| 一类Lyness方程解的性质 |
| |
| 引用本文： | 李雪臣,亓正申.一类Lyness方程解的性质[J].数学的实践与认识,2006,36(9):292-298. |
| |
| 作者姓名： | 李雪臣 亓正申 |
| |
| 作者单位： | 1. 许昌学院数学系,河南,许昌,461000
2. 许昌职业技术学院信息工程系,河南,许昌,461000 |
| |
| 基金项目： | 河南省自然科学基金;河南省高校青年骨干教师资助项目;河南省教育厅自然科学基金 |
| |
| 摘 要： | 考虑差分方程xn+1=a+b0xn+b1xn-1+…+bk-1xn-(k-1)xn-k其中a,bi是非负实数,a+∑k-1i=0bi>0,k∈{1,2,…}.证明了当k+1为素数时,方程的任半环不超过(2k+2)项;当k+1为合数且只有一个bi≠0时,方程的任半环不超过2k+1+km+0 1项,其中m0=min{m m为k+1的大于1的因数}.结果部分回答了C.Darwen and W.T.Patula提出的公开问题.
|
| 关 键 词： | Lyness方程 半环长 |
| 修稿时间： | 2004年10月16 |
Properties of Solution in A Class Lyness Equation |
| |
| LI Xue-chen,QI Zheng-shen.Properties of Solution in A Class Lyness Equation[J].Mathematics in Practice and Theory,2006,36(9):292-298. |
| |
| Authors: | LI Xue-chen QI Zheng-shen |
| |
| Abstract: | In this paper,we study further on the cycle length for the difference equationx_(n+1)=(a+∑k-1]i=0b_ix_(n-i))]x_(n-k)where a and b_i are nonnegative numbers and(a+∑k-1]i=0b_i)>0.It is showed that if k+1 is a prime number,then every semicycle has no more than(2k+2) terms;if k+1 is a composite number and only one b_i≠0,then every semicycle has no more than 2k+1+k+1]m_0.where m_0=min{m|m>1,is a factor of k+1}.This result partially answer the open question posed by C.Darwen and W.T.Patula. |
| |
| Keywords: | lyness equation semicycle length |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
