Kinetics of Cd~(2+) and Cr~(3+) Sorption from Aqueous Solutions Using Mercaptoacetic Acid Modified a

• 作 者: A. A. Abia E. D. Asuquo
• 机 构: Department of Pure and Industrial Chemistry University of Port Harcourt B. M. B. 5323 Choba Port Ha
• 出 处: Tsinghua Science and Technology
• 发表日期: 2007年04期
• 关键词: adsorbent mirror sorption equivalence inverse operators implies Modified polynom

In this paper, we mainly study the relation of two cyclically reduced words w and w ′on the condi- tion they have the same trace polynomial (i.e., tr w= trw ′). By defining an equivalence relation through such operators on words as inverse, cyclically left shift, and mirror, it is straightforward to get that w ~ w ′ implies tr w = tr w ′. We show by a counter example that tr w = tr w ′ does not imply w ~ w ′. And in two special cases, we prove that tr w = tr w ′ if and only if w ~ w ′.

In this paper, we mainly study the relation of two cyclically reduced words w and w ’on the condi- tion they have the same trace polynomial (ie, tr w = trw’). By defining an equivalence relation through such operators on words as inverse, cyclically left shift, and mirror, it is straightforward to get that w ~ w ’implies tr w = tr w’. We show by a counter example that tr w = tr w ’does not imply w ~ w’. And in two special cases, we prove that tr w = tr w ’if and only if w ~ w’.