期刊文献+

缠绕方程组的解法 被引量:2

The method of solving tangle equations
下载PDF
导出
摘要 考虑缠绕方程组N(O+iR)=Ki(i=0,1,2,3),其中O是有理缠绕或者是2个有理缠绕的和,R是有理缠绕,并且O和R都是未知的缠绕,iR表示i个R的缠绕和,N是缠绕的分子的构造,Ki是已知的纽结或链环.解出上述模型中的未知缠绕O和R.通过将有理缠绕与有理纽结或链环(二桥结)联系起来,对于方程组N(O+iR)=Ki(i=0,1,2,3),从Ki(0≤i≤3)的交叉点数入手,得到了方程组的一般解法. In this paper ,we give the methods of solving the tangle equations N(O+ iR)= Ki(i=0 ,1 , 2 ,3) ,where O is a rational tangle or the summand of two rational tangles ,and R is a rational tangle . In addition ,O and R are unknown tangles ,iR denotes the tangle sum of i copies of R ,N is the nu-merator construction of the tangle ,and Ki are the known knots or links .Then our task is working out the unknow n tangles O and R in the above mathematical model .In order to simplify the calcula-tion ,we give the vector representation of tangles by the constructions of the tangles and get the gen-eral solution of the equations N(O+ iR)= Ki(i=0 ,1 ,2 ,3) by using the crossing numbers of Ki(0≤i≤3) .
出处 《辽宁师范大学学报(自然科学版)》 CAS 2013年第4期443-448,共6页 Journal of Liaoning Normal University:Natural Science Edition
基金 国家自然科学基金项目(11071106) 辽宁省高等学校优秀人才支持计划项目(LR2011031)
关键词 缠绕 二桥结 DNA tangle 2-bridge knot DNA
  • 相关文献

参考文献10

  • 1ERNST C,SUMMERS D W. A calculus for rational tangles:applications to DNA recombination[J]. Math Proc Camb Phil Soc,1990,108..489-515.
  • 2ERNST C, SUMMERS D W. Solving tangles equations arising in a DNA recombination model[J]. Math Proe Camb Phil Soc, 1999, 126(1) :23-36.
  • 3SUMMERS D W. Untangling DNA[J]. Math Intelligencer, 1994,112(3):71-80.
  • 4SUMMERS D W,ERNST C,COZZARELLI N R,et al. Mathematical analysis of the mechanisms of DNA recombination using tan- gles, Quart[J]. Rev of Biophys, 1995,28.. 253-313.
  • 5CONWAY J H. An enumeration of knots and links and some of their related properties[C]//In Computational Problems in Ab- stract Algebra. Proc Conf Oxford:Pergamon Press, 1967 : 329-358.
  • 6LICKORISH W B R. Prime knots and tangles[J]. Trans Amer Math Soc, 1981,267:321-332.
  • 7ERNST C, SUMMERS D W. The growth of the number of prime knots[J]. Math Proe Cambridge Philos Soc, 1987,102:303-315.
  • 8BURDE G, ZIESCHANG H. Knots(de Gruyter, 1985) [J]. Mathematics Subject Classification, 2000, 57-02 ; 57M25,20F34,20F36.
  • 9ERNST C. Tangle equations[J]. J of Knot Theory and Its Ramifications, 1996,5:145-159.
  • 10GOLDMAN J R,KAUFFMAN L H. Rational tangles[J]. Adv in Appl Math, 1997,18(3) :300-332.

同被引文献18

  • 1Ernst C, Summers D W. A calculus for rational tangles: applications to DNA recombination[J]. Mathematics Proceedings Cambridge Philosophical Society, 1990, 108(3):489-515.
  • 2Ernst C, Sumners D W. Solving tangles equations arising in a DNA recombination model[J]. Mathematics Proceedings Cambridge Philosophical Society, 1999, 126(1):23-36.
  • 3Sumners D W. Untangling DNA[J]. Mathematics, Intelligencer, 1994, 12(3):71-80.
  • 4Sumners D W, Ernst C, Cozzarelli N R, et al. Spengler.Mathematical analysis of the mechanisms of DNA recombination using tangles[J]. Quarter Review o] Biophys, 1995, 28(2):253-313.
  • 5Lickorish W B R. Prime knots and tangles[J]. Transactions American Mathematical[J]. Society, 1981, 267(2):321-332.
  • 6Ernst C, Sumners D W. The growth of the number of prime knots[J]. Mathematics Proceedings Cambridge Philosophical Society, 1987, 102(2):303-315.
  • 7Darcy I K. Biological distances on DNA knots and links:applications to Xer recombination. Knots in Hellas'98. J.Knot Theory Ramifications, 2001, 10(2):269-294.
  • 8Ernst C. Tangle equations[J]. Journal of Knot theory and its ramifications, 1996, 5(1):145--159.
  • 9Goldman J R, Kauffman L H. Rational tangles[J]. Advance in Applications Mathematics. 1997, 18(2):300 332.
  • 10Ernst C. Tangle equations II[J]. Journal of Knot theory and its ramifications, 1997, 6(1):1 11.

引证文献2

二级引证文献2

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部