
| 卷号 | 40期号:1页码:1-15 |
| 关键词 | Hilbert problem 15 nonstandard analysis enumeration geometry |
| ISSN号 | 0252-9602 |
| DOI | 10.1007/s10473-020-0101-4 |
| 英文摘要 | 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. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000511674600001 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/50738]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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