Farey序列中某些特殊连续性的构造
Construction of some special subsequences within a Farey sequence
摘要：
近年来，人们发现Farey序列中某些特殊的双折射对确定可积导数非线性Schrodinger模型中量子孤子态存在的耦合常数范围起着至关重要的作用。在这篇文章中，我们找到了一个新的映射，它连接两个这样的序列属于不同的顺序的Farey序列。通过使用这个映射，我们构造了一个算法，以产生所有这些特殊的序列内的Farey序列。我们还推导出所有属于一个子序列的元素的连分式展开式，并观察到相应的展开系数之间的密切联系。
英文摘要：
Recently it has been found that some special subsequences within a Farey sequence play a crucial role in determining the ranges of coupling constant for which quantum soliton states can exist for an integrable derivative nonlinear Schrodinger model. In this article, we find a novel mapping which connects two such subsequences belonging to Farey sequences of different orders. By using this mapping, we construct an algorithm to generate all of these special subsequences within a Farey sequence. We also derive the continued fraction expansions for all the elements belonging to a subsequence and observe a close connection amongst the corresponding expansion coefficients.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
