ALGEBRAIC ENTROPIES OF NATURAL NUMBERS WITH ONE OR TWO PRIME FACTORS

被引：2

作者：

Jeong, Seungpil ^{[1
]}

Kim, Kyong Hoon ^{[1
]}

Kim, Gwangil ^{[1
]}

机构：

[1] Gyeongsang Natl Univ, Dept Math, Jinju 52828, South Korea

来源：

JOURNAL OF THE KOREAN SOCIETY OF MATHEMATICAL EDUCATION SERIES B-PURE AND APPLIED MATHEMATICS | 2016年 / 23卷 / 03期

关键词：

entropy; partition function; additive entropy; multiplicative entropy; relative comparison density;

D O I：

10.7468/jksmeb.2016.23.3.205

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We formulate the additive entropy of a natural number in terms of the additive partition function, and show that its multiplicative entropy is directly related to the multiplicative partition function. We give a practical formula for the multiplicative entropy of natural numbers with two prime factors. We use this formula to analyze the comparative density of additive and multiplicative entropy, prove that this density converges to zero as the number tends to infinity, and empirically observe this asymptotic behavior.

引用

页码：205 / 221

页数：17