Statistical Destribution on Symmetry Groups

对称群的统计分布

• 批准号: 61540171
• 负责人: ITOH Yoshiaki
• 金额: $ 0.64万
• 依托单位: The Institute of Statistical Mathematics
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1986
• 资助国家: 日本
• 起止时间: 1986 至 1987
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-61540171/
• 关键词: Statistical distribution; crystal group; crystal structure; stochastic model; ランダムパッキング; 幾何学的対称性; 群論; 点群; 空間群; 結晶

Group theory is successfully applied to analysis of crystal structure. The symmetry of a crystalline substance is represented by one of the 32 point groups In this note a stochastic model is introduced for the distribution of crystalline substances among the 32 point groups. Consider a point group x. and take possible symmetry operations.which can be added to the x. at random. Assume the number of operations is given by Poisson distribution. Add the operations to the x and we get a point group generated by the operations and the x. A simulation study is carried out by the model to compave the result with the data of the distribution of crystalline substances.

群论成功地应用于晶体结构的分析。晶体物质的对称性由32个点群中的一个表示。本文介绍了晶体物质在32个点群中分布的随机模型。考虑一个点群x。并采取可能的对称操作，其可以被添加到x。随意假设运算次数服从泊松分布。把这些运算加到x上，我们得到一个由这些运算和x生成的点群。利用该模型进行了模拟研究，并将模拟结果与晶体物质分布数据进行了比较。

项目成果

Yoshiaki Itoh;Herbert Solomon: Journal of Applied Probability. 123. 688-695 (1986)

伊藤义明；赫伯特·所罗门：应用概率杂志。

Masaaki Sibuya;Yoshiaki Itoh: Annals of The Institute of Statistical Mathematics. 39. 69-84 (1987)

Masaaki Sibuya；Yoshiaki Itoh：统计数学研究所年鉴。

Yoshiaki Itoh,Herbert Solomon: "Random Sequential Coding by Hamming Distance" Journal of Applied Probability. 23. 688-695 (1986)

Yoshiaki Itoh，Herbert Solomon：“汉明距离随机顺序编码”应用概率杂志。

Yoshiaki ltoh: Journal of Appliecl Probability. 23. 688-695 (1986)

Yoshiaki ltoh：应用概率杂志。

伊藤栄明: 統計数理. 35. 73-80 (1987)

伊藤英明：统计数学。35. 73-80 (1987)