| 强正则 $(alpha,beta)$-族和平移强正则 $(alpha,beta)$-几何 |
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| 引用本文： | 李秀丽. 强正则 $(alpha,beta)$-族和平移强正则 $(alpha,beta)$-几何[J]. 数学研究及应用, 2008, 28(4): 928-934 |
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| 作者姓名： | 李秀丽 |
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| 作者单位： | 青岛科技大学数理学院, 山东 青岛 266042 |
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| 基金项目： | 青岛科技大学科研启动基金(No.0022327). |
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| 摘 要： | 本文给出了强正则$(alpha,beta)-$族的概念,它是[4]和[5]中$SPG-$族概念的推广.进一步,给出了一种用强正则 $(alpha,beta)-$族构造强正则$(alpha,beta)-$几何的方法.另外,本文还证明了由强正则$(alpha,beta)-$线汇构造的强正则$(alpha,beta)-$几何是平移强正则$(alpha,beta)-$几何;当$t-r>beta$时,反之亦成立.
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| 关 键 词： | 射影空间 强正则$(alpha,beta)-$线汇 强正则$(alpha,beta)-$族 强正则 $(alpha,beta)-$几何. |
| 收稿时间： | 2006-06-22 |
| 修稿时间： | 2008-04-18 |
Strongly Regular $(alpha,beta)$-Families and Translation Strongly Regular $(alpha,beta)$-Geometries |
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| LI Xiu Li. Strongly Regular $(alpha,beta)$-Families and Translation Strongly Regular $(alpha,beta)$-Geometries[J]. Journal of Mathematical Research with Applications, 2008, 28(4): 928-934 |
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| Authors: | LI Xiu Li |
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| Affiliation: | School of Mathematics and Physics, Qingdao University of Science and Technology, Shandong 266042, China |
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| Abstract: | In this paper, we introduce the concept of a strongly regular $(alpha,beta)$-family. It generalizes the concept of an SPG-family in [4] and [5]. We provide a method of constructing strongly regular $(alpha,beta)$-geometries from strongly regular $(alpha,beta)$-families. Furthermore, we prove that each strongly regular $(alpha,beta)$-geometry constructed from a strongly regular $(alpha,beta)$-regulus translation is isomorphic to a translation strongly regular $(alpha,beta)$-geometry; while $t-r>beta$, the converse is also true. |
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| Keywords: | projective space strongly regular $(alpha,beta)$-regulus strongly regular $(alpha,beta)$-geometry. |
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